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Copyright © 2012 Pearson Education Inc. Work and Energy Physics 7C lecture 06 Thursday October 17, 8:00 AM – 9:20 AM Engineering Hall 1200

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Copyright © 2012 Pearson Education Inc. Introduction The simple methods we’ve learned using Newton’s laws are inadequate when the forces are not constant. In this chapter, the introduction of the new concepts of work, energy, and the conservation of energy will allow us to deal with such problems.

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Copyright © 2012 Pearson Education Inc. Work A force on a body does work if the body undergoes a displacement. Figures 6.1 and 6.2 illustrate forces doing work.

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Copyright © 2012 Pearson Education Inc. Work done by a constant force The work done by a constant force acting at an angle to the displacement is W = Fs cos . Figure 6.3 illustrates this point. Follow Example 6.1.

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Copyright © 2012 Pearson Education Inc. Positive, negative, and zero work A force can do positive, negative, or zero work depending on the angle between the force and the displacement. Refer to Figure 6.4.

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© 2012 Pearson Education, Inc. Q6.1 A. The cable does positive work on the elevator, and the elevator does positive work on the cable. v Motor Cable Elevator An elevator is being lifted at a constant speed by a steel cable attached to an electric motor. Which statement is correct? B. The cable does positive work on the elevator, and the elevator does negative work on the cable. C. The cable does negative work on the elevator, and the elevator does positive work on the cable. D. The cable does negative work on the elevator, and the elevator does negative work on the cable.

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© 2012 Pearson Education, Inc. A6.1 A. The cable does positive work on the elevator, and the elevator does positive work on the cable. An elevator is being lifted at a constant speed by a steel cable attached to an electric motor. Which statement is correct? B. The cable does positive work on the elevator, and the elevator does negative work on the cable. C. The cable does negative work on the elevator, and the elevator does positive work on the cable. D. The cable does negative work on the elevator, and the elevator does negative work on the cable. v Motor Cable Elevator

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© 2012 Pearson Education, Inc. Q6.2 A. The cable does positive work on the elevator, and the elevator does positive work on the cable. v Motor Cable Elevator An elevator is being lowered at a constant speed by a steel cable attached to an electric motor. Which statement is correct? B. The cable does positive work on the elevator, and the elevator does negative work on the cable. C. The cable does negative work on the elevator, and the elevator does positive work on the cable. D. The cable does negative work on the elevator, and the elevator does negative work on the cable.

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© 2012 Pearson Education, Inc. A6.2 A. The cable does positive work on the elevator, and the elevator does positive work on the cable. An elevator is being lowered at a constant speed by a steel cable attached to an electric motor. Which statement is correct? B. The cable does positive work on the elevator, and the elevator does negative work on the cable. C. The cable does negative work on the elevator, and the elevator does positive work on the cable. D. The cable does negative work on the elevator, and the elevator does negative work on the cable. v Motor Cable Elevator

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Copyright © 2012 Pearson Education Inc. Work done by several forces W = W traction + W friction or W = (T x + f x ). x

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© 2012 Pearson Education, Inc. A tractor driving at a constant speed pulls a sled loaded with firewood. There is friction between the sled and the road. A. positive. B. negative. C. zero. D. not enough information given to decide Q6.4 The total work done on the sled after it has moved a distance d is

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© 2012 Pearson Education, Inc. A tractor driving at a constant speed pulls a sled loaded with firewood. There is friction between the sled and the road. A. positive. B. negative. C. zero. D. not enough information given to decide A6.4 The total work done on the sled after it has moved a distance d is

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Copyright © 2012 Pearson Education Inc. Kinetic energy The kinetic energy of a particle is K = 1/2 mv 2. The net work on a body changes its speed and therefore its kinetic energy, as shown in Figure 6.8 below.

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Copyright © 2012 Pearson Education Inc. The work-energy theorem The work-energy theorem: The work done by the net force on a particle equals the change in the particle’s kinetic energy. Mathematically, the work-energy theorem is expressed as W tot = K 2 – K 1 = K.

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© 2012 Pearson Education, Inc. A nonzero net force acts on an object. Which of the following quantities could be constant? A. the object ’ s kinetic energy B. the object ’ s velocity C. both of the above D. none of the above Q6.5

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© 2012 Pearson Education, Inc. A nonzero net force acts on an object. Which of the following quantities could be constant? A6.5 A. the object ’ s kinetic energy B. the object ’ s velocity C. both of the above D. none of the above

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Copyright © 2012 Pearson Education Inc. The work-energy theorem W tot = K 2 – K 1 = K. Proof: F = m dV/dt anddx = V dt multiply: F dx = m V dV = d(½ m V 2 ) = d K Since: d W = F dx we have: d W = d K or W = K2 – K1

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Copyright © 2012 Pearson Education Inc. Using work and energy to calculate speed with 1 N push, what is V2?

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© 2012 Pearson Education, Inc. Three blocks are connected as shown. The ropes and pulleys are of negligible mass. When released, block C moves downward, block B moves up the ramp, and block A moves to the right. A. positive work on A, B, and C. B. zero work on A, positive work on B, and negative work on C. C. zero work on A, negative work on B, and positive work on C. D. none of these Q6.8 After each block has moved a distance d, the force of gravity has done

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© 2012 Pearson Education, Inc. Three blocks are connected as shown. The ropes and pulleys are of negligible mass. When released, block C moves downward, block B moves up the ramp, and block A moves to the right. A. positive work on A, B, and C. B. zero work on A, positive work on B, and negative work on C. C. zero work on A, negative work on B, and positive work on C. D. none of these A6.8 After each block has moved a distance d, the force of gravity has done

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Copyright © 2012 Pearson Education Inc. Work and energy with varying forces—Figure 6.16 Many forces, such as the force to stretch a spring, are not constant. In Figure 6.16, we approximate the work by dividing the total displacement into many small segments.

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Copyright © 2012 Pearson Education Inc. Stretching a spring The force required to stretch a spring a distance x is proportional to x: F x = kx. k is the force constant (or spring constant) of the spring. The area under the graph represents the work done on the spring to stretch it a distance X: W = 1/2 kX 2.

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Copyright © 2012 Pearson Education Inc. Motion with a varying force An air-track glider is attached to a spring, so the force on the glider is varying. For initial speed v1, how long can the spring extend?

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Copyright © 2012 Pearson Education Inc. Motion with a varying force For initial speed v1, how long can the spring extend? ½ m v1 2 = ½ k x 2

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Copyright © 2012 Pearson Education Inc. Motion with a varying force For initial speed v1, how long can the spring extend? ½ m v1 2 = ½ k x 2 + f k x

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Copyright © 2012 Pearson Education Inc. Motion on a curved path—Example 6.8 A child on a swing moves along a curved path. write down all the work(s)

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Copyright © 2012 Pearson Education Inc. Motion on a curved path—Example 6.8 gravity: mg R (1-cos θ) push: F R sin θ tension in the string: 0 (Why?)

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© 2012 Pearson Education, Inc. Q6.6 A 6.00-kg block and an 8.00-kg block are connected as shown. When released, the 6.00-kg block accelerates downward and the 8.00-kg block accelerates to the right. After each block has moved 2.00 cm, the force of gravity has done A. more work on the 8.00-kg block than on the 6.00-kg block. B. the same amount of work on both blocks. C. less work on the 8.00-kg block than on the 6.00-kg block. D. not enough information given to decide

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© 2012 Pearson Education, Inc. A 6.00-kg block and an 8.00-kg block are connected as shown. When released, the 6.00-kg block accelerates downward and the 8.00-kg block accelerates to the right. After each block has moved 2.00 cm, the force of gravity has done A. more work on the 8.00-kg block than on the 6.00-kg block. B. the same amount of work on both blocks. C. less work on the 8.00-kg block than on the 6.00-kg block. D. not enough information given to decide A6.6

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© 2012 Pearson Education, Inc. A 6.00-kg block and an 8.00-kg block are connected as shown. When released, the 6.00-kg block accelerates downward and the 8.00-kg block accelerates to the right. After each block has moved 2.00 cm, the total work done on the 8.00-kg block A. is greater than the total work done on the 6.00-kg block. B. is the same as the total work done on the 6.00-kg block. C. is less than the total work done on the 6.00-kg block. D. not enough information given to decide Q6.7

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© 2012 Pearson Education, Inc. A 6.00-kg block and an 8.00-kg block are connected as shown. When released, the 6.00-kg block accelerates downward and the 8.00-kg block accelerates to the right. After each block has moved 2.00 cm, the total work done on the 8.00-kg block A. is greater than the total work done on the 6.00-kg block. B. is the same as the total work done on the 6.00-kg block. C. is less than the total work done on the 6.00-kg block. D. not enough information given to decide A6.7

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Copyright © 2012 Pearson Education Inc. Power Power is the rate at which work is done. Average power is P av = W/ t and instantaneous power is P = dW/dt. The SI unit of power is the watt (1 W = 1 J/s), but other familiar units are the horsepower and the kilowatt-hour.

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© 2012 Pearson Education, Inc. An object is initially at rest. A net force (which always points in the same direction) is applied to the object so that the power of the net force is constant. As the object gains speed, A. the magnitude of the net force remains constant. B. the magnitude of the net force increases. C. the magnitude of the net force decreases. D. not enough information given to decide Q6.10

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© 2012 Pearson Education, Inc. An object is initially at rest. A net force (which always points in the same direction) is applied to the object so that the power of the net force is constant. As the object gains speed, A. the magnitude of the net force remains constant. B. the magnitude of the net force increases. C. the magnitude of the net force decreases. D. not enough information given to decide A6.10

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Copyright © 2012 Pearson Education Inc. Summary Calculate the work done by a force Kinetic energy: E k = ½ m v 2 work - energy theorem To relate work and kinetic energy when the forces are not constant or the body follows a curved path power P = dW/dt

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Copyright © 2012 Pearson Education Inc.

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