Chapter 7 Work and Kinetic Energy Work Done by a Constant Force Kinetic Energy and the Work-Energy Theorem Work Done by a Variable Force Power

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1 Chapter 7 Work and Kinetic Energy Work Done by a Constant Force Kinetic Energy and the Work-Energy Theorem Work Done by a Variable Force Power

2 7-1 Work Done by a Constant Force The definition of work, when the force is parallel to the displacement: SI unit: newton-meter (N m) = joule, J (7-1)

3 7-1 Work Done by a Constant Force If the force is at an angle to the displacement: (7-3)

4 7-1 Work Done by a Constant Force The work can also be written as the dot product of the force and the displacement:

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Picture the Problem: The boat and skier are both moving toward the left but the rope is pulling at an angle. Strategy: Solve equation 7-3 for the angle between the force and the direction of motion.

6 Picture the Problem: The boat and skier are both moving toward the left but the rope is pulling at an angle. Strategy: Solve equation 7-3 for the angle between the force and the direction of motion. Solution: 1. Solve eq. 7-3 for the angle: W Fdcos cos W Fd 2. Calculate the angle: W 3500 J cos cos 21 Fd 75 N 50 m 1 1 o Insight: Only the component of the force along the direction of the motion does any work. The work the boat does on the skier is balanced by the negative work friction does on the skier, so that the kinetic energy of the skier is constant. 6

7 7-1 Work Done by a Constant Force The work done may be positive, zero, or negative, depending on the angle between the force and the displacement:

8 7-1 Work Done by a Constant Force If there is more than one force acting on an object, we can find the work done by each force, and also the work done by the net force: (7-5)

9 7-2 Kinetic Energy and the Work-Energy Theorem When positive work is done on an object, its speed increases; when negative work is done, its speed decreases. Gravity is doing work on apple: positive W Speed of apple increases Gravity is doing work on apple: negative W Speed of apple increases

10 7-2 Kinetic Energy and the Work-Energy Theorem After algebraic manipulations of the equations of motion, we find: Therefore, we define the kinetic energy: (7-6)

11 7-2 Kinetic Energy and the Work-Energy Theorem Work-Energy Theorem: The total work done on an object is equal to its change in kinetic energy. (7-7)

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13 Picture the Problem: The paint can is lifted vertically. Strategy: Multiply the force by the distance because the two vectors point in the same direction in part (a). In part (b) the distance traveled is zero, and in part (c) the force and distance are antiparallel. mg 1.8 m Solution: 1. (a) Apply equation 7-1: W Fd mgd W kg 9.81 m/s 1.8 m 60 J 2. (b) Now the force and distance are perpendicular: W 0 3. (c) Now the force and distance are antiparallel: W mgd 60 J kj 13

14 7-3 Work Done by a Variable Force If the force is constant, we can interpret the work done graphically:

15 7-3 Work Done by a Variable Force The force needed to stretch a spring an amount x is F = kx. Therefore, the work done in stretching the spring is (7-8)

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17 7-3 Work Done by a Variable Force If the force takes on several successive constant values:

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19 This car stopped, i.e. lost all of its KE 18

20 This car stopped, i.e. lost all of its KE The KE was absorbed by the deforming metal, NO hard shove to my car, No wiplash for me. 18

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