Chapter 10 Energy and Work PowerPoint Lectures for College Physics: A Strategic Approach, Second Edition
10 Energy and Work Slide 10-2
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Reading Quiz 1. If a system is isolated, the total energy of the system A. increases constantly. B. decreases constantly. C. is constant. D. depends on work into the system. E. depends on work out of the system. Slide 10-6
Answer 1. If a system is isolated, the total energy of the system A. increases constantly. B. decreases constantly. C. is constant. D. depends on work into the system. E. depends on work out of the system. Slide 10-7
Reading Quiz 2. Which of the following is an energy transfer? A. Kinetic energy B. Heat C. Potential energy D. Chemical energy E. Thermal energy Slide 10-8
Answer 2. Which of the following is an energy transfer? A. Kinetic energy B. Heat C. Potential energy D. Chemical energy E. Thermal energy Slide 10-9
Reading Quiz 3. If you raise an object to a greater height, you are increasing A. kinetic energy. B. heat. C. potential energy. D. chemical energy. E. thermal energy. Slide 10-10
Answer 3. If you raise an object to a greater height, you are increasing A. kinetic energy. B. heat. C. potential energy. D. chemical energy. E. thermal energy. Slide 10-11
Forms of Energy Mechanical Energy K U g U s Thermal Energy Other forms include E th E chem E nuclear Slide 10-12
The Basic Energy Model Slide 10-13
Energy Transformations Kinetic energy K = energy of motion Potential energy U = energy of position Thermal energy E th = energy associated with temperature System energy E = K + U + E th + E chem +... Within the System, all interactions are internal Energy can be transformed within the system without loss. Energy is a property of a system. Slide 10-14
Some Energy Transformations E chem U g K E th E chem E th U s K U g Here s another example Slide 10-15
Checking Understanding A skier is moving down a slope at a constant speed. What energy transformation is taking place? A. K U g B. U g E th C. U s U g D. U g K E. K E th Slide 10-16
Answer A skier is moving down a slope at a constant speed. What energy transformation is taking place? A. K U g B. U g E th C. U s U g D. U g K E. K E th Slide 10-17
Checking Understanding A child is on a playground swing, motionless at the highest point of his arc. As he swings back down to the lowest point of his motion, what energy transformation is taking place? A. K U g B. U g E th C. U s U g D. U g K E. K E th Slide 10-18
Answer A child is on a playground swing, motionless at the highest point of his arc. As he swings back down to the lowest point of his motion, what energy transformation is taking place? A. K U g B. U g E th C. U s U g D. U g K E. K E th Slide 10-19
Energy Transfers These change the energy of the system through interactions with the environment. Work is the mechanical transfer of energy to or from a system via pushes and pulls. A few things to note: Work can be positive (work in) or negative (work out) We are, for now, ignoring heat we will deal with it in Chapter 11 Thermal energy is special. When energy changes to thermal energy, the change is irreversible. Slide 10-20
Energy Transfers: Work W K W E th W U s Slide 10-21
The Work-Energy Equation mechanical energy = K + U g + U s ΔK + ΔU g + ΔU s = W K f K i + U g f U g i + U s f U s i = W K f + U g f + U s f = W + K i + U g i + U g i Slide 10-22
The Law of Conservation of Energy Slide 10-23
Conservation of Mechanical Energy ΔK + ΔU g + ΔU s = 0 K f K i + U g f U g i + U s f U s i = 0 K f + U g f + U s f = K i + U g i + U s i However Remember that conservation of energy applies to all forms Slide 10-24
Conceptual Example Problem A car sits at rest at the top of a hill. A small push sends it rolling down a hill. After its height has dropped by 5.0 m, it is moving at a good clip. Write down the equation for conservation of energy, noting the choice of system, the initial and final states, and what energy transformation has taken place. Slide 10-25
Conceptual Example Problem A car sits at rest at the top of a hill. A small push sends it rolling down a hill. After its height has dropped by 5.0 m, it is moving at a good clip. Write down the equation for conservation of energy, noting the choice of system, the initial and final states, and what energy transformation has taken place. Slide 10-25
Checking Understanding Three balls are thrown off a cliff with the same speed, but in different directions. Which ball has the greatest speed just before it hits the ground? A. Ball A B. Ball B C. Ball C D. All balls have the same speed Slide 10-26
Answer Three balls are thrown off a cliff with the same speed, but in different directions. Which ball has the greatest speed just before it hits the ground? A. Ball A B. Ball B C. Ball C D. All balls have the same speed Slide 10-27
Answer Three balls are thrown off a cliff with the same speed, but in different directions. Which ball has the greatest speed just before it hits the ground? The balls have the same speed because they start from the same height with the same K i. As each of them falls from that height, it adds an additional amount of kinetic energy equal to the U g i (relative to the ground) it had to begin with, so that the kinetic energy just before it hits is K f = K i + U g i. (If they had been dropped from rest they would have gained the same additional amount of kinetic energy.) Ball C is a little different. It rises to a height higher than the top of the cliff as its K i is transformed to additional U g : K i ΔU g. Then it falls, converting ΔU g K i by the time it reaches the height of the cliff. After that it falls just like the other two balls. Slide 10-27
Quantifying Work Slide 10-28
Work Done by Force at an Angle to Displacement Slide 10-29
Energy Equations Consider the work done by wind on the sailboard: W = ΔK = K f K i v f 2 = v i 2 + 2ad W = Fd = mad ad = W m 2 m W = v f 2 2 v i W = 1 2 mv f 2 1 2 mv i 2 Slide 10-30
Energy Equations Consider a point particle in a rotating object: It has a kinetic energy given by K = 1 2 mv2 = 1 m rω 2 2 Sum up the K for all the point particles in the object to get the rotational kinetic energy: K rot = 1 2 m 1r 2 1 ω 2 + 1 2 m 2r 2 2 ω 2 + = 1 2 mr2 ω 2 Slide 10-30
Energy Equations Consider an object being lifted: Work is being done against gravity: W = ΔU g = U gf U gi FΔy = U gf U gi mgδy = U gf U gi mgy f mgy i = U gf U gi Slide 10-30
Energy Equations Consider a spring being compressed (or stretched): W = ΔU s = U s x 0 Fx = U s (x) The problem here is that F is not constant, so use average: F avg = F i + F f 2 = 0 + kx 2 = 1 2 kx F avg x = 1 2 kx x = U s(x) Slide 10-30
Checking Understanding Each of the boxes, with masses noted, is pulled for 10 m across a level, frictionless floor by the noted force. Which box experiences the largest change in kinetic energy? Slide 10-31
Answer Each of the boxes, with masses noted, is pulled for 10 m across a level, frictionless floor by the noted force. Which box experiences the largest change in kinetic energy? D. Slide 10-32
Checking Understanding Each of the boxes, with masses noted, is pulled for 10 m across a level, frictionless floor by the noted force. Which box experiences the smallest change in kinetic energy? Slide 10-33
Answer Each of the boxes, with masses noted, is pulled for 10 m across a level, frictionless floor by the noted force. Which box experiences the smallest change in kinetic energy? C. Slide 10-34
Checking Understanding Each of the boxes, with masses noted, is pulled for 10 m across a level, frictionless floor by the noted force. Which box experiences the largest change in speed? Slide 10-33
Answer Each of the boxes, with masses noted, is pulled for 10 m across a level, frictionless floor by the noted force. Which box experiences the largest change in speed? C. Slide 10-34
Example Problem A 200 g block on a frictionless surface is pushed against a spring with spring constant 500 N/m, compressing the spring by 2.0 cm. When the block is released, at what speed does it shoot away from the spring? K f = (U s ) i 1 2 mv2 = 1 2 k Δx 2 mv 2 = k Δx 2 v 2 = k Δx 2 m v = k Δx 2 m = 500 N/m 0.020 m 2 0.200 kg = 1.0 m/s Slide 10-35
Example Problem A 2.0 g desert locust can achieve a takeoff speed of 3.6 m/s (comparable to the best human jumpers) by using energy stored in an internal spring near the knee joint. A. When the locust jumps, what energy transformation takes place? B. What is the minimum amount of energy stored in the internal spring? C. If the locust were to make a vertical leap, how high could it jump? Ignore air resistance and use conservation of energy concepts to solve this problem. D. If 50% of the initial kinetic energy is transformed to thermal energy because of air resistance, how high will the locust jump? Slide 10-36
Example Problem A. The initial energy transformation is U s K B. There must be at least as much elastic energy in the spring as the bug s kinetic energy moving at takeoff speed: U s min = K takeoff U s min = 1 2 2.0 10 3 kg 3.6 m/s 2 U s min = 1.3 10 2 J C. In a vertical leap the locust s takeoff K at the bottom would transform to U g at the top: A 2.0 g desert locust can achieve a takeoff speed of 3.6 m/s (comparable to the best human jumpers) by using energy stored in an internal spring near the knee joint. A. When the locust jumps, what energy transformation takes place? B. What is the minimum amount of energy stored in the internal spring? C. If the locust were to make a vertical leap, how high could it jump? Ignore air resistance and use conservation of energy concepts to solve this problem. D. If 50% of the initial kinetic energy is transformed to thermal energy because of air resistance, how high will the locust jump? Δy = U g f = K takeoff mgδy = 1.3 10 2 J 1.3 10 2 J 2.0 10 3 kg 9.8 m/s 2 = 0.66 m D. If 50% of K takeoff is lost to air resistance: U g f = 0.50K takeoff mgδy = 0.65 10 2 J Δy = 0.33 m Slide 10-36
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Elastic Collisions Using conservation of momentum and conservation of energy you get: Slide 10-38
Power Slide 10-39
Power Same mass... Both reach 60 mph... Same final kinetic energy, but different times mean different powers. Slide 10-40
Checking Understanding Five toy cars accelerate from rest to their top speed in a certain amount of time. The masses of the cars, the final speeds, and the time to reach this speed are noted in the table. Which car has the greatest power? Car Mass (g) Speed (m/s) Time (s) A 100 3 2 B 200 2 2 C 200 2 3 D 300 2 3 E 300 1 4 Slide 10-41
Answer Five toy cars accelerate from rest to their top speed in a certain amount of time. The masses of the cars, the final speeds, and the time to reach this speed are noted in the table. Which car has the greatest power? Car Mass (g) Speed (m/s) Time (s) A 100 3 2 B 200 2 2 C 200 2 3 D 300 2 3 E 300 1 4 Slide 10-42
Checking Understanding Five toy cars accelerate from rest to their top speed in a certain amount of time. The masses of the cars, the final speeds, and the time to reach this speed are noted in the table. Which car has the smallest power? Car Mass (g) Speed (m/s) Time (s) A 100 3 2 B 200 2 2 C 200 2 3 D 300 2 3 E 300 1 4 Slide 10-43
Answer Four toy cars accelerate from rest to their top speed in a certain amount of time. The masses of the cars, the final speeds, and the time to reach this speed are noted in the table. Which car has the smallest power? Car Mass (g) Speed (m/s) Time (s) A 100 3 2 B 200 2 2 C 200 2 3 D 300 2 3 E 300 1 4 Slide 10-44
Example Problem In a typical tee shot, a golf ball is hit by the 300 g head of a club moving at a speed of 40 m/s. The collision with the ball happens so fast that the collision can be treated as the collision of a 300 g mass with a stationary ball the shaft of the club and the golfer can be ignored. The 46 g ball takes off with a speed of 70 m/s. A. What is the change in momentum of the ball? B. What is the speed of the club head immediately after the collision? C. What fraction of the club s kinetic energy is transferred to the ball? D. What fraction of the club s kinetic energy is lost to thermal energy? Slide 10-45
Example Problem In a typical tee shot, a golf ball is hit by the 300 g head of a club moving at a speed of 40 m/s. The collision with the ball happens so fast that the collision can be treated as the collision of a 300 g mass with a stationary ball the shaft of the club and the golfer can be ignored. The 46 g ball takes off with a speed of 70 m/s. A. What is the change in momentum of the ball? B. What is the speed of the club head immediately after the collision? C. What fraction of the club s kinetic energy is transferred to the ball? D. What fraction of the club s kinetic energy is lost to thermal energy? (A) Change in momentum of ball: Δp b = 0.046 kg 70 m = 3.2 kg m s s (B) Conservation of momentum gives: (C) Δp b = mv bf 0 = mv bf m c v cf + m b v bf = m c v ci m c v cf = m c v ci m b v bf v cf = m cv ci m b v bf m c v cf = 0.300 kg 40 m 0.046 kg s 0.300 kg 1 K bf = 2 m 2 bv bf K ci 1 2 m 2 cv ci 70 m s = m 2 bv bf 2 m c v = 0.046 kg 70 m s ci 0.300 kg 40 m s = 29 m s (D) The amount of K lost as E th is the difference between the club s initial K i and the total K f of club and ball: 1 K i K f = 2 m cv ci K i 2 1 2 m cv 2 cf 1 2 m 2 bv bf = 1 2 m 2 cv ci 240 J 126 J 113 J 240 J 2 2 = 0.47 = 0.0048 Slide 10-45
Example Problem A typical human head has a mass of 5.0 kg. If the head is moving at some speed and strikes a fixed surface, it will come to rest. A helmet can help protect against injury; the foam in the helmet allows the head to come to rest over a longer distance, reducing the force on the head. The foam in helmets is generally designed to fail at a certain large force below the threshold of damage to the head. If this force is exceeded, the foam begins to compress. If the foam in a helmet compresses by 1.5 cm under a force of 2500 N (below the threshold for damage to the head), what is the maximum speed the head could have on impact without compressing the foam? Use energy concepts to solve this problem. Slide 10-46
Example Problem A typical human head has a mass of 5.0 kg. If the head is moving at some speed and strikes a fixed surface, it will come to rest. A helmet can help protect against injury; the foam in the helmet allows the head to come to rest over a longer distance, reducing the force on the head. The foam in helmets is generally designed to fail at a certain large force below the threshold of damage to the head. If this force is exceeded, the foam begins to compress. If the foam in a helmet compresses by 1.5 cm under a force of 2500 N (below the threshold for damage to the head), what is the maximum speed the head could have on impact without compressing the foam? Use energy concepts to solve this problem. Slide 10-46
Example Problem Data for one stage of the 2004 Tour de France show that Lance Armstrong s average speed was 15 m/s, and that keeping Lance and his bike moving at this zippy pace required a power of 450 W. A. What was the average forward force keeping Lance and his bike moving forward? B. To put this in perspective, compute what mass would have this weight. Slide 10-47
Summary Slide 10-48
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Additional Questions Trucks with the noted masses moving at the noted speeds crash into barriers that bring them to rest with a constant force. Which truck compresses the barrier by the largest distance? Slide 10-54
Answer Trucks with the noted masses moving at the noted speeds crash into barriers that bring them to rest with a constant force. Which truck compresses the barrier by the largest distance? E. Slide 10-55
Additional Questions Trucks with the noted masses moving at the noted speeds crash into barriers that bring them to rest with a constant force. Which truck compresses the barrier by the smallest distance? Slide 10-56
Answer Trucks with the noted masses moving at the noted speeds crash into barriers that bring them to rest with a constant force. Which truck compresses the barrier by the smallest distance? B. Slide 10-57
Additional Questions A 20-cm-long spring is attached to a wall. When pulled horizontally with a force of 100 N, the spring stretches to a length of 22 cm. What is the value of the spring constant? A. 5000 N/m B. 500 N/m C. 454 N/m Slide 10-58
Answer A 20-cm-long spring is attached to a wall. When pulled horizontally with a force of 100 N, the spring stretches to a length of 22 cm. What is the value of the spring constant? A. 5000 N/m B. 500 N/m C. 454 N/m Slide 10-59
Additional Questions I swing a ball around my head at constant speed in a circle with circumference 3 m. What is the work done on the ball by the 10 N tension force in the string during one revolution of the ball? A. 30 J B. 20 J C. 10 J D. 0 J Slide 10-60
Answer I swing a ball around my head at constant speed in a circle with circumference 3 m. What is the work done on the ball by the 10 N tension force in the string during one revolution of the ball? A. 30 J B. 20 J C. 10 J D. 0 J Slide 10-61