1. Work, Power, Energy and Motion Work, Power, Energy and Motion moving train cars moving electrons nuclear forces chemical forces gravitational force Electrical force

2. Work and Force Go Together Too Let work be defined as work = force × displacement

3. Work Done by a Constant Force In the SI system, the units of work are joules: A complication: As long as this person does not lift or lower the bag of groceries, he is doing no work on it. The force he exerts has no component in the direction of motion.

4. Work Done by a Constant Force The work done by a constant force is defined as the distance moved multiplied by the component of the force in the direction of displacement: W = Fx cos θ

5. Hooke’s Law Lab

6. Work on a spring Work can also be done on a spring when it is compressed or stretched; the figure below shows work yielding kinetic energy.

7. Work on a spring The force required to compress or stretch a spring is: where k is called the spring constant, and needs to be measured for each spring. W = ½ kx 2

8. Concept Question 1 Is it possible to do work on an object that remains at rest? 1) yes 2) no

9. Concept Question 1 If there is no displacement, there is no work done. If there is no displacement, there is no work done. Work requires that there be a force acting over a distance. Is it possible to do work on an object that remains at rest? 1) yes 2) no

10. Concept Question 2 A box is being pulled across a rough floor at a constant speed. What can you say about the work done by friction? 1) Friction does no work at all 2)Friction does negative work 3)Friction does positive work 4)Work is not defined for friction as friction acts on the floor and the box

11. Concept Question 2 A box is being pulled across a rough floor at a constant speed. What can you say about the work done by friction? 1) Friction does no work at all 2)Friction does negative work 3)Friction does positive work 4)Work is not defined for friction as friction acts on the floor and the box Work is defined for all forces. The friction acts opposite to the direction of displacement and is therefore negative here. f N mg displacement Pull

12. Concept Question 3 Can friction ever do positive work? 1) yes 2)no

13. Concept Question 3 Can friction ever do positive work? 1) yes 2)no Consider the book on your car seat. If you accelerate slowly the book does not slide on the seat but stays stationary with respect to the car. Friction is causing the book to move along with the car and hence force and displacement are in the same direction. Work is positive.

14. Concept Question A box is being pulled up a rough incline by a rope connected to a pulley. How many forces are doing work on the box? 1) one force 2)two forces 3)three forces 4)four forces 5)No forces are doing any work

15. Concept Question A box is being pulled up a rough incline by a rope connected to a pulley. How many forces are doing work on the box? 1) one force 2)two forces 3)three forces 4)four forces 5)No forces are doing any work no work positiveworknegative worknegative work Any force not perpendicular to the motion will do work: N does no work, T does positive work, f does negative work, mg does negative work

16. Power Power is the rate at which work is done. It can be thought of as work per second. Power = Work / sec. Power = Work / time P = W / t Question: Can you name 2 units for power?

17. Power Power has the same trade-offs as work. A motor produces the same amount of power. So, you can make a robot that’s fast, but weak. Or you can make a robot that’s slow, but strong. P = Fv The total power in must equal the total power out (with an exception)... Work / Power Worksheet

18. Kinetic Energy and the Work-Energy Principle Because work and kinetic energy can be equated, they must have the same units: kinetic energy is measured in joules.

19. Kinetic Energy, and the Work- Energy Principle Energy is defined as the ability to do work. Mechanical energy is the energy associated with motion, i.e. masses which move. Sometimes the motion is ongoing (non-zero velocity) and sometimes it just involves a change of position (motion occurred between time t 0 and t 1 ).

20. Kinetic Energy Defined: Let work be defined as work = force × displacement Kinetic energy must = work. How’s my deriving?

21. Kinetic Energy, and the Work- Energy Principle If we write the acceleration in terms of the velocity and the distance, we define that the work done here is We define the kinetic energy: (6-2) (6-3) The work-energy principle

22. Kinetic Energy, and the Work- Energy Principle We define the work done to be equal to the change in the kinetic energy: If the net work is positive, the kinetic energy increases. If the net work is negative, the kinetic energy decreases. CHAPTER 11 # 5, 17, 36, 38 & 41 Here’s why work and kinetic energy go together:

23. Concept Question Two stones, one twice the mass of the other, are dropped from a cliff. Just before hitting the ground, what is the kinetic energy of the heavy stone compared to the light one? 1) quarter as much 2) half as much 3) they are equal 4) twice as much 5) four times as much

24. Concept Question Two stones, one twice the mass of the other, are dropped from a cliff. Just before hitting the ground, what is the kinetic energy of the heavy stone compared to the light one? 1) quarter as much 2) half as much 3) they are equal 4) twice as much 5) four times as much Consider the work done by gravity to make the stone fall distance d: DKE = W net = F d cosθ DKE = mg d greater massgreater KE twice Thus, the stone with the greater mass has the greater KE, which is twice as big for the heavy stone.

25. Concept Question Is it possible for the kinetic energy of an object to be negative? 1) No. 2)Yes. 3) Maybe.

26. Concept Question Is it possible for the kinetic energy of an object to be negative? 1) No. 2)Yes. 3) Maybe. In Newtonian mechanics, the answer is no. The kinetic energy is always positive since the velocity squared and the mass are always positive. Curiously, in quantum mechanics and relativity there are no such constraints. We believe it to still be true, but we are open to the possibility that it may not.