# 3 Work, Power and Energy

Size: px
Start display at page:

Transcription

1 3 Work, Power and Energy At the end of this section you should be able to: a. describe potential energy as energy due to position and derive potential energy as mgh b. describe kinetic energy as energy due to motion and derive kinetic energy as mv / c. state conservation of energy laws and solve problems where energy is conserved d. define power as rate of energy transfer e. define couple, torque and calculate work done by variable force or torque f. solve problems where energy is lost due to friction Table of contents: 3 Work, Power and Energy Work done by a constant force Work done by a variable force Energy Potential Energy Formulae for gravitational potential energy Kinetic energy Formulae for kinetic energy Kinetic energy and work done Conservation of energy Power Moment, couple and torque Work done by a constant torque Power transmitted by a constant torque Work done by a variable torque...15 Page numbers on the same topic in, Applied Mechanics, 3 rd Edition, Hannah & Hillier Secti notes Section in Hannah & Hillier Page No. in Hanna & Hiller All of Section 3 Chapter Excluding sections 10.4, 10.9, 10.11, 10.16, 1.17 Fundamentals of Mechanics Kinetics: Section 3 - Work, Powers and Energy 1

2 3.1 Work done by a constant force When the point at which a force acts moves, the force is said to have done work. When the force is constant, the work done is defined as the product of the force and distance moved. work done force distance moved in direction of force Consider the example in Figure 3.1, a force F acting at the angle θ moves a body from point A to point B. F s cos θ A θ s B The distance moved in the direction of the force is given by So the work done by the force F is Figure 3.1: Notation for work done by a force Distance in direction of force s cosθ Work done F s cosθ Equation 3.1 If the body moves in the same direction as the force the angle is 0.0 so Work done Fs When the angle is 90 then the work done is zero. The SI units for work are Joules J (with force, F, in Newton's N and distance, s, in metres m). Worked Example 3.1 How much work is done when a force of 5 kn moves its point of application 600mm in the directio the force. work done 3 3 ( 5 10 ) ( ) 3000 J 3kJ Worked Example 3. Find the work done in raising 100 kg of water through a vertical distance of 3m. The force is the weight of the water, so Fundamentals of Mechanics Kinetics: Section 3 - Work, Powers and Energy

3 work done ( ) 943J 3 3. Work done by a variable force Forces in practice will often vary. In these cases Equation 3.1 cannot be used. Consider the case where the force varies as in Figure 3. For the thin strip with width ds - shown shaded in Figure 3. - the force can be considered constant at F. The work done over the distance ds is then This is the area of the shaded strip. work done F ds The total work done for distance s is the sum of the areas of all such strips. This is the same as the area under the Forcedistance curve. force F 0 ds s distance So for a variable force Figure 3.: Work done by a variable force work done area under force/distance curve Equation 3. Clearly this also works for a constant force - the curve is then a horizontal line. In general you must uses some special integration technique to obtain the area under a curve. Three common techniques are the trapezoidal, mid-ordinate and Simpson's rule. They are not detailed here but may be found in many mathematical text book. 3.3 Energy A body which has the capacity to do work is said to possess energy. For example, water in a reservoir is said to possesses energy as it could be used to drive a turbine lower down the valley. There are many forms of energy e.g trical, chemical heat, nuclear, mechanical etc. The SI units are the same as those for work, Joules J. In this module only purely mechanical energy will be considered. This may be of two kinds, potential and kinetic. Fundamentals of Mechanics Kinetics: Section 3 - Work, Powers and Energy 3

4 3.3.1 Potential Energy There are different forms of potential energy two examples are: i) a pile driver raised ready to fall on to its target possesses gravitational potential energy while (ii) a coiled spring which is compressed possesses an internal potential energy. Only gravitational potential energy will be considered here. It may be described as energy due to position relative to a standard position (normally chosen to be he earth's surface.) The potential energy of a body may be defined as the amount of work it would do if it were to move from the its current position to the standard position Formulae for gravitational potential energy A body is at rest on the earth's surface. It is then raised a vertical distance h above the surface. The work required to do this is the force required times the distance h. Since the force required is it's weight, and weight, W mg, then the work required is mgh. The body now possesses this amount of energy - stored as potential energy - it has the capacity to do this amount of work, and would do so if allowed to fall to earth. Potential energy is thus given b where h is the height above the earth's surface. potential energy mgh Equation 3.3 Worked example 3.3 What is the potential energy of a 10kg mass: a) 100m above the surface of the earth b) at the bottom of a vertical mine shaft 1000m deep. Fundamentals of Mechanics Kinetics: Section 3 - Work, Powers and Energy 4

5 a) b) potential energy potential energy mgh J 9.81kJ mgh J 98.1kJ ( 1000) Kinetic energy Kinetic energy may be described as energy due to motion. The kinetic energy of a body may be defined as the amount of work it can do before being brought to rest. For example when a hammer is used to knock in a nail, work is done on the nail by the hammer and hence the hammer must have possessed energy. Only linear motion will be considered here Formulae for kinetic energy Let a body of mass m moving with speed v be brought to rest with uniform deceleration by a constant force F over a distance s. Using Equation 1.4 v u + as 0 u v s a + as And work done is given by work done force distance Fs v F a Fundamentals of Mechanics Kinetics: Section 3 - Work, Powers and Energy 5

6 The force is F ma so v work done ma a 1 mv Thus the kinetic energy is given by kinetic energy 1 mv Equation Kinetic energy and work done When a body with mass m has its speed increased from u to v in a distance s by a constant force F which produces an acceleration a, then from Equation 1.3 we know 1 v v 1 u u as + as multiplying this by m give an expression of the increase in kinetic energy (the difference in kinetic energy at the end and the start) 1 1 mv mu mas Thus since F ma increase in kinetic energy Fs but also we know Fs work done So the relationship between kinetic energy can be summed up as Work done by forces acting on a body change of kinetic energy in the body Equation 3.5 This is sometimes known as the work-energy theorem. Worked examp.4 A car of mass 1000 kg travelling at 30m/s has its speed reduced to 10m/s by a constant breaking force over a distance of 75m. Find: a) The cars initial kinetic energy b) The final kinetic energy c) The breaking force a) Fundamentals of Mechanics Kinetics: Section 3 - Work, Powers and Energy 6

7 b) c) Initial kinetic energy Final kinetic energy 1 mv J 450kJ 1 mv J 50kJ Change in kinetic energy 400 kj By Equation 3.5 work done change in kinetic energy so Fs change in kinetic energy Breaking force Breaking force 5333N 3.4 Conservation of energy The principle of conservation of energy state that the total energy of a system remains constant. Energy cannot be created or destroyed but may be converted from one form to another. Take the case of a crate on a slope. Initially it is at rest, all its energy is potential energy. As it accelerates, some of it potential energy is converted into kinetic energy and some used to overcome friction. This energy used to overcome friction is not lost but converted into heat. At the bottom of the slope the energy will be purely kinetic (assuming the datum for potential energy is the bottom of the slope.) If we consider a body falling freely in air, neglecting air resistance, then mechanical energy is conserved, as potential energy is lost and equal amount of kinetic energy is gained as speed increases. If the motion involves friction or collisions then the principle of conservation of energy is true, but conservation of mechanical energy is not applicable as some energy is converted to heat and perhaps sound. Worked Example 3.5 A cyclist and his bicycle has a mass of 80 kg. After 100m he reaches the top of a hill, with slope 1 in 0 measured along the slope, at a speed of m/s. He then free wheels the 100m to the bottom of the hill where his speed has increased 9m/s. How much energy has he lost on the hill? 100m h If the hill is 100m long then the height is: Figure 3.3: Dimensions of the hill in worked example 3.5 Fundamentals of Mechanics Kinetics: Section 3 - Work, Powers and Energy 7

8 1 h 100 5m 0 So potential energy lost is Increase in kinetic energy is mgh J mv 1 mu 1 m v 40 ( u ) 1 ( 81 4) 3080 J By the principle of conservation of energy Initial energy Final energy + loss of energy(due to friction etc.) loss of energy (due to friction etc.) J 3.5 Power Power is the rate at which work is done, or the rate at which energy is used transferred. work done Power time taken Equation 3.6 The SI unit for power is the watt W. A power of 1W means that work is being done at the rate of 1J/s. Larger units for power are the kilowatt kw (1kW 1000 W 10 3 W) and the megawatt MW (1 MW W 10 6 W). If work is being done by a machine moving at speed v against a constant force, or resistance, F, then since work doe is force times distance, work done per second is, which is the same as power. Power Fv Equation 3.7 Worked Example 3.6 A constant force of kn pulls a crate along a level floor a distance of 10 m in 50s. What is the power used? Work done force distance J Fundamentals of Mechanics Kinetics: Section 3 - Work, Powers and Energy 8

9 Power work done time taken W Alternatively we could have calculated the speed first distance v time and then calculated power Worked Example Fv 0.m / s Power Force Speed W A hoist operated by an electric motor ha of 500 kg. It raises a load of 300 kg vertically at a steady speed of 0. m/s. Frictional resistance can be taken to be constant at 100 N. What is the power required? Total mass m 800kg Weight N Total force N Fundamentals of Mechanics Kinetics: Section 3 - Work, Powers and Energy 9

10 From Equation 3.7 Power force speed W 1.81kW Worked example 3.8 A car of mass 900 kg has an engine with power output of 4 kw. It can achieve a maximum speed of 10 km/h along the level. a) What is the resistance to motion? b) If the maximum power and the resistance remained the same what would be the maximum speed the car could achieve up an incline of 1 in 40 along the slope? N Wsinθ 100 N 40 1 Wcosθ θ W 900g First get the information into the correct units: Figure 3.4: Forces on the car on a slope in Worked Example km / h m / s a) Calculate the resistance Power Force speed Resistance speed 4000 Resistance Resistance 160 N Fundamentals of Mechanics Kinetics: Section 3 - Work, Powers and Energy 10

11 b) Total force down the incline frictional force + component of mg sinθ N 1 40 weight down incline Or in km/h Power force speed Speed Power force m / s 3600 Speed km / h 3.6 Moment, couple and torque The moment of a force F about a point is its turning effect about the point. It is quantified as the product of the force and the perpendicular distance from the point to the line of action of the force. F d O In Figure 3.5 the moment of F about point O is Figure 3.4: Moment of a force moment Fd Equation 3.8 A couple is a pair of equal and parallel but opposite forces as shown in Figure 3.6: Fundamentals of Mechanics Kinetics: Section 3 - Work, Powers and Energy 11

12 F p F Figure 3.6: A couple The moment of a couple about any point in its plane is the product of one force and the perpendicular distance between them: Moment of couple Fp Equation 3.9 Example of a couple include turning on/off a tap, or winding a clock. The SI units for a moment or a couple are Newton metres, Nm. In engineering the moment of a force or couple is know as torque. A spanner tightening a nut is said to exert a torque on the nut, similarly a belt turning a pulley exerts a torque on the pulley Work done by a constant torque Let a force F turn a light rod OA with length r through an angle of θ to position OB, as shown in Figure 3.7. O F r θ B r s F A Figure 3.7: Work done by a constant torque The tor T Q exerted about O is force times perpendicular distance from O. T Q Fr Equation 3.10 Now work done by F is work done Fs s is the arc of the circle, when θ is measure in radians s rθ Fundamentals of Mechanics Kinetics: Section 3 - Work, Powers and Energy 1

13 work done Frθ work done T Q θ Equation 3.11 The work done by a constant torque T Q is thus the product of the torque and the angle through which it turns (where the angle is measured in radians.) As the SI units for work is Joules, T Q must be in Nm 3.6. Power transmitted by a constant torque Power is rate of doing work. It the rod in Figure 3.7 rotates at n revolutions per second, then in one second the angle turned through is θ πn radians, and the work done per second will be, by Equation 3.11 as angular speed is then work done per second power ω πn power πnt power ωt Q Q T Q πn Equation 3.1 The units of power are Watts, W, with n in rev/s, ω in rad/s and T Q in Nm. Worked Example 3.9 A spanner that is used to tighten a nut is 300mm long. The force exerted on the end of a spanner is 100 N. a) What is the torque exerted on the nut? b) What is the work done when the nut turns through 30? Fundamentals of Mechanics Kinetics: Section 3 - Work, Powers and Energy 13

14 a) Calculate the torque by Equation 3.10 b) Calculate the work done by Equation 3.11 T Q Fr Nm 3 ( ) work done T Q θ π J Worked Example 3.10 An electric motor is rated at 400 W. If its efficiency is 80%, find the maximum torque which it can exert when running at 85 Calculate the speed in rev/s using Equation 3.1 power πnt power n πt n Q Q rev / s Calculate the power as the motor is 80% efficient 80 power W 100 power πnt T Q Q power πn 30 π Nm Fundamentals of Mechanics Kinetics: Section 3 - Work, Powers and Energy 14

### Work Energy & Power. September 2000 Number 05. 1. Work If a force acts on a body and causes it to move, then the force is doing work.

PhysicsFactsheet September 2000 Number 05 Work Energy & Power 1. Work If a force acts on a body and causes it to move, then the force is doing work. W = Fs W = work done (J) F = force applied (N) s = distance

### Weight The weight of an object is defined as the gravitational force acting on the object. Unit: Newton (N)

Gravitational Field A gravitational field as a region in which an object experiences a force due to gravitational attraction Gravitational Field Strength The gravitational field strength at a point in

### 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

### 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

### Chapter 6. Work and Energy

Chapter 6 Work and Energy The concept of forces acting on a mass (one object) is intimately related to the concept of ENERGY production or storage. A mass accelerated to a non-zero speed carries energy

### 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 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 6 Work and Energy

Chapter 6 WORK AND ENERGY PREVIEW Work is the scalar product of the force acting on an object and the displacement through which it acts. When work is done on or by a system, the energy of that system

### WORK DONE BY A CONSTANT FORCE

WORK DONE BY A CONSTANT FORCE The definition of work, W, when a constant force (F) is in the direction of displacement (d) is W = Fd SI unit is the Newton-meter (Nm) = Joule, J If you exert a force of

### 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

### Gravitational Potential Energy

Gravitational Potential Energy Consider a ball falling from a height of y 0 =h to the floor at height y=0. A net force of gravity has been acting on the ball as it drops. So the total work done on the

### 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

### Work, Energy and Power

Work, Energy and Power In this section of the Transport unit, we will look at the energy changes that take place when a force acts upon an object. Energy can t be created or destroyed, it can only be changed

### 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

### 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

### Physics Notes Class 11 CHAPTER 6 WORK, ENERGY AND POWER

1 P a g e Work Physics Notes Class 11 CHAPTER 6 WORK, ENERGY AND POWER When a force acts on an object and the object actually moves in the direction of force, then the work is said to be done by the force.

### 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

### Chapter 7 WORK, ENERGY, AND Power Work Done by a Constant Force Kinetic Energy and the Work-Energy Theorem Work Done by a Variable Force Power

Chapter 7 WORK, ENERGY, AND Power Work Done by a Constant Force Kinetic Energy and the Work-Energy Theorem Work Done by a Variable Force Power Examples of work. (a) The work done by the force F on this

### Problem Set 1. Ans: a = 1.74 m/s 2, t = 4.80 s

Problem Set 1 1.1 A bicyclist starts from rest and after traveling along a straight path a distance of 20 m reaches a speed of 30 km/h. Determine her constant acceleration. How long does it take her to

### 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-

### 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.

### Curso2012-2013 Física Básica Experimental I Cuestiones Tema IV. Trabajo y energía.

1. A body of mass m slides a distance d along a horizontal surface. How much work is done by gravity? A) mgd B) zero C) mgd D) One cannot tell from the given information. E) None of these is correct. 2.

### 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

### 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

### 9. The kinetic energy of the moving object is (1) 5 J (3) 15 J (2) 10 J (4) 50 J

1. If the kinetic energy of an object is 16 joules when its speed is 4.0 meters per second, then the mass of the objects is (1) 0.5 kg (3) 8.0 kg (2) 2.0 kg (4) 19.6 kg Base your answers to questions 9

### Using mechanical energy for daily

unit 3 Using mechanical energy for daily activities Physics Chapter 3 Using mechanical energy for daily activities Competency Uses mechanical energy for day-to-day activities Competency level 3.1 Investigates

### Name Class Date. You do twice as much work. b. You lift two identical books one meter above the ground.

Exercises 9.1 Work (pages 145 146) 1. Circle the letter next to the correct mathematical equation for work. work = force distance work = distance force c. work = force distance d. work = force distance

### Ch 7 Kinetic Energy and Work. Question: 7 Problems: 3, 7, 11, 17, 23, 27, 35, 37, 41, 43

Ch 7 Kinetic Energy and Work Question: 7 Problems: 3, 7, 11, 17, 23, 27, 35, 37, 41, 43 Technical definition of energy a scalar quantity that is associated with that state of one or more objects The state

### At the skate park on the ramp

At the skate park on the ramp 1 On the ramp When a cart rolls down a ramp, it begins at rest, but starts moving downward upon release covers more distance each second When a cart rolls up a ramp, it rises

### 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

### 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

### 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

### MECHANICAL PRINCIPLES OUTCOME 4 MECHANICAL POWER TRANSMISSION TUTORIAL 1 SIMPLE MACHINES

MECHANICAL PRINCIPLES OUTCOME 4 MECHANICAL POWER TRANSMISSION TUTORIAL 1 SIMPLE MACHINES Simple machines: lifting devices e.g. lever systems, inclined plane, screw jack, pulley blocks, Weston differential

### 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

### Mechanical Principles

Unit 4: Mechanical Principles Unit code: F/60/450 QCF level: 5 Credit value: 5 OUTCOME 3 POWER TRANSMISSION TUTORIAL BELT DRIVES 3 Power Transmission Belt drives: flat and v-section belts; limiting coefficient

### 8. Potential Energy and Conservation of Energy Potential Energy: When an object has potential to have work done on it, it is said to have potential

8. Potential Energy and Conservation of Energy Potential Energy: When an object has potential to have work done on it, it is said to have potential energy, e.g. a ball in your hand has more potential energy

### 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

### Work. Work = Force x parallel distance (parallel component of displacement) F v

Work Work = orce x parallel distance (parallel component of displacement) W k = d parallel d parallel Units: N m= J = " joules" = ( kg m2/ s2) = average force computed over the distance r r When is not

### 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

### 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

### physics 111N work & energy

physics 111N work & energy conservation of energy entirely gravitational potential energy kinetic energy turning into gravitational potential energy gravitational potential energy turning into kinetic

### TOP VIEW. FBD s TOP VIEW. Examination No. 2 PROBLEM NO. 1. Given:

RLEM N. 1 Given: Find: vehicle having a mass of 500 kg is traveling on a banked track on a path with a constant radius of R = 1000 meters. t the instant showing, the vehicle is traveling with a speed of

### ENGINEERING COUNCIL DYNAMICS OF MECHANICAL SYSTEMS D225 TUTORIAL 1 LINEAR AND ANGULAR DISPLACEMENT, VELOCITY AND ACCELERATION

ENGINEERING COUNCIL DYNAMICS OF MECHANICAL SYSTEMS D225 TUTORIAL 1 LINEAR AND ANGULAR DISPLACEMENT, VELOCITY AND ACCELERATION This tutorial covers pre-requisite material and should be skipped if you are

### Chapter 6. Work and Energy

Chapter 6 Work and Energy ENERGY IS THE ABILITY TO DO WORK = TO APPLY A FORCE OVER A DISTANCE= Example: push over a distance, pull over a distance. Mechanical energy comes into 2 forms: Kinetic energy

### 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,

### WORKSHEET: KINETIC AND POTENTIAL ENERGY PROBLEMS

WORKSHEET: KINETIC AND POTENTIAL ENERGY PROBLEMS 1. Stored energy or energy due to position is known as Potential energy. 2. The formula for calculating potential energy is mgh. 3. The three factors that

### Work, Power, Energy Multiple Choice. PSI Physics. Multiple Choice Questions

Work, Power, Energy Multiple Choice PSI Physics Name Multiple Choice Questions 1. A block of mass m is pulled over a distance d by an applied force F which is directed in parallel to the displacement.

### Work-Energy Bar Charts

Name: Work-Energy Bar Charts Read from Lesson 2 of the Work, Energy and Power chapter at The Physics Classroom: http://www.physicsclassroom.com/class/energy/u5l2c.html MOP Connection: Work and Energy:

### 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

### 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

### 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

### 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

### 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

### 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

### Work, Energy & Momentum Homework Packet Worksheet 1: This is a lot of work!

Work, Energy & Momentum Homework Packet Worksheet 1: This is a lot of work! 1. A student holds her 1.5-kg psychology textbook out of a second floor classroom window until her arm is tired; then she releases

### Name: Partners: Period: Coaster Option: 1. In the space below, make a sketch of your roller coaster.

1. In the space below, make a sketch of your roller coaster. 2. On your sketch, label different areas of acceleration. Put a next to an area of negative acceleration, a + next to an area of positive acceleration,

### General Physical Science

General Physical Science Chapter 4 Work and Energy Work The work done by a constant force F acting upon an object is the product of the magnitude of the force (or component of the force) and the parallel

### 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

### PHYSICS STUDY GUIDE CHAPTER 10: WORK-ENERGY. WORK: Potential to do something ( A transfer of energy into or out of the system ).

TOPICS: Work Power Kinetic Energy Gravitational Potential Energy Elastic Potential Energy Conservation of Mechanical energy DEFINITIONS PHYSICS STDY GIDE CHAPTER 10: WORK-ENERGY WORK: Potential to do something

### 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

### 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,

### 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.

### Work, Energy and Power Practice Test 1

Name: ate: 1. How much work is required to lift a 2-kilogram mass to a height of 10 meters?. 5 joules. 20 joules. 100 joules. 200 joules 5. ar and car of equal mass travel up a hill. ar moves up the hill

### 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

### KE =? v o. Page 1 of 12

Page 1 of 12 CTEnergy-1. A mass m is at the end of light (massless) rod of length R, the other end of which has a frictionless pivot so the rod can swing in a vertical plane. The rod is initially horizontal

### SOLID MECHANICS DYNAMICS TUTORIAL PULLEY DRIVE SYSTEMS. This work covers elements of the syllabus for the Edexcel module HNC/D Mechanical Principles.

SOLID MECHANICS DYNAMICS TUTORIAL PULLEY DRIVE SYSTEMS This work covers elements of the syllabus for the Edexcel module HNC/D Mechanical Principles. On completion of this tutorial you should be able to

### 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

### 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

### SOLID MECHANICS DYNAMICS TUTORIAL CENTRIPETAL FORCE

SOLID MECHANICS DYNAMICS TUTORIAL CENTRIPETAL FORCE This work coers elements of the syllabus for the Engineering Council Exam D5 Dynamics of Mechanical Systems C10 Engineering Science. This tutorial examines

### 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

### Work and Conservation of Energy

Work and Conservation of Energy Topics Covered: 1. The definition of work in physics. 2. The concept of potential energy 3. The concept of kinetic energy 4. Conservation of Energy General Remarks: Two

### 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

### 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

### Classical Physics I. PHY131 Lecture 7 Friction Forces and Newton s Laws. Lecture 7 1

Classical Phsics I PHY131 Lecture 7 Friction Forces and Newton s Laws Lecture 7 1 Newton s Laws: 1 & 2: F Net = ma Recap LHS: All the forces acting ON the object of mass m RHS: the resulting acceleration,

### Chapter 8: Potential Energy and Conservation of Energy. Work and kinetic energy are energies of motion.

Chapter 8: Potential Energy and Conservation of Energy Work and kinetic energy are energies of motion. Consider a vertical spring oscillating with mass m attached to one end. At the extreme ends of travel

### 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

### 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

### PHYS 101 Lecture 10 - Work and kinetic energy 10-1

PHYS 101 Lecture 10 - Work and kinetic energy 10-1 Lecture 10 - Work and Kinetic Energy What s important: impulse, work, kinetic energy, potential energy Demonstrations: block on plane balloon with propellor

### 10.1 Quantitative. Answer: A Var: 50+

Chapter 10 Energy and Work 10.1 Quantitative 1) A child does 350 J of work while pulling a box from the ground up to his tree house with a rope. The tree house is 4.8 m above the ground. What is the mass

### FLUID MECHANICS. TUTORIAL No.7 FLUID FORCES. When you have completed this tutorial you should be able to. Solve forces due to pressure difference.

FLUID MECHANICS TUTORIAL No.7 FLUID FORCES When you have completed this tutorial you should be able to Solve forces due to pressure difference. Solve problems due to momentum changes. Solve problems involving

### 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,

### Name Period WORKSHEET: KINETIC AND POTENTIAL ENERGY PROBLEMS. 1. Stored energy or energy due to position is known as energy.

Name Period Date WORKSHEET: KINETIC AND POTENTIAL ENERGY PROBLEMS 1. Stored energy or energy due to position is known as energy. 2. The formula for calculating potential energy is. 3. The three factors

### 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

### 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

### 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,

### 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

### Two-Body System: Two Hanging Masses

Specific Outcome: i. I can apply Newton s laws of motion to solve, algebraically, linear motion problems in horizontal, vertical and inclined planes near the surface of Earth, ignoring air resistance.

### 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

### 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

### 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

### State Newton's second law of motion for a particle, defining carefully each term used.

5 Question 1. [Marks 20] An unmarked police car P is, travelling at the legal speed limit, v P, on a straight section of highway. At time t = 0, the police car is overtaken by a car C, which is speeding

### Work, Energy & Power. AP Physics B

ork, Energy & Power AP Physics B There are many dierent TYPES o Energy. Energy is expressed in JOULES (J) 4.19 J = 1 calorie Energy can be expressed more speciically by using the term ORK() ork = The Scalar

### 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 person on a sled coasts down a hill and then goes over a slight rise with speed 2.7 m/s.

### 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

### 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

### 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

### 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.