Physics 207 Lecture 25. Lecture 25. For Thursday, read through all of Chapter 18. Angular Momentum Exercise

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Physics 207 Lecture 25. Lecture 25. For Thursday, read through all of Chapter 18. Angular Momentum Exercise"

Transcription

1 Lecture 5 Today Review: Exam covers Chapters plus angular momentum, statics Assignment For Thursday, read through all of Chapter 18 Physics 07: Lecture 5, Pg 1 Angular Momentum Exercise A mass m=0.10 kg is attached to a cord passing through a small hole in a frictionless, horizontal surface as in the Figure. The mass is initially orbiting with speed ω i = 5 rad / s in a circle of radius r i = 0.0 m. The cord is then slowly pulled from below, and the radius decreases to r = 0.10 m. What is the final angular velocity? Underlying concept: Conservation of Momentum r i ω i Physics 07: Lecture 5, Pg Page 1

2 Angular Momentum Exercise A mass m=0.10 kg is attached to a cord passing through a small hole in a frictionless, horizontal surface as in the Figure. The mass is initially orbiting with speed ω i = 5 rad / s in a circle of radius r i = 0.0 m. The cord is then slowly pulled from below, and the radius decreases to r = 0.10 m. What is the final angular velocity? No external torque implies L = 0 or L i = L c r i I i ω i = I f ω f ω i I for a point mass is mr where r is the distance to the axis of rotation m r i ω i = m r f ω f ω f = r i ω i / r f = (0.0/0.10) 5 rad/s = 0 rad/s Physics 07: Lecture 5, Pg 3 Example: Throwing ball from stool A student sits on a stool, initially at rest, but which is free to rotate. The moment of inertia of the student plus the stool is I. They throw a heavy ball of mass M with speed v such that its velocity vector has a perpendicular distance d from the axis of rotation. What is the angular speed ω F of the student-stool system after they throw the ball? M I ω F I r d Mv Top view: before after Physics 07: Lecture 5, Pg 4 Page

3 Example: Throwing ball from stool What is the angular speed ω F of the student-stool system after they throw the ball? Process: (1) Define system () Identify Conditions (1) System: student, stool and ball (No Ext. torque, L is constant) () Momentum is conserved (check L = r p sin θ for sign) L init = 0 = L final = M v d + I ω f M I ω F I d v Top view: before after Physics 07: Lecture 5, Pg 5 Walking the plank A uniform rectangular beam of length L= 5 m and mass M=40 kg is supported, but not attached, to two posts which are length D=3 m apart. A child of mass W=0 kg starts walking along the beam. 40 kg 5 m 0 kg 3 m Assuming infinitely rigid posts, how close can the child get to the right end of the beam without it falling over? [Hint: The upward force exerted by the beam on the left cannot be negative this is the limiting condition on how far the child can be to the right. Set up the static equilibrium condition with the pivot about the left end of the beam.] Physics 07: Lecture 5, Pg 6 Page 3

4 Walking the plank A uniform rectangular beam of length L= 5 m and mass M=40 kg is supported, but not attached, to two posts which are length D=3 m apart. A child of mass W=0 kg starts walking along the beam. N L N R 0.5 m 400 N 00 N Sum of forces and torques are zero As the child walks from left to right N L goes from positive to negative If N L < 0 (a pull) then the board will tip. Choose blue dot as pivot point. Physics 07: Lecture 5, Pg 7 Walking the plank A uniform rectangular beam of length L= 5 m and mass M=40 kg is supported, but not attached, to two posts which are length D=3 m apart. A child of mass W=0 kg starts walking along the beam. N L N R 0.5 m 400 N 00 N Σ τ = 0 = -N L x x N R x 0 - d 00 0 = d 00 d = 1 meter from pivot point which is.0 meter from right side distance to end ( 1) meters or 1 meter Physics 07: Lecture 5, Pg 8 Page 4

5 Velocity and Acceleration Position: x(t) = A cos(ωt + φ) Velocity: v(t) = -ωa sin(ωt + φ) Acceleration: a(t) = -ω A cos(ωt + φ) x max = A v max = ωa a max = ω A by taking derivatives, since: dx( t ) v( t ) = dt a( t ) = dv t dt ( ) k m 0 x Physics 07: Lecture 5, Pg 9 Measuring g To measure the magnitude of the acceleration due to gravity, g, in an unorthodox manner, a student places a ball bearing on the concave side of a flexible speaker cone. The speaker cone acts as a simple harmonic oscillator whose amplitude is A and whose frequency ω can be varied. The student can measure both A and ω. The equations of motion for the speaker are Position: y(t) = A cos(ωt + φ) Velocity: v y (t) = -ωa sin(ωt + φ) Acceleration: a y (t) = -ω A cos(ωt + φ) If the ball bearing is in contact with the speaker, then Σ F y = ma y = - mg+ N so that N = mg + ma y N = mg - mω A cos(ωt + φ) Maximum: N = mg + mω A Minimum: mg - mω A but must be > 0! Physics 07: Lecture 5, Pg 10 Page 5

6 Ideal Fluid Bernoulli Equation P 1 + ½ ρ v 1 + ρ g y 1 = constant A 5 cm radius horizontal pipe carries water at 10 m/s into a 10 cm radius. ( ρ water =10 3 kg/m 3 ) What is the pressure difference? P 1 + ½ ρ v 1 = P + ½ ρ v P = ½ ρ v - ½ ρ v 1 P = ½ ρ (v - v 1 ) and A 1 v 1 = A v v y v 1 V p y 1 p 1 P = ½ ρ v (1 (A /A 1 ) ) = 0.5 x 1000 kg/m x 100 m /s (1- (5/100) ) = Pa Physics 07: Lecture 5, Pg 11 A water fountain A fountain, at sea level, consists of a 10 cm radius pipe with a 5 cm radius nozzle. The water sprays up to a height of 0 m. What is the velocity of the water as it leaves the nozzle? What volume of the water per second as it leaves the nozzle? What is the velocity of the water in the pipe? What is the pressure in the pipe? How many watts must the water pump supply? Physics 07: Lecture 5, Pg 1 Page 6

7 A water fountain A fountain, at sea level, consists of a 10 cm radius pipe with a 5 cm radius nozzle. The water sprays up to a height of 0 m. What is the velocity of the water as it leaves the nozzle? Simple Picture: ½mv =mgh v=(gh) ½ = (x10x0) ½ = 0 m/s What volume of the water per second as it leaves the nozzle? Q = A v n = x 0 x 3.14 = m 3 /s What is the velocity of the water in the pipe? A n v n = A p v p v p = Q /4 = 5 m/s What is the pressure in the pipe? 1atm + ½ ρ v n = 1 atm + P + ½ ρ v p 1.9 x 10 5 N/m How many watts must the water pump supply? Power = Q ρ g h = m 3 /s x 10 3 kg/m 3 x 9.8 m/s x 0 m = 3x10 4 W Physics 07: Lecture 5, Pg 13 Fluids Buoyancy A metal cylinder, 0.5 m in radius and 4.0 m high is lowered, as shown, from a massles rope into a vat of oil and water. The tension, T, in the rope goes to zero when the cylinder is half in the oil and half in the water. The densities of the oil is 0.9 gm/cm 3 and the water is 1.0 gm/cm 3 What is the average density of the cylinder? What was the tension in the rope when the cylinder was submerged in the oil? Physics 07: Lecture 5, Pg 14 Page 7

8 r = 0.5 m, h= 4.0 m Fluids Buoyancy ρ oil = 0.9 gm/cm 3 ρ water = 1.0 gm/cm 3 What is the average density of the cylinder? When T = 0 F buoyancy = W cylinder F buoyancy = ρ oil g ½ V cyl. + ρ water g ½ V cyl. W cylinder = ρ cyl g V cyl. ρ cyl g V cyl. = ρ oil g ½ V cyl. + ρ water g ½ V cyl. ρ cyl = ½ ρ oill. + ½ ρ water What was the tension in the rope when the cylinder was submerged in the oil? Use a Free Body Diagram! Physics 07: Lecture 5, Pg 15 r = 0.5 m, h= 4.0 m Fluids Buoyancy V cyl. = π r h ρ oil = 0.9 gm/cm 3 ρ water = 1.0 gm/cm 3 What is the average density of the cylinder? When T = 0 F buoyancy = W cylinder F buoyancy = ρ oil g ½ V cyl. + ρ water g ½ V cyl. W cylinder = ρ cyl g V cyl. ρ cyl g V cyl. = ρ oil g ½ V cyl. + ρ water g ½ V cyl. ρ cyl = ½ ρ oill. + ½ ρ water = 0.95 gm/cm 3 What was the tension in the rope when the cylinder was submerged in the oil? Use a Free Body Diagram! Σ F z = 0 = T - W cylinder + F buoyancy T = W cyl - F buoy = g ( ρ cyl. - ρ oil ) V cyl T = 9.8 x 0.05 x 10 3 x π x 0.5 x 4.0 = 1500 N Physics 07: Lecture 5, Pg 16 Page 8

9 Fluids Buoyancy r = 0.5 m, h= 4.0 m V cyl. = π r h ρ oil = 0.9 gm/cm 3 ρ water = 1.0 gm/cm 3 What is the average density of the cylinder? When T = 0 F buoyancy = W cylinder. ρ cyl = ½ ρ oill. + ½ ρ water = 0.95 gm/cm 3 What was the tension in the rope when the cylinder was submerged in the oil? Use a Free Body Diagram! Σ F z = 0 = T - W cylinder + F buoyancy T = W cyl - F buoy = g ( ρ cyl. - ρ oil ) V cyl T = 9.8 x 0.05 x 10 3 x π x 0.5 x 4.0 = 1500 N Physics 07: Lecture 5, Pg 17 A new trick Two trapeze artists, of mass 100 kg and 50 kg respectively are testing a new trick and want to get the timing right. They both start at the same time using ropes of 10 m in length and, at the turnaround point the smaller grabs hold of the larger artist and together they swing back to the starting platform. A model of the stunt is shown at right. How long will this stunt require if the angle is small? Physics 07: Lecture 5, Pg 18 Page 9

10 A new trick How long will this stunt require? Period of a pendulum is just ω = (g/l) ½ T = π (L/g) ½ Time before ½ period Time after ½ period So, t = T = π(l/g) ½ = π sec Key points: Period is one full swing and independent of mass (this is SHM but very different than a spring. SHM requires only a linear restoring force.) Physics 07: Lecture 5, Pg 19 Example A Hooke s Law spring, k=00 N/m, is on a horizontal frictionless surface is stretched.0 m from its equilibrium position. A 1.0 kg mass is initially attached to the spring however, at a displacement of 1.0 m a.0 kg lump of clay is dropped onto the mass. The clay sticks. M What is the new amplitude? k m k M m - 0( X eq ) Physics 07: Lecture 5, Pg 0 Page 10

11 Example A Hooke s Law spring, k=00 N/m, is on a horizontal frictionless surface is stretched.0 m from its equilibrium position. A 1.0 kg mass is initially attached to the spring however, at a displacement of 1.0 m a.0 kg lump of clay is dropped onto the mass. What is the new amplitude? M Sequence: SHM, collision, SHM ½ k A 0 = const. ½ k A 0 = ½ mv + ½ k (A 0 /) k m ¾ k A 0 = m v v = ( ¾ k A 0 / m ) ½ k M v = (0.75*00*4 / 1 ) ½ = 4.5 m/s Conservation of x-momentum: mv= (m+m) V V = mv/(m+m) V = 4.5/3 m/s = 8. m/s m - 0( X eq ) Physics 07: Lecture 5, Pg 1 Example A Hooke s Law spring, k=00 N/m, is on a horizontal frictionless surface is stretched.0 m from its equilibrium position. A 1.0 kg mass is initially attached to the spring however, at a displacement of 1.0 m a.0 kg lump of clay is dropped onto the mass. The clay sticks. M What is the new amplitude? Sequence: SHM, collision, SHM k V = 4.5/3 m/s = 8. m/s m ½ k A f = const. ½ k A f = ½ (m+m)v + ½ k (A i ) k M A f = [(m+m)v /k + (A i ) ] ½ A f = [3 x 8. /00 + (1) ] ½ A f = [1 + 1] ½ A f = 1.4 m m - 0( X eq ) Key point: K+U is constant in SHM Physics 07: Lecture 5, Pg Page 11

12 Fluids Buoyancy & SHM A metal cylinder, 0.5 m in radius and 4.0 m high is lowered, as shown, from a rope into a vat of oil and water. The tension, T, in the rope goes to zero when the cylinder is half in the oil and half in the water. The densities of the oil is 0.9 gm/cm 3 and the water is 1.0 gm/cm 3 Refer to earlier example Now the metal cylinder is lifted slightly from its equilibrium position. What is the relationship between the displacement and the rope s tension? If the rope is cut and the drum undergoes SHM, what is the period of the oscillation if undamped? Physics 07: Lecture 5, Pg 3 Refer to earlier example Fluids Buoyancy & SHM Now the metal cylinder is lifted y from its equilibrium position. What is the relationship between the displacement and the rope s tension? 0 = T + F buoyancy W cylinder T = - F buoyancy + W cylinder T =-[ρ o g(h/+ y) A c +ρ w ga c (h/- y)] + W cyl T =-[gha c (ρ o +ρ w )/ + y ga c (ρ o -ρ w )]+ W cyl T =-[W cyl + y ga c (ρ o -ρ w )]+ W cyl T = [ g A c (ρ w -ρ o ) ] y If the is rope cut, net force is towards equilibrium position with a proportionality constant g A c (ρ w -ρ o ) [& with g=10 m/s ] If F = - k y then k = g A c (ρ o -ρ w ) = π/4 x10 3 N/m Physics 07: Lecture 5, Pg 4 Page 1

13 Fluids Buoyancy & SHM A metal cylinder, 0.5 m in radius and 4.0 m high is lowered, as shown, from a rope into a vat of oil and water. The tension, T, in the rope goes to zero when the cylinder is half in the oil and half in the water. The densities of the oil is 0.9 gm/cm 3 and the water is 1.0 gm/cm 3 If the rope is cut and the drum undergoes SHM, what is the period of the oscillation if undamped? F = ma = - k y and with SHM. ω = (k/m) ½ where k is a spring constant and m is the inertial mass (resistance to motion), the cylinder So ω = (1000π /4 m cyl ) ½ = (1000π / 4ρ cyl V cyl ) ½ = ( 0.5/0.95 ) ½ = 0.51 rad/sec T = 3. sec Physics 07: Lecture 5, Pg 5 Underdamped SHM bt cos( ω + ) if m x( t) = A exp( ) t φ If the period is.0 sec and, after four cycles, the amplitude drops by 75%, what is the time constant τ if τ m / b? 1. ωo > b / m Four cycles implies 8 sec So A 0.5 A 0 = A 0 exp(-8b / m) 0-0. ln(1/4)= -8 1/τ τ = -8/ ln(1/4) = 5.8 sec -0.8 ωt Physics 07: Lecture 5, Pg 6 Page 13

14 Anti-global warming or the nuclear winter scenario Assume P/A = P = 1340 W/m from the sun is incident on a thick dust cloud above the Earth and this energy is absorbed, equilibrated and then reradiated towards space where the Earth s surface is in thermal equilibrium with cloud. Let e (the emissivity) be unity for all wavelengths of light. What is the Earth s temperature? P = σ A T 4 = σ (4π r ) T 4 = P π r T = [P / (4 x σ )] ¼ σ = W/m K 4 T = 77 K (A little on the chilly side.) Physics 07: Lecture 5, Pg 7 Time for a swim At solar equinox, how much could you reasonably expect for the top 1 meter of water in a lake at 45 deg. latitude to warm on a calm but bright sunny day assuming that the sun s flux (P/A) is 1340 W/m if all the sun s energy were absorbed in that layer? At 45 deg., sin 45 deg or x 1340 or 950 W/m But only 6 hours of full sun So Q available is 6 x 60 x 60 seconds with 950 J/s/m Q = x 10 7 J in one square meter Q = m c T with m 10 3 kg/m 3 and c = 4. x 10 3 J/kg-K about 5 K per day. Physics 07: Lecture 5, Pg 8 Page 14

15 0.0 moles of an ideal monoatomic gas are cycled clockwise through the pv sequence shown at right (A D C B A). (R = 8.3 J/K mol) What are the temperatures of the two isotherms? Fill out the table below with the appropriate values. Q, W and E TH (a) pv = nrt T = pv/nr T A = x 0.10 / (0.0 x 8.3) T A = 1000 K T B = 500 K (b) E TH =W + Q Ideal Gas at constant V Q = n C V T Physics 07: Lecture 5, Pg 9 Ch. 1 L =mvr perpendicular Physics 07: Lecture 5, Pg 30 Page 15

16 Ch. 1 Physics 07: Lecture 5, Pg 31 Hooke s Law Springs and a Restoring Force Key fact: ω = (k / m) ½ is general result where k reflects a constant of the linear restoring force and m is the inertial response (e.g., the physical pendulum where ω = (κ / I) ½ Physics 07: Lecture 5, Pg 3 Page 16

17 Simple Harmonic Motion Maximum potential energy Maximum kinetic energy Physics 07: Lecture 5, Pg 33 Resonance and damping Energy transfer is optimal when the driving force varies at the resonant frequency. Types of motion Undamped Underdamped Critically damped Overdamped Physics 07: Lecture 5, Pg 34 Page 17

18 Fluid Flow Physics 07: Lecture 5, Pg 35 Density and pressure Physics 07: Lecture 5, Pg 36 Page 18

19 Response to forces Physics 07: Lecture 5, Pg 37 States of Matter and Phase Diagrams Physics 07: Lecture 5, Pg 38 Page 19

20 Ideal gas equation of state Physics 07: Lecture 5, Pg 39 pv diagrams Physics 07: Lecture 5, Pg 40 Page 0

21 Thermodynamics Physics 07: Lecture 5, Pg 41 Work, Pressure, Volume, Heat T can change! In steady-state T=constant and so heat in equals heat out Physics 07: Lecture 5, Pg 4 Page 1

22 Gas Processes Physics 07: Lecture 5, Pg 43 Lecture 5 Exam covers Chapters plus angular momentum, statics Assignment For Thursday, read through all of Chapter 18 Physics 07: Lecture 5, Pg 44 Page

Physics 41 HW Set 1 Chapter 15

Physics 41 HW Set 1 Chapter 15 Physics 4 HW Set Chapter 5 Serway 8 th OC:, 4, 7 CQ: 4, 8 P: 4, 5, 8, 8, 0, 9,, 4, 9, 4, 5, 5 Discussion Problems:, 57, 59, 67, 74 OC CQ P: 4, 5, 8, 8, 0, 9,, 4, 9, 4, 5, 5 Discussion Problems:, 57, 59,

More information

AP Physics C. Oscillations/SHM Review Packet

AP Physics C. Oscillations/SHM Review Packet AP Physics C Oscillations/SHM Review Packet 1. A 0.5 kg mass on a spring has a displacement as a function of time given by the equation x(t) = 0.8Cos(πt). Find the following: a. The time for one complete

More information

226 Chapter 15: OSCILLATIONS

226 Chapter 15: OSCILLATIONS Chapter 15: OSCILLATIONS 1. In simple harmonic motion, the restoring force must be proportional to the: A. amplitude B. frequency C. velocity D. displacement E. displacement squared 2. An oscillatory motion

More information

Physics 1120: Simple Harmonic Motion Solutions

Physics 1120: Simple Harmonic Motion Solutions Questions: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Physics 1120: Simple Harmonic Motion Solutions 1. A 1.75 kg particle moves as function of time as follows: x = 4cos(1.33t+π/5) where distance is measured

More information

Spring Simple Harmonic Oscillator. Spring constant. Potential Energy stored in a Spring. Understanding oscillations. Understanding oscillations

Spring Simple Harmonic Oscillator. Spring constant. Potential Energy stored in a Spring. Understanding oscillations. Understanding oscillations Spring Simple Harmonic Oscillator Simple Harmonic Oscillations and Resonance We have an object attached to a spring. The object is on a horizontal frictionless surface. We move the object so the spring

More information

Midterm Solutions. mvr = ω f (I wheel + I bullet ) = ω f 2 MR2 + mr 2 ) ω f = v R. 1 + M 2m

Midterm Solutions. mvr = ω f (I wheel + I bullet ) = ω f 2 MR2 + mr 2 ) ω f = v R. 1 + M 2m Midterm Solutions I) A bullet of mass m moving at horizontal velocity v strikes and sticks to the rim of a wheel a solid disc) of mass M, radius R, anchored at its center but free to rotate i) Which of

More information

PHYSICS 111 HOMEWORK SOLUTION #10. April 10, 2013

PHYSICS 111 HOMEWORK SOLUTION #10. April 10, 2013 PHYSICS 111 HOMEWORK SOLUTION #10 April 10, 013 0.1 Given M = 4 i + j 3 k and N = i j 5 k, calculate the vector product M N. By simply following the rules of the cross product: i i = j j = k k = 0 i j

More information

www.mathsbox.org.uk Displacement (x) Velocity (v) Acceleration (a) x = f(t) differentiate v = dx Acceleration Velocity (v) Displacement x

www.mathsbox.org.uk Displacement (x) Velocity (v) Acceleration (a) x = f(t) differentiate v = dx Acceleration Velocity (v) Displacement x Mechanics 2 : Revision Notes 1. Kinematics and variable acceleration Displacement (x) Velocity (v) Acceleration (a) x = f(t) differentiate v = dx differentiate a = dv = d2 x dt dt dt 2 Acceleration Velocity

More information

Solution: F = kx is Hooke s law for a mass and spring system. Angular frequency of this system is: k m therefore, k

Solution: F = kx is Hooke s law for a mass and spring system. Angular frequency of this system is: k m therefore, k Physics 1C Midterm 1 Summer Session II, 2011 Solutions 1. If F = kx, then k m is (a) A (b) ω (c) ω 2 (d) Aω (e) A 2 ω Solution: F = kx is Hooke s law for a mass and spring system. Angular frequency of

More information

Oscillations. Vern Lindberg. June 10, 2010

Oscillations. Vern Lindberg. June 10, 2010 Oscillations Vern Lindberg June 10, 2010 You have discussed oscillations in Vibs and Waves: we will therefore touch lightly on Chapter 3, mainly trying to refresh your memory and extend the concepts. 1

More information

Hooke s Law. Spring. Simple Harmonic Motion. Energy. 12/9/09 Physics 201, UW-Madison 1

Hooke s Law. Spring. Simple Harmonic Motion. Energy. 12/9/09 Physics 201, UW-Madison 1 Hooke s Law Spring Simple Harmonic Motion Energy 12/9/09 Physics 201, UW-Madison 1 relaxed position F X = -kx > 0 F X = 0 x apple 0 x=0 x > 0 x=0 F X = - kx < 0 x 12/9/09 Physics 201, UW-Madison 2 We know

More information

Simple Harmonic Motion(SHM) Period and Frequency. Period and Frequency. Cosines and Sines

Simple Harmonic Motion(SHM) Period and Frequency. Period and Frequency. Cosines and Sines Simple Harmonic Motion(SHM) Vibration (oscillation) Equilibrium position position of the natural length of a spring Amplitude maximum displacement Period and Frequency Period (T) Time for one complete

More information

PHYS 211 FINAL FALL 2004 Form A

PHYS 211 FINAL FALL 2004 Form A 1. Two boys with masses of 40 kg and 60 kg are holding onto either end of a 10 m long massless pole which is initially at rest and floating in still water. They pull themselves along the pole toward each

More information

Simple Harmonic Motion

Simple Harmonic Motion Simple Harmonic Motion Restating Hooke s law The equation of motion Phase, frequency, amplitude Simple Pendulum Damped and Forced oscillations Resonance Harmonic Motion A lot of motion in the real world

More information

Chapter 13, example problems: x (cm) 10.0

Chapter 13, example problems: x (cm) 10.0 Chapter 13, example problems: (13.04) Reading Fig. 13-30 (reproduced on the right): (a) Frequency f = 1/ T = 1/ (16s) = 0.0625 Hz. (since the figure shows that T/2 is 8 s.) (b) The amplitude is 10 cm.

More information

IMPORTANT NOTE ABOUT WEBASSIGN:

IMPORTANT NOTE ABOUT WEBASSIGN: Week 8 homework IMPORTANT NOTE ABOUT WEBASSIGN: In the WebAssign versions of these problems, various details have been changed, so that the answers will come out differently. The method to find the solution

More information

PHY121 #8 Midterm I 3.06.2013

PHY121 #8 Midterm I 3.06.2013 PHY11 #8 Midterm I 3.06.013 AP Physics- Newton s Laws AP Exam Multiple Choice Questions #1 #4 1. When the frictionless system shown above is accelerated by an applied force of magnitude F, the tension

More information

Lecture L22-2D Rigid Body Dynamics: Work and Energy

Lecture L22-2D Rigid Body Dynamics: Work and Energy J. Peraire, S. Widnall 6.07 Dynamics Fall 008 Version.0 Lecture L - D Rigid Body Dynamics: Work and Energy In this lecture, we will revisit the principle of work and energy introduced in lecture L-3 for

More information

AP1 Oscillations. 1. Which of the following statements about a spring-block oscillator in simple harmonic motion about its equilibrium point is false?

AP1 Oscillations. 1. Which of the following statements about a spring-block oscillator in simple harmonic motion about its equilibrium point is false? 1. Which of the following statements about a spring-block oscillator in simple harmonic motion about its equilibrium point is false? (A) The displacement is directly related to the acceleration. (B) The

More information

Physics 271 FINAL EXAM-SOLUTIONS Friday Dec 23, 2005 Prof. Amitabh Lath

Physics 271 FINAL EXAM-SOLUTIONS Friday Dec 23, 2005 Prof. Amitabh Lath Physics 271 FINAL EXAM-SOLUTIONS Friday Dec 23, 2005 Prof. Amitabh Lath 1. The exam will last from 8:00 am to 11:00 am. Use a # 2 pencil to make entries on the answer sheet. Enter the following id information

More information

Lecture 17. Last time we saw that the rotational analog of Newton s 2nd Law is

Lecture 17. Last time we saw that the rotational analog of Newton s 2nd Law is Lecture 17 Rotational Dynamics Rotational Kinetic Energy Stress and Strain and Springs Cutnell+Johnson: 9.4-9.6, 10.1-10.2 Rotational Dynamics (some more) Last time we saw that the rotational analog of

More information

Version PREVIEW Practice 8 carroll (11108) 1

Version PREVIEW Practice 8 carroll (11108) 1 Version PREVIEW Practice 8 carroll 11108 1 This print-out should have 12 questions. Multiple-choice questions may continue on the net column or page find all choices before answering. Inertia of Solids

More information

Physics 1A Lecture 10C

Physics 1A Lecture 10C Physics 1A Lecture 10C "If you neglect to recharge a battery, it dies. And if you run full speed ahead without stopping for water, you lose momentum to finish the race. --Oprah Winfrey Static Equilibrium

More information

So if ω 0 increases 3-fold, the stopping angle increases 3 2 = 9-fold.

So if ω 0 increases 3-fold, the stopping angle increases 3 2 = 9-fold. Name: MULTIPLE CHOICE: Questions 1-11 are 5 points each. 1. A safety device brings the blade of a power mower from an angular speed of ω 1 to rest in 1.00 revolution. At the same constant angular acceleration,

More information

Ch.8 Rotational Equilibrium and Rotational Dynamics.

Ch.8 Rotational Equilibrium and Rotational Dynamics. Ch.8 Rotational Equilibrium and Rotational Dynamics. Conceptual question # 1, 2, 9 Problems# 1, 3, 7, 9, 11, 13, 17, 19, 25, 28, 33, 39, 43, 47, 51, 55, 61, 79 83 Torque Force causes acceleration. Torque

More information

PHY231 Section 2, Form A March 22, 2012. 1. Which one of the following statements concerning kinetic energy is true?

PHY231 Section 2, Form A March 22, 2012. 1. Which one of the following statements concerning kinetic energy is true? 1. Which one of the following statements concerning kinetic energy is true? A) Kinetic energy can be measured in watts. B) Kinetic energy is always equal to the potential energy. C) Kinetic energy is always

More information

7. Kinetic Energy and Work

7. Kinetic Energy and Work Kinetic Energy: 7. Kinetic Energy and Work The kinetic energy of a moving object: k = 1 2 mv 2 Kinetic energy is proportional to the square of the velocity. If the velocity of an object doubles, the kinetic

More information

A1. An object of mass m is projected vertically from the surface of a planet of radius R p and mass M p with an initial speed v i.

A1. An object of mass m is projected vertically from the surface of a planet of radius R p and mass M p with an initial speed v i. OBAFMI AWOLOWO UNIVRSITY, IL-IF, IF, NIGRIA. FACULTY OF SCINC DPARTMNT OF PHYSICS B.Sc. (Physics) Degree xamination PHY GNRAL PHYSICS I TUTORIAL QUSTIONS IN GRAVITATION, FLUIDS AND OSCILLATIONS SCTION

More information

Tennessee State University

Tennessee State University Tennessee State University Dept. of Physics & Mathematics PHYS 2010 CF SU 2009 Name 30% Time is 2 hours. Cheating will give you an F-grade. Other instructions will be given in the Hall. MULTIPLE CHOICE.

More information

C B A T 3 T 2 T 1. 1. What is the magnitude of the force T 1? A) 37.5 N B) 75.0 N C) 113 N D) 157 N E) 192 N

C B A T 3 T 2 T 1. 1. What is the magnitude of the force T 1? A) 37.5 N B) 75.0 N C) 113 N D) 157 N E) 192 N Three boxes are connected by massless strings and are resting on a frictionless table. Each box has a mass of 15 kg, and the tension T 1 in the right string is accelerating the boxes to the right at a

More information

Simple Harmonic Motion

Simple Harmonic Motion Simple Harmonic Motion 1 Object To determine the period of motion of objects that are executing simple harmonic motion and to check the theoretical prediction of such periods. 2 Apparatus Assorted weights

More information

Physics 9 Fall 2009 Homework 2 - Solutions

Physics 9 Fall 2009 Homework 2 - Solutions Physics 9 Fall 009 Homework - s 1. Chapter 7 - Exercise 5. An electric dipole is formed from ±1.0 nc charges spread.0 mm apart. The dipole is at the origin, oriented along the y axis. What is the electric

More information

PHYS 101-4M, Fall 2005 Exam #3. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

PHYS 101-4M, Fall 2005 Exam #3. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. PHYS 101-4M, Fall 2005 Exam #3 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A bicycle wheel rotates uniformly through 2.0 revolutions in

More information

Physics 211 Week 12. Simple Harmonic Motion: Equation of Motion

Physics 211 Week 12. Simple Harmonic Motion: Equation of Motion Physics 11 Week 1 Simple Harmonic Motion: Equation of Motion A mass M rests on a frictionless table and is connected to a spring of spring constant k. The other end of the spring is fixed to a vertical

More information

Practice Test SHM with Answers

Practice Test SHM with Answers Practice Test SHM with Answers MPC 1) If we double the frequency of a system undergoing simple harmonic motion, which of the following statements about that system are true? (There could be more than one

More information

People s Physics book 3e Ch 25-1

People s Physics book 3e Ch 25-1 The Big Idea: In most realistic situations forces and accelerations are not fixed quantities but vary with time or displacement. In these situations algebraic formulas cannot do better than approximate

More information

Solution Derivations for Capa #11

Solution Derivations for Capa #11 Solution Derivations for Capa #11 1) A horizontal circular platform (M = 128.1 kg, r = 3.11 m) rotates about a frictionless vertical axle. A student (m = 68.3 kg) walks slowly from the rim of the platform

More information

Periodic Motion or Oscillations. Physics 232 Lecture 01 1

Periodic Motion or Oscillations. Physics 232 Lecture 01 1 Periodic Motion or Oscillations Physics 3 Lecture 01 1 Periodic Motion Periodic Motion is motion that repeats about a point of stable equilibrium Stable Equilibrium Unstable Equilibrium A necessary requirement

More information

3600 s 1 h. 24 h 1 day. 1 day

3600 s 1 h. 24 h 1 day. 1 day Week 7 homework IMPORTANT NOTE ABOUT WEBASSIGN: In the WebAssign versions of these problems, various details have been changed, so that the answers will come out differently. The method to find the solution

More information

Elementary Physics November 16, 2015

Elementary Physics November 16, 2015 Circle your Recitation: A01 A03 A04 A08 A05 A06 A07 A02 Myers Yang Pepe Myers Pepe Sanders Sanders Yang (8:30 a.m.) (11:40 a.m.) (1:15 p.m.) (1:15 p.m.) (2:50 p.m.) (4:25 p.m.) (6:00 p.m.) (7:35 p.m.)

More information

Problem Set V Solutions

Problem Set V Solutions Problem Set V Solutions. Consider masses m, m 2, m 3 at x, x 2, x 3. Find X, the C coordinate by finding X 2, the C of mass of and 2, and combining it with m 3. Show this is gives the same result as 3

More information

Physics Exam 2 Formulas

Physics Exam 2 Formulas INSTRUCTIONS: Write your NAME on the front of the blue exam booklet. The exam is closed book, and you may have only pens/pencils and a calculator (no stored equations or programs and no graphing). Show

More information

Glossary of Physics Formulas

Glossary of Physics Formulas Glossary of Physics Formulas 1. Kinematic relations in 1-D at constant velocity Mechanics, velocity, position x - x o = v (t -t o ) or x - x o = v t x o is the position at time = t o (this is the beginning

More information

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Exam Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 1) A lawn roller in the form of a uniform solid cylinder is being pulled horizontally by a horizontal

More information

Lab 8: Ballistic Pendulum

Lab 8: Ballistic Pendulum Lab 8: Ballistic Pendulum Equipment: Ballistic pendulum apparatus, 2 meter ruler, 30 cm ruler, blank paper, carbon paper, masking tape, scale. Caution In this experiment a steel ball is projected horizontally

More information

PHY231 Section 1, Form B March 22, 2012

PHY231 Section 1, Form B March 22, 2012 1. A car enters a horizontal, curved roadbed of radius 50 m. The coefficient of static friction between the tires and the roadbed is 0.20. What is the maximum speed with which the car can safely negotiate

More information

F mg (10.1 kg)(9.80 m/s ) m

F mg (10.1 kg)(9.80 m/s ) m Week 9 homework IMPORTANT NOTE ABOUT WEBASSIGN: In the WebAssign versions of these problems, various details have been changed, so that the answers will come out differently. The method to find the solution

More information

Angular acceleration α

Angular acceleration α Angular Acceleration Angular acceleration α measures how rapidly the angular velocity is changing: Slide 7-0 Linear and Circular Motion Compared Slide 7- Linear and Circular Kinematics Compared Slide 7-

More information

Center of Gravity. We touched on this briefly in chapter 7! x 2

Center of Gravity. We touched on this briefly in chapter 7! x 2 Center of Gravity We touched on this briefly in chapter 7! x 1 x 2 cm m 1 m 2 This was for what is known as discrete objects. Discrete refers to the fact that the two objects separated and individual.

More information

Physics 9e/Cutnell. correlated to the. College Board AP Physics 1 Course Objectives

Physics 9e/Cutnell. correlated to the. College Board AP Physics 1 Course Objectives Physics 9e/Cutnell correlated to the College Board AP Physics 1 Course Objectives Big Idea 1: Objects and systems have properties such as mass and charge. Systems may have internal structure. Enduring

More information

MECHANICS IV - SIMPLE HARMONIC MOTION

MECHANICS IV - SIMPLE HARMONIC MOTION M-IV-p.1 A. OSCILLATIONS B. SIMPLE PENDULUM C. KINEMATICS OF SIMPLE HARMONIC MOTION D. SPRING-AND-MASS SYSTEM E. ENERGY OF SHM F. DAMPED HARMONIC MOTION G. FORCED VIBRATION A. OSCILLATIONS A to-and-fro

More information

Physics 231 Lecture 15

Physics 231 Lecture 15 Physics 31 ecture 15 Main points of today s lecture: Simple harmonic motion Mass and Spring Pendulum Circular motion T 1/f; f 1/ T; ω πf for mass and spring ω x Acos( ωt) v ωasin( ωt) x ax ω Acos( ωt)

More information

Homework 4. problems: 5.61, 5.67, 6.63, 13.21

Homework 4. problems: 5.61, 5.67, 6.63, 13.21 Homework 4 problems: 5.6, 5.67, 6.6,. Problem 5.6 An object of mass M is held in place by an applied force F. and a pulley system as shown in the figure. he pulleys are massless and frictionless. Find

More information

Physics 117.3 Tutorial #1 January 14 to 25, 2013

Physics 117.3 Tutorial #1 January 14 to 25, 2013 Physics 117.3 Tutorial #1 January 14 to 25, 2013 Rm 130 Physics 8.79. The location of a person s centre of gravity can be determined using the arrangement shown in the figure. A light plank rests on two

More information

Phys101 Third Major Exam Term 142

Phys101 Third Major Exam Term 142 Phys0 Third Major Exam Term 4 Q. The angular position of a point on the rim of a rotating wheel of radius R is given by: θ (t) = 6.0 t + 3.0 t.0 t 3, where θ is in radians and t is in seconds. What is

More information

Chapter 24 Physical Pendulum

Chapter 24 Physical Pendulum Chapter 4 Physical Pendulum 4.1 Introduction... 1 4.1.1 Simple Pendulum: Torque Approach... 1 4. Physical Pendulum... 4.3 Worked Examples... 4 Example 4.1 Oscillating Rod... 4 Example 4.3 Torsional Oscillator...

More information

ANALYTICAL METHODS FOR ENGINEERS

ANALYTICAL METHODS FOR ENGINEERS UNIT 1: Unit code: QCF Level: 4 Credit value: 15 ANALYTICAL METHODS FOR ENGINEERS A/601/1401 OUTCOME - TRIGONOMETRIC METHODS TUTORIAL 1 SINUSOIDAL FUNCTION Be able to analyse and model engineering situations

More information

Practice Exam Three Solutions

Practice Exam Three Solutions MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics Physics 8.01T Fall Term 2004 Practice Exam Three Solutions Problem 1a) (5 points) Collisions and Center of Mass Reference Frame In the lab frame,

More information

EQUILIBRIUM AND ELASTICITY

EQUILIBRIUM AND ELASTICITY Chapter 12: EQUILIBRIUM AND ELASTICITY 1 A net torque applied to a rigid object always tends to produce: A linear acceleration B rotational equilibrium C angular acceleration D rotational inertia E none

More information

Columbia University Department of Physics QUALIFYING EXAMINATION

Columbia University Department of Physics QUALIFYING EXAMINATION Columbia University Department of Physics QUALIFYING EXAMINATION Monday, January 13, 2014 1:00PM to 3:00PM Classical Physics Section 1. Classical Mechanics Two hours are permitted for the completion of

More information

Advanced Higher Physics: MECHANICS. Simple Harmonic Motion

Advanced Higher Physics: MECHANICS. Simple Harmonic Motion Advanced Higher Physics: MECHANICS Simple Harmonic Motion At the end of this section, you should be able to: Describe examples of simple harmonic motion (SHM). State that in SHM the unbalanced force is

More information

Wave topics 1. Waves - multiple choice

Wave topics 1. Waves - multiple choice Wave topics 1 Waves - multiple choice When an object is oscillating in simple harmonic motion in the vertical direction, its maximum speed occurs when the object (a) is at its highest point. (b) is at

More information

Physics 125 Practice Exam #3 Chapters 6-7 Professor Siegel

Physics 125 Practice Exam #3 Chapters 6-7 Professor Siegel Physics 125 Practice Exam #3 Chapters 6-7 Professor Siegel Name: Lab Day: 1. A concrete block is pulled 7.0 m across a frictionless surface by means of a rope. The tension in the rope is 40 N; and the

More information

Chapter 11. h = 5m. = mgh + 1 2 mv 2 + 1 2 Iω 2. E f. = E i. v = 4 3 g(h h) = 4 3 9.8m / s2 (8m 5m) = 6.26m / s. ω = v r = 6.

Chapter 11. h = 5m. = mgh + 1 2 mv 2 + 1 2 Iω 2. E f. = E i. v = 4 3 g(h h) = 4 3 9.8m / s2 (8m 5m) = 6.26m / s. ω = v r = 6. Chapter 11 11.7 A solid cylinder of radius 10cm and mass 1kg starts from rest and rolls without slipping a distance of 6m down a house roof that is inclined at 30 degrees (a) What is the angular speed

More information

AP2 Fluids. Kinetic Energy (A) stays the same stays the same (B) increases increases (C) stays the same increases (D) increases stays the same

AP2 Fluids. Kinetic Energy (A) stays the same stays the same (B) increases increases (C) stays the same increases (D) increases stays the same A cart full of water travels horizontally on a frictionless track with initial velocity v. As shown in the diagram, in the back wall of the cart there is a small opening near the bottom of the wall that

More information

Center of Mass/Momentum

Center of Mass/Momentum Center of Mass/Momentum 1. 2. An L-shaped piece, represented by the shaded area on the figure, is cut from a metal plate of uniform thickness. The point that corresponds to the center of mass of the L-shaped

More information

Physics 2A, Sec B00: Mechanics -- Winter 2011 Instructor: B. Grinstein Final Exam

Physics 2A, Sec B00: Mechanics -- Winter 2011 Instructor: B. Grinstein Final Exam Physics 2A, Sec B00: Mechanics -- Winter 2011 Instructor: B. Grinstein Final Exam INSTRUCTIONS: Use a pencil #2 to fill your scantron. Write your code number and bubble it in under "EXAM NUMBER;" an entry

More information

Mechanics 1. Revision Notes

Mechanics 1. Revision Notes Mechanics 1 Revision Notes July 2012 MECHANICS 1... 2 1. Mathematical Models in Mechanics... 2 Assumptions and approximations often used to simplify the mathematics involved:... 2 2. Vectors in Mechanics....

More information

1 of 10 11/23/2009 6:37 PM

1 of 10 11/23/2009 6:37 PM hapter 14 Homework Due: 9:00am on Thursday November 19 2009 Note: To understand how points are awarded read your instructor's Grading Policy. [Return to Standard Assignment View] Good Vibes: Introduction

More information

PHYSICS 111 HOMEWORK SOLUTION #10. April 8, 2013

PHYSICS 111 HOMEWORK SOLUTION #10. April 8, 2013 PHYSICS HOMEWORK SOLUTION #0 April 8, 203 0. Find the net torque on the wheel in the figure below about the axle through O, taking a = 6.0 cm and b = 30.0 cm. A torque that s produced by a force can be

More information

A ball, attached to a cord of length 1.20 m, is set in motion so that it is swinging backwards and forwards like a pendulum.

A ball, attached to a cord of length 1.20 m, is set in motion so that it is swinging backwards and forwards like a pendulum. MECHANICS: SIMPLE HARMONIC MOTION QUESTIONS THE PENDULUM (2014;2) A pendulum is set up, as shown in the diagram. The length of the cord attached to the bob is 1.55 m. The bob has a mass of 1.80 kg. The

More information

Physics 201 Homework 8

Physics 201 Homework 8 Physics 201 Homework 8 Feb 27, 2013 1. A ceiling fan is turned on and a net torque of 1.8 N-m is applied to the blades. 8.2 rad/s 2 The blades have a total moment of inertia of 0.22 kg-m 2. What is the

More information

Chapter 8- Rotational Motion

Chapter 8- Rotational Motion Chapter 8- Rotational Motion Textbook (Giancoli, 6 th edition): Assignment 9 Due on Thursday, November 26. 1. On page 131 of Giancoli, problem 18. 2. On page 220 of Giancoli, problem 24. 3. On page 221

More information

A B = AB sin(θ) = A B = AB (2) For two vectors A and B the cross product A B is a vector. The magnitude of the cross product

A B = AB sin(θ) = A B = AB (2) For two vectors A and B the cross product A B is a vector. The magnitude of the cross product 1 Dot Product and Cross Products For two vectors, the dot product is a number A B = AB cos(θ) = A B = AB (1) For two vectors A and B the cross product A B is a vector. The magnitude of the cross product

More information

Solution Derivations for Capa #10

Solution Derivations for Capa #10 Solution Derivations for Capa #10 1) The flywheel of a steam engine runs with a constant angular speed of 172 rev/min. When steam is shut off, the friction of the bearings and the air brings the wheel

More information

Applications of Second-Order Differential Equations

Applications of Second-Order Differential Equations Applications of Second-Order Differential Equations Second-order linear differential equations have a variety of applications in science and engineering. In this section we explore two of them: the vibration

More information

Chapter 7 Homework solutions

Chapter 7 Homework solutions Chapter 7 Homework solutions 8 Strategy Use the component form of the definition of center of mass Solution Find the location of the center of mass Find x and y ma xa + mbxb (50 g)(0) + (10 g)(5 cm) x

More information

9 ROTATIONAL DYNAMICS

9 ROTATIONAL DYNAMICS CHAPTER 9 ROTATIONAL DYNAMICS CONCEPTUAL QUESTIONS 1. REASONING AND SOLUTION The magnitude of the torque produced by a force F is given by τ = Fl, where l is the lever arm. When a long pipe is slipped

More information

PSI AP Physics I Rotational Motion

PSI AP Physics I Rotational Motion PSI AP Physics I Rotational Motion Multiple-Choice questions 1. Which of the following is the unit for angular displacement? A. meters B. seconds C. radians D. radians per second 2. An object moves from

More information

Physics 2101, First Exam, Fall 2007

Physics 2101, First Exam, Fall 2007 Physics 2101, First Exam, Fall 2007 September 4, 2007 Please turn OFF your cell phone and MP3 player! Write down your name and section number in the scantron form. Make sure to mark your answers in the

More information

Higher Technological Institute Civil Engineering Department. Lectures of. Fluid Mechanics. Dr. Amir M. Mobasher

Higher Technological Institute Civil Engineering Department. Lectures of. Fluid Mechanics. Dr. Amir M. Mobasher Higher Technological Institute Civil Engineering Department Lectures of Fluid Mechanics Dr. Amir M. Mobasher 1/14/2013 Fluid Mechanics Dr. Amir Mobasher Department of Civil Engineering Faculty of Engineering

More information

Physics 53. Oscillations. You've got to be very careful if you don't know where you're going, because you might not get there.

Physics 53. Oscillations. You've got to be very careful if you don't know where you're going, because you might not get there. Physics 53 Oscillations You've got to be very careful if you don't know where you're going, because you might not get there. Yogi Berra Overview Many natural phenomena exhibit motion in which particles

More information

TIME OF COMPLETION NAME SOLUTION DEPARTMENT OF NATURAL SCIENCES. PHYS 1111, Exam 3 Section 1 Version 1 December 6, 2005 Total Weight: 100 points

TIME OF COMPLETION NAME SOLUTION DEPARTMENT OF NATURAL SCIENCES. PHYS 1111, Exam 3 Section 1 Version 1 December 6, 2005 Total Weight: 100 points TIME OF COMPLETION NAME SOLUTION DEPARTMENT OF NATURAL SCIENCES PHYS 1111, Exam 3 Section 1 Version 1 December 6, 2005 Total Weight: 100 points 1. Check your examination for completeness prior to starting.

More information

Lab 7: Rotational Motion

Lab 7: Rotational Motion Lab 7: Rotational Motion Equipment: DataStudio, rotary motion sensor mounted on 80 cm rod and heavy duty bench clamp (PASCO ME-9472), string with loop at one end and small white bead at the other end (125

More information

charge is detonated, causing the smaller glider with mass M, to move off to the right at 5 m/s. What is the

charge is detonated, causing the smaller glider with mass M, to move off to the right at 5 m/s. What is the This test covers momentum, impulse, conservation of momentum, elastic collisions, inelastic collisions, perfectly inelastic collisions, 2-D collisions, and center-of-mass, with some problems requiring

More information

11. Rotation Translational Motion: Rotational Motion:

11. Rotation Translational Motion: Rotational Motion: 11. Rotation Translational Motion: Motion of the center of mass of an object from one position to another. All the motion discussed so far belongs to this category, except uniform circular motion. Rotational

More information

Ph\sics 2210 Fall 2012 - Novcmbcr 21 David Ailion

Ph\sics 2210 Fall 2012 - Novcmbcr 21 David Ailion Ph\sics 2210 Fall 2012 - Novcmbcr 21 David Ailion Unid: Discussion T A: Bryant Justin Will Yuan 1 Place answers in box provided for each question. Specify units for each answer. Circle correct answer(s)

More information

Sample Questions for the AP Physics 1 Exam

Sample Questions for the AP Physics 1 Exam Sample Questions for the AP Physics 1 Exam Sample Questions for the AP Physics 1 Exam Multiple-choice Questions Note: To simplify calculations, you may use g 5 10 m/s 2 in all problems. Directions: Each

More information

Discussion Session 1

Discussion Session 1 Physics 102 Fall 2016 NAME: Discussion Session 1 Math Review and Temperature The goal of Physics is to explain the Universe in terms of equations, and so the ideas of mathematics are central to your success

More information

Response to Harmonic Excitation Part 2: Damped Systems

Response to Harmonic Excitation Part 2: Damped Systems Response to Harmonic Excitation Part 2: Damped Systems Part 1 covered the response of a single degree of freedom system to harmonic excitation without considering the effects of damping. However, almost

More information

P113 University of Rochester NAME S. Manly Fall 2013

P113 University of Rochester NAME S. Manly Fall 2013 Final Exam (December 19, 2013) Please read the problems carefully and answer them in the space provided. Write on the back of the page, if necessary. Show all your work. Partial credit will be given unless

More information

AP Physics B Free Response Solutions

AP Physics B Free Response Solutions AP Physics B Free Response Solutions. (0 points) A sailboat at rest on a calm lake has its anchor dropped a distance of 4.0 m below the surface of the water. The anchor is suspended by a rope of negligible

More information

SOLUTIONS TO CONCEPTS CHAPTER 15

SOLUTIONS TO CONCEPTS CHAPTER 15 SOLUTIONS TO CONCEPTS CHAPTER 15 1. v = 40 cm/sec As velocity of a wave is constant location of maximum after 5 sec = 40 5 = 00 cm along negative x-axis. [(x / a) (t / T)]. Given y = Ae a) [A] = [M 0 L

More information

Linear Centripetal Tangential speed acceleration acceleration A) Rω Rω 2 Rα B) Rω Rα Rω 2 C) Rω 2 Rα Rω D) Rω Rω 2 Rω E) Rω 2 Rα Rω 2 Ans: A

Linear Centripetal Tangential speed acceleration acceleration A) Rω Rω 2 Rα B) Rω Rα Rω 2 C) Rω 2 Rα Rω D) Rω Rω 2 Rω E) Rω 2 Rα Rω 2 Ans: A 1. Two points, A and B, are on a disk that rotates about an axis. Point A is closer to the axis than point B. Which of the following is not true? A) Point B has the greater speed. B) Point A has the lesser

More information

Rotation. Moment of inertia of a rotating body: w I = r 2 dm

Rotation. Moment of inertia of a rotating body: w I = r 2 dm Rotation Moment of inertia of a rotating body: w I = r 2 dm Usually reasonably easy to calculate when Body has symmetries Rotation axis goes through Center of mass Exams: All moment of inertia will be

More information

Rotation, Angular Momentum

Rotation, Angular Momentum This test covers rotational motion, rotational kinematics, rotational energy, moments of inertia, torque, cross-products, angular momentum and conservation of angular momentum, with some problems requiring

More information

Updated 2013 (Mathematica Version) M1.1. Lab M1: The Simple Pendulum

Updated 2013 (Mathematica Version) M1.1. Lab M1: The Simple Pendulum Updated 2013 (Mathematica Version) M1.1 Introduction. Lab M1: The Simple Pendulum The simple pendulum is a favorite introductory exercise because Galileo's experiments on pendulums in the early 1600s are

More information

Forces. Definition Friction Falling Objects Projectiles Newton s Laws of Motion Momentum Universal Forces Fluid Pressure Hydraulics Buoyancy

Forces. Definition Friction Falling Objects Projectiles Newton s Laws of Motion Momentum Universal Forces Fluid Pressure Hydraulics Buoyancy Forces Definition Friction Falling Objects Projectiles Newton s Laws of Motion Momentum Universal Forces Fluid Pressure Hydraulics Buoyancy Definition of Force Force = a push or pull that causes a change

More information

Objective: Equilibrium Applications of Newton s Laws of Motion I

Objective: Equilibrium Applications of Newton s Laws of Motion I Type: Single Date: Objective: Equilibrium Applications of Newton s Laws of Motion I Homework: Assignment (1-11) Read (4.1-4.5, 4.8, 4.11); Do PROB # s (46, 47, 52, 58) Ch. 4 AP Physics B Mr. Mirro Equilibrium,

More information

1) The gure below shows the position of a particle (moving along a straight line) as a function of time. Which of the following statements is true?

1) The gure below shows the position of a particle (moving along a straight line) as a function of time. Which of the following statements is true? Physics 2A, Sec C00: Mechanics -- Winter 2011 Instructor: B. Grinstein Final Exam INSTRUCTIONS: Use a pencil #2 to ll your scantron. Write your code number and bubble it in under "EXAM NUMBER;" an entry

More information