# Solution Derivations for Capa #11

Size: px
Start display at page:

Transcription

2 m = Given in grams L = Given M = Given in grams ω = Given I =? The moment of inertia of the system about the axis P is the sum of the moments of inertia for each rod and mass. Since the rods are equal length and mass and since they are attached in a line, they can be treated as a single rod of mass 2M and length 2L. I = 1 3 (2M) (2L)2 + mr mr 2 2 Since the masses are given in grams, first convert them to kilograms by dividing by The radius to the first mass is the length of the first rod. The radius of the second mass is the length of both rods. Units for moment of inertia are kg m 2. I = 8 3 ML2 + ml 2 + m (2L) 2 3) A large plate is balanced at its center and two students of equal mass stand at its center. The plate is rotated on a frictionless pivot about an axis through its center and perpendicular to its face. The students then begin to walk out towards opposite edges. (Select T-True, F-False, I-Increases, D-Decreases, S-Stays the same. ). QUESTION: A) The rate of rotation... as the students walk outward. B) The students produce a net torque on the plate. C) When the students reach the edge and stop, the plate will have the same angular speed as when they started. D) The students do work in walking outward E) The total angular momentum of the system... as the students walk outward. ANSWER: A) D. As the mass of the students gets further away from the axis of rotation, the rate slows down (remember the skater with arms out). B) T. No explanation currently... C) F. The plate slows down as they get further out. The rotation rate does not matter if they are moving or not. D) T. The students exert a force on the plate (and the plate on the students) when walking out. Thus, that force over the distance walked causes word to be down. Consequently the force of the plate on the students is what slows the rotation rate. E) S. Angular momentum is conserved. 2

3 4) In the Figure, a block m 1 sits on a table. There is static friction between the block and table. Block m 2 hangs from a knot, as shown. Call the tension in the rope connecting the knot to m 1, T1. Call the tension in the rope connecting the knot to m 2, T2. Call the tension in the third rope (the one tipped up by an angle θ, connecting the knot to the wall, T3. The system is in equilibrium. Which of the following statements are true? (If A and E are true, and the others are not, enter TFFFT) QUESTION: A) T3 is equal in magnitude to T1. B) The net force on the knot is zero. C) If the table was completely frictionless, the system as shown could not be in equilibrium. D) The tension T2 must equal m 2 g. E) The force of static friction on m 1 equals T1. ANSWER: A) F. Since T3 is directed an and angle θ above the horizontal, it is not equal. T3 s horizontal component, is, however. B) T. Since the system is in equilibrium, all the forces sum to 0. C) T. If there was no horizontal force (from friction) opposing T3 s horizontal component, the system would not be in equilibrium. D) F. Since the mass is the only object connected to the string, it must equal the weight. E) T. Again, since the mass is the only object connected to the string, it must equal to the force of friction. 5) In the previous problem, block m 1 weighs 709 N. The coefficient of static friction between the block and the table is 0.27 and the angle θ is Find the maximum weight of block m 2 for which block m 1 will remain at rest. (Answer ins Newtons, N) m 1 = Given µ s = Given θ = Given From a free body diagram, we can see that Fy = T 2 + T 3 sin θ T 3 sin θ = m 2 g T 3 = m 2g sin θ Fx = T 3 cos θ T 1 T 1 = T 3 cos θ = m 2g sin θ cos θ m 2 = T 1 sin θ g cos θ = T 1 g tan θ 3

4 Since T 1 is due to friction, T 1 = µ s N = µ s m 1 g m 2 = µ sm 1 g tan θ = µ s m 1 tan θ g 6) A physics student is sitting on a frictionless platform that is rotating with an angular speed of ω i = 3.8 rad/s. His arms are outstretched, and he is holding a heavy weight in each hand. The moment of inertia of the student, the extended weights, and the platform about the rotation axis is I i = 8.5 kg m 2. When the student pulls the weights inward toward his body, the moment of inertia decreases to I f = 5.0 kg m 2. What is the resulting angular speed, ω f, of the platform? ω i = Given I i = Given I f = Given ω f =? This is another conservation of angular momentum problem. This will give you an answer in rad/s. L i = L f I i ω i = I f ω f ω f = I iω i I f 7) By how much is the kinetic energy of the system increased? (Think about where this increase in energy comes from!) 4

5 Kinetic energy is related to the moment of inertia and the angular speed. KE = 1 2 Iω2 To find the increase in kinetic energy, subtract the initial from the final. KE = 1 2 I fωf I iωi 2 = 1 ( ) If ωf 2 I i ωi 2 2 8) Compact discs and long-playing records are made from similar materials. The former have a diameter of about 12 cm, and the latter, about 32 cm. When in use, records spin at 33 1 rev/min, and compact discs spin at, say, 365 rev/min. Ignoring the holes in both 3 objects and assuming that a compact disc has half the thickness of a record and 0.90 of its density, what is the ratio of the angular momentum of a compact disc in use to that of a record? R CD = Given R LP = Given ω LP = Given ω CD = Given h CD = Thickness of the CD = Given in terms of the record (LP). Assume it is a coefficient, y, times h LP. That is, if your CD height is half of your record height, y = 1 2. d CD = Given as a coefficient times d LP. Assume it is a coefficient, x, times d LP. That is, if your CD density is 90% of your record density, x = 0.9. This problem deals with angular momentum. L = Iω In this case, you are asked to ignore the holes in the CD and LP, so the object is just like a solid disk. The moment of inertia for a disk is given by 1 2 mr2. So, L = 1 2 mr2 ω You are asked to find the ratio of the angular of momentum of the CD to that of a record 1 L CD = m 2 CDRCDω 2 CD 1 L LP m = mcdr2 CDω CD 2 LP RLP 2 ω LP m LP RLP 2 ω LP We know everything but the mass of the CD and record. Density is mass/volume. So mass = density * volume. To find the volume of a CD, use the formula for a right cylinder (i.e. πr 2 h). The h in this case will be y h LP. So the volume of the CD is πrcd 2 y h LP. To find the mass of the CD, multiply the density 5

6 given by the volume. The given density is in terms of the density of the record (x d LP ). So, the mass of the CD is just m CD = v d m CD = πr 2 CD y h LP x d LP The mass of the record can be found also by finding its volume (πr 2 LP h LP ) and its density (d LP ). Don t worry that some of these terms are unknown because they will cancel in the end. So, m LP = v d m LP = πr 2 LP h LP d LP Plugging these back into the ratio of angular momenta, L CD L LP = m CDR 2 CDω CD m LP R 2 LP ω LP = πr2 CD y h LP x d LP R 2 CDω CD πr 2 LP h LP d LP R 2 LP ω LP Look what cancels. π, h LP, and d LP. Simplifying, L CD L LP = R2 CD y x R 2 CDω CD R 2 LP R 2 LP ω LP = R4 CD y x ω CD R 4 LP ω LP This is your answer, and ratio s have no units. 9) A uniform horizontal bar of length L = 2 m and weight 219 N is pinned to a vertical wall and supported by a thin wire that makes an angle of θ = 24 with the horizontal. A mass M, with a weight of 311 N, can be moved anywhere along the bar. The wire can withstand a maximum tension of 515 N. What is the maximum possible distance from the wall at which mass M can be placed before the wire breaks? L = Given mg = Given (weight of rod) θ = Given Mg = Given (weight of mass) 6

7 T max = Given r =? (radius to mass from axis A) This system is obviously in equilibrium. In order for a system to be in equilibrium, the sum of forces must be zero and the sum of torques must be zero. However, we only need to be concerned with the torques for this part of the problem. Looking at a free-body diagram, we can find the torques about the axis A. The sum of torques is equal to the torque of the wire, the torque of the rod, and the torque of the mass. Remember τ = rf sin θ Solving for r, τ = T L sin θ 1 Lmg rmg = 0 2 T L sin θ 1 Lmg = rmg 2 T L sin θ 1 2 Lmg Mg = r 10) With M placed at this maximum distance what is the horizontal component of the force exerted on the bar by the pin at A? To find the horizontal component of the force, we can again look at the free-body diagram. The only forces acting in the horizontal direction are the component of the tension, and the force of the wall on the rod at point A. So, they must be equal. F x = T cos θ 11) Misako is about to do a push-up. Her center of gravity lies directly above a point on the floor which is d 1 = 1.04 m from her feet and d 2 = 0.62 m from her hands. If her mass is 55.0 kg, what is the force exerted by the floor on her hands? d 1 = Given d 2 = Given m = Given This problem involves torque once again. The person is pushing on the floor in two different spots. She is exerting a torque on each spot on the ground. Since she nor the ground is moving, the torque must be equal. In most cases, the center of gravity will also be the center of mass. Call the force of her hands (a distance of d 2 from the center of gravity) F 2. Call the force of her feet (a distance of d 1 from her center of gravity) F 1. Since she is pushing at right angles on the ground, and the force of her hands is exerting an opposite torque due to the force of her feet so the total torque can be calculated by τ = F 1 d 1 F 2 d 2 = 0 7

8 However, we must find F 1 and F 2 now. Realizing that her mass is m, she is only exerting a force of mg on the ground. Thus, F 1 + F 2 = mg Solving for F 1 in this equation will give F 2 in the second equation (the force of her hands on the ground). This is also the force of the ground on her hands since the ground pushes back with an equal and opposite force. Plugging back into the torque equation, Force has units of Newtons (N). F 1 = mg F 2 0 = d 1 (mg F 2 ) F 2 d 2 0 = d 1 mg d 1 F 2 F 2 d 2 d 1 F 2 + d 2 F 2 = d 1 mg F 2 (d 1 + d 2 ) = d 1 mg F 2 = d 1mg d 1 + d 2 12) What is the force exerted by the floor on her feet? This problem is simply an extension of the last. Since we know F 2, you can use the equation F 1 + F 2 = mg to find the other force (the force of the ground on her feet). So, F 1 = mg F 2 13) The weightless horizontal bar in the figure below is in equilibrium. Scale B reads 4.40 kg. The distances in the figure (which is not to scale) are: D1 = 6.0 cm, D2 = 7.5 cm, and D3 = 6.0 cm. The mass of block X is 0.98 kg and the mass of block Y is 2.04 kg. Determine what the reading on scale A must be. B = Given D 1 = Given D 2 = Given D 3 = Given m x = Given m y = Given A =? This problem involves the torque. The torque on A must equal the torque on B since the system is not moving. The torque on B can be found by summing the torque from mass x and mass y. Since mass z is on the axis of rotation (at B), it produces no torque. τ B = (D 2 + D 3 )m x + D 3 m y 8

9 The torque on A can be calculated by referencing it from B. In other words, what torque must be applied at A to counteract the torques from m x and m y? This can by found by denoting the variable m a to represent the mass (the scale reading) at A to counteract the torque calculated above. That is, m a (D 1 + D 2 + D 3 ) = (D 2 + D 3 )m x + D 3 m y Thus, the scale reading at A (that is, m a ) m a = (D 2 + D 3 )m x + D 3 m y D 1 + D 2 + D 3 9

### 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

### 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

### 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-

### 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

### 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

### 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.

### 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

### 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

### 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

### 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,

### Rotational Inertia Demonstrator

WWW.ARBORSCI.COM Rotational Inertia Demonstrator P3-3545 BACKGROUND: The Rotational Inertia Demonstrator provides an engaging way to investigate many of the principles of angular motion and is intended

### Unit 4 Practice Test: Rotational Motion

Unit 4 Practice Test: Rotational Motion Multiple Guess Identify the letter of the choice that best completes the statement or answers the question. 1. How would an angle in radians be converted to an angle

### Chapter 10 Rotational Motion. Copyright 2009 Pearson Education, Inc.

Chapter 10 Rotational Motion Angular Quantities Units of Chapter 10 Vector Nature of Angular Quantities Constant Angular Acceleration Torque Rotational Dynamics; Torque and Rotational Inertia Solving Problems

### PHYSICS 111 HOMEWORK SOLUTION #9. April 5, 2013

PHYSICS 111 HOMEWORK SOLUTION #9 April 5, 2013 0.1 A potter s wheel moves uniformly from rest to an angular speed of 0.16 rev/s in 33 s. Find its angular acceleration in radians per second per second.

### Chapter 3.8 & 6 Solutions

Chapter 3.8 & 6 Solutions P3.37. Prepare: We are asked to find period, speed and acceleration. Period and frequency are inverses according to Equation 3.26. To find speed we need to know the distance traveled

### 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

### 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

### 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,

### SOLID MECHANICS DYNAMICS TUTORIAL MOMENT OF INERTIA. This work covers elements of the following syllabi.

SOLID MECHANICS DYNAMICS TUTOIAL MOMENT OF INETIA This work covers elements of the following syllabi. Parts of the Engineering Council Graduate Diploma Exam D5 Dynamics of Mechanical Systems Parts of the

### Rotational Motion: Moment of Inertia

Experiment 8 Rotational Motion: Moment of Inertia 8.1 Objectives Familiarize yourself with the concept of moment of inertia, I, which plays the same role in the description of the rotation of a rigid body

### 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

### v v ax v a x a v a v = = = Since F = ma, it follows that a = F/m. The mass of the arrow is unchanged, and ( )

Week 3 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

### 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

### Lecture 6. Weight. Tension. Normal Force. Static Friction. Cutnell+Johnson: 4.8-4.12, second half of section 4.7

Lecture 6 Weight Tension Normal Force Static Friction Cutnell+Johnson: 4.8-4.12, second half of section 4.7 In this lecture, I m going to discuss four different kinds of forces: weight, tension, the normal

### Chapter 4. Forces and Newton s Laws of Motion. continued

Chapter 4 Forces and Newton s Laws of Motion continued 4.9 Static and Kinetic Frictional Forces When an object is in contact with a surface forces can act on the objects. The component of this force acting

### 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.

### 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

### 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

### Lecture Presentation Chapter 7 Rotational Motion

Lecture Presentation Chapter 7 Rotational Motion Suggested Videos for Chapter 7 Prelecture Videos Describing Rotational Motion Moment of Inertia and Center of Gravity Newton s Second Law for Rotation Class

### Chapter 18 Static Equilibrium

Chapter 8 Static Equilibrium 8. Introduction Static Equilibrium... 8. Lever Law... Example 8. Lever Law... 4 8.3 Generalized Lever Law... 5 8.4 Worked Examples... 7 Example 8. Suspended Rod... 7 Example

### Lecture 16. Newton s Second Law for Rotation. Moment of Inertia. Angular momentum. Cutnell+Johnson: 9.4, 9.6

Lecture 16 Newton s Second Law for Rotation Moment of Inertia Angular momentum Cutnell+Johnson: 9.4, 9.6 Newton s Second Law for Rotation Newton s second law says how a net force causes an acceleration.

### AP Physics: Rotational Dynamics 2

Name: Assignment Due Date: March 30, 2012 AP Physics: Rotational Dynamics 2 Problem A solid cylinder with mass M, radius R, and rotational inertia 1 2 MR2 rolls without slipping down the inclined plane

### Chapter 8: Rotational Motion of Solid Objects

Chapter 8: Rotational Motion of Solid Objects 1. An isolated object is initially spinning at a constant speed. Then, although no external forces act upon it, its rotational speed increases. This must be

### 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

### 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

### 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

### 8.012 Physics I: Classical Mechanics Fall 2008

MIT OpenCourseWare http://ocw.mit.edu 8.012 Physics I: Classical Mechanics Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. MASSACHUSETTS INSTITUTE

### 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

### CHAPTER 15 FORCE, MASS AND ACCELERATION

CHAPTER 5 FORCE, MASS AND ACCELERATION EXERCISE 83, Page 9. A car initially at rest accelerates uniformly to a speed of 55 km/h in 4 s. Determine the accelerating force required if the mass of the car

### Chapter 11 Equilibrium

11.1 The First Condition of Equilibrium The first condition of equilibrium deals with the forces that cause possible translations of a body. The simplest way to define the translational equilibrium of

### SOLID MECHANICS TUTORIAL MECHANISMS KINEMATICS - VELOCITY AND ACCELERATION DIAGRAMS

SOLID MECHANICS TUTORIAL MECHANISMS KINEMATICS - VELOCITY AND ACCELERATION DIAGRAMS This work covers elements of the syllabus for the Engineering Council exams C105 Mechanical and Structural Engineering

### F N A) 330 N 0.31 B) 310 N 0.33 C) 250 N 0.27 D) 290 N 0.30 E) 370 N 0.26

Physics 23 Exam 2 Spring 2010 Dr. Alward Page 1 1. A 250-N force is directed horizontally as shown to push a 29-kg box up an inclined plane at a constant speed. Determine the magnitude of the normal force,

### AP Physics - Chapter 8 Practice Test

AP Physics - Chapter 8 Practice Test Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A single conservative force F x = (6.0x 12) N (x is in m) acts on

### Physics 111: Lecture 4: Chapter 4 - Forces and Newton s Laws of Motion. Physics is about forces and how the world around us reacts to these forces.

Physics 111: Lecture 4: Chapter 4 - Forces and Newton s Laws of Motion Physics is about forces and how the world around us reacts to these forces. Whats a force? Contact and non-contact forces. Whats a

### 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

### Torque and Rotary Motion

Torque and Rotary Motion Name Partner Introduction Motion in a circle is a straight-forward extension of linear motion. According to the textbook, all you have to do is replace displacement, velocity,

### Mercury is poured into a U-tube as in Figure (14.18a). The left arm of the tube has crosssectional

Chapter 14 Fluid Mechanics. Solutions of Selected Problems 14.1 Problem 14.18 (In the text book) Mercury is poured into a U-tube as in Figure (14.18a). The left arm of the tube has crosssectional area

### PHYSICS 111 HOMEWORK SOLUTION, week 4, chapter 5, sec 1-7. February 13, 2013

PHYSICS 111 HOMEWORK SOLUTION, week 4, chapter 5, sec 1-7 February 13, 2013 0.1 A 2.00-kg object undergoes an acceleration given by a = (6.00î + 4.00ĵ)m/s 2 a) Find the resultatnt force acting on the object

### Torque and Rotation. Physics

Torque and Rotation Physics Torque Force is the action that creates changes in linear motion. For rotational motion, the same force can cause very different results. A torque is an action that causes objects

### If you put the same book on a tilted surface the normal force will be less. The magnitude of the normal force will equal: N = W cos θ

Experiment 4 ormal and Frictional Forces Preparation Prepare for this week's quiz by reviewing last week's experiment Read this week's experiment and the section in your textbook dealing with normal forces

### 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

### Chapter 5 Using Newton s Laws: Friction, Circular Motion, Drag Forces. Copyright 2009 Pearson Education, Inc.

Chapter 5 Using Newton s Laws: Friction, Circular Motion, Drag Forces Units of Chapter 5 Applications of Newton s Laws Involving Friction Uniform Circular Motion Kinematics Dynamics of Uniform Circular

### Acceleration due to Gravity

Acceleration due to Gravity 1 Object To determine the acceleration due to gravity by different methods. 2 Apparatus Balance, ball bearing, clamps, electric timers, meter stick, paper strips, precision

### HW Set VI page 1 of 9 PHYSICS 1401 (1) homework solutions

HW Set VI page 1 of 9 10-30 A 10 g bullet moving directly upward at 1000 m/s strikes and passes through the center of mass of a 5.0 kg block initially at rest (Fig. 10-33 ). The bullet emerges from the

### 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

### 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

### Mechanical Principles

Unit 4: Mechanical Principles Unit code: F/601/1450 QCF level: 5 Credit value: 15 OUTCOME 4 POWER TRANSMISSION TUTORIAL 2 BALANCING 4. Dynamics of rotating systems Single and multi-link mechanisms: slider

### Physics: Principles and Applications, 6e Giancoli Chapter 4 Dynamics: Newton's Laws of Motion

Physics: Principles and Applications, 6e Giancoli Chapter 4 Dynamics: Newton's Laws of Motion Conceptual Questions 1) Which of Newton's laws best explains why motorists should buckle-up? A) the first law

### VELOCITY, ACCELERATION, FORCE

VELOCITY, ACCELERATION, FORCE velocity Velocity v is a vector, with units of meters per second ( m s ). Velocity indicates the rate of change of the object s position ( r ); i.e., velocity tells you how

### SOLID MECHANICS BALANCING TUTORIAL BALANCING OF ROTATING BODIES

SOLID MECHANICS BALANCING TUTORIAL BALANCING OF ROTATING BODIES This work covers elements of the syllabus for the Edexcel module 21722P HNC/D Mechanical Principles OUTCOME 4. On completion of this tutorial

### Rotation: Moment of Inertia and Torque

Rotation: Moment of Inertia and Torque Every time we push a door open or tighten a bolt using a wrench, we apply a force that results in a rotational motion about a fixed axis. Through experience we learn

### 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

### D Alembert s principle and applications

Chapter 1 D Alembert s principle and applications 1.1 D Alembert s principle The principle of virtual work states that the sum of the incremental virtual works done by all external forces F i acting in

### 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

### 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

### Copyright 2011 Casa Software Ltd. www.casaxps.com. Centre of Mass

Centre of Mass A central theme in mathematical modelling is that of reducing complex problems to simpler, and hopefully, equivalent problems for which mathematical analysis is possible. The concept of

### 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

### 5. Forces and Motion-I. Force is an interaction that causes the acceleration of a body. A vector quantity.

5. Forces and Motion-I 1 Force is an interaction that causes the acceleration of a body. A vector quantity. Newton's First Law: Consider a body on which no net force acts. If the body is at rest, it will

### 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,

### Linear Motion vs. Rotational Motion

Linear Motion vs. Rotational Motion Linear motion involves an object moving from one point to another in a straight line. Rotational motion involves an object rotating about an axis. Examples include a

### Torque Analyses of a Sliding Ladder

Torque Analyses of a Sliding Ladder 1 Problem Kirk T. McDonald Joseph Henry Laboratories, Princeton University, Princeton, NJ 08544 (May 6, 2007) The problem of a ladder that slides without friction while

### Physics 590 Homework, Week 6 Week 6, Homework 1

Physics 590 Homework, Week 6 Week 6, Homework 1 Prob. 6.1.1 A descent vehicle landing on the moon has a vertical velocity toward the surface of the moon of 35 m/s. At the same time it has a horizontal

### 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,

### FRICTION, WORK, AND THE INCLINED PLANE

FRICTION, WORK, AND THE INCLINED PLANE Objective: To measure the coefficient of static and inetic friction between a bloc and an inclined plane and to examine the relationship between the plane s angle

### EDUH 1017 - SPORTS MECHANICS

4277(a) Semester 2, 2011 Page 1 of 9 THE UNIVERSITY OF SYDNEY EDUH 1017 - SPORTS MECHANICS NOVEMBER 2011 Time allowed: TWO Hours Total marks: 90 MARKS INSTRUCTIONS All questions are to be answered. Use

### Chapter 21 Rigid Body Dynamics: Rotation and Translation about a Fixed Axis

Chapter 21 Rigid Body Dynamics: Rotation and Translation about a Fixed Axis 21.1 Introduction... 1 21.2 Translational Equation of Motion... 1 21.3 Translational and Rotational Equations of Motion... 1

### 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

### Serway_ISM_V1 1 Chapter 4

Serway_ISM_V1 1 Chapter 4 ANSWERS TO MULTIPLE CHOICE QUESTIONS 1. Newton s second law gives the net force acting on the crate as This gives the kinetic friction force as, so choice (a) is correct. 2. As

### 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

### EXPERIMENT: MOMENT OF INERTIA

OBJECTIVES EXPERIMENT: MOMENT OF INERTIA to familiarize yourself with the concept of moment of inertia, I, which plays the same role in the description of the rotation of a rigid body as mass plays in

### STATIC AND KINETIC FRICTION

STATIC AND KINETIC FRICTION LAB MECH 3.COMP From Physics with Computers, Vernier Software & Technology, 2000. INTRODUCTION If you try to slide a heavy box resting on the floor, you may find it difficult

### Awell-known lecture demonstration1

Acceleration of a Pulled Spool Carl E. Mungan, Physics Department, U.S. Naval Academy, Annapolis, MD 40-506; mungan@usna.edu Awell-known lecture demonstration consists of pulling a spool by the free end

### Lecture 07: Work and Kinetic Energy. Physics 2210 Fall Semester 2014

Lecture 07: Work and Kinetic Energy Physics 2210 Fall Semester 2014 Announcements Schedule next few weeks: 9/08 Unit 3 9/10 Unit 4 9/15 Unit 5 (guest lecturer) 9/17 Unit 6 (guest lecturer) 9/22 Unit 7,

### 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.

### Physics 11 Assignment KEY Dynamics Chapters 4 & 5

Physics Assignment KEY Dynamics Chapters 4 & 5 ote: for all dynamics problem-solving questions, draw appropriate free body diagrams and use the aforementioned problem-solving method.. Define the following

### Fundamental Mechanics: Supplementary Exercises

Phys 131 Fall 2015 Fundamental Mechanics: Supplementary Exercises 1 Motion diagrams: horizontal motion A car moves to the right. For an initial period it slows down and after that it speeds up. Which of

### CHAPTER 6 WORK AND ENERGY

CHAPTER 6 WORK AND ENERGY CONCEPTUAL QUESTIONS. REASONING AND SOLUTION The work done by F in moving the box through a displacement s is W = ( F cos 0 ) s= Fs. The work done by F is W = ( F cos θ). s From

### Exercises on Work, Energy, and Momentum. A B = 20(10)cos98 A B 28

Exercises on Work, Energy, and Momentum Exercise 1.1 Consider the following two vectors: A : magnitude 20, direction 37 North of East B : magnitude 10, direction 45 North of West Find the scalar product

### Answer, Key Homework 7 David McIntyre 45123 Mar 25, 2004 1

Answer, Key Hoework 7 David McIntyre 453 Mar 5, 004 This print-out should have 4 questions. Multiple-choice questions ay continue on the next colun or page find all choices before aking your selection.

### Let s first see how precession works in quantitative detail. The system is illustrated below: ...

lecture 20 Topics: Precession of tops Nutation Vectors in the body frame The free symmetric top in the body frame Euler s equations The free symmetric top ala Euler s The tennis racket theorem As you know,

### E X P E R I M E N T 8

E X P E R I M E N T 8 Torque, Equilibrium & Center of Gravity Produced by the Physics Staff at Collin College Copyright Collin College Physics Department. All Rights Reserved. University Physics, Exp 8:

### Experiment: Static and Kinetic Friction

PHY 201: General Physics I Lab page 1 of 6 OBJECTIVES Experiment: Static and Kinetic Friction Use a Force Sensor to measure the force of static friction. Determine the relationship between force of static

### 1. Units of a magnetic field might be: A. C m/s B. C s/m C. C/kg D. kg/c s E. N/C m ans: D

Chapter 28: MAGNETIC FIELDS 1 Units of a magnetic field might be: A C m/s B C s/m C C/kg D kg/c s E N/C m 2 In the formula F = q v B: A F must be perpendicular to v but not necessarily to B B F must be

### Conceptual Questions: Forces and Newton s Laws

Conceptual Questions: Forces and Newton s Laws 1. An object can have motion only if a net force acts on it. his statement is a. true b. false 2. And the reason for this (refer to previous question) is

### 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

### AP Physics Applying Forces

AP Physics Applying Forces This section of your text will be very tedious, very tedious indeed. (The Physics Kahuna is just as sorry as he can be.) It s mostly just a bunch of complicated problems and

### Problem Set #8 Solutions

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics Department 8.01L: Physics I November 7, 2015 Prof. Alan Guth Problem Set #8 Solutions Due by 11:00 am on Friday, November 6 in the bins at the intersection