1. Is the force of friction doing work?

2. Walking on pavement

3. Is the force of friction doing work? 15 20 The packages stay on the sled by means of static friction.

4. Work with scalar product - example Children slide a basket of toys with a mass of 10.0 kg from rest down a straight rope. The rope starts in a height of 4.00 m at a second-story window, and leads 8.00 m away from the house. – Write the force of gravity in form of (x,y) components. – Write the displacement vector s in form of (x,y) components. – Use the scalar product in order to calculate the work done by gravity. – The rope is providing a normal force in order to guide the bucket down the rope. How much work is the normal force doing?

5. 3 - variable force parallel to displacement F x x F dx F Need to know F(x)

6. Example for variable force The force of a spring is proportional to the distance at which the spring has been stretched or compressed away from equilibrium. We can phrase this observation as F= - kx, in which x is the distance from the equilibrium position, the constant k denotes the spring constant, and the minus sign indicates the fact that the force of the spring will always be directed back toward equilibrium. Determine the amount of work done by the spring, if it has a spring constant of 30 N/m if the spring has been stretched by 20 cm. 0 x F x F

7. D Variable force and variable angle 1 2 Line integral Need to know: -path -force as function of position

8. For which path does gravity do the most work? Path 1 Path 2 Path 3

9. Reading Assignment 6.2: Which of the following is the kinetic energy- work theorem? A B C D

10. Kinetic energy and Work 1. Several forces can act on an object at the same time. A crate sliding down an incline:

11. Kinetic energy and Work 1. Several forces can act on an object at the same time. A crate sliding down an incline: Net force: 2. The net force is the sum of these forces.

12. Kinetic energy and Work 1. Several forces can act on an object at the same time. A crate sliding down an incline: 2. The net force is the sum of these forces. Acceleration: X direction: Y direction: 3. Any net force results in acceleration.

13. Kinetic energy and Work 1. Several forces can act on an object at the same time. A crate sliding down an incline: 2. The net force is the sum of these forces. Work: 3. Any net force results in acceleration. 4. Any single force does work.

14. Kinetic energy and Work 1. Several forces can act on an object at the same time. A crate sliding down an incline: 2. The net force is the sum of these forces. Net Work: 3. Any net force results in acceleration. 4. Any single force does work. 5. The net work is the work done by the net force. Ok!

15. Kinetic energy and Work 1. Several forces can act on an object at the same time. A crate sliding down an incline: 2. The net force is the sum of these forces. Net Work and net force: 3. Any net force results in acceleration. 4. Any single force does work. 5. The net work is the work done by the net force. Net force in direction of motion: 6. Net work is also related to a change in motion.

16. Kinetic energy and Work 1. Several forces can act on an object at the same time. A crate sliding down an incline: 2. The net force is the sum of these forces. 4. Any single force does work. 5. The net work is the work done by the net force. 6. Net work is also related to a change in motion. Distance: Acceleration: Work it out. 7. The net work is equal to the change in kinetic energy. 3. Any net force results in acceleration.

17. Kinetic energy – work theorem Positive net work?Kinetic energy increases. negative net work?Kinetic energy decreases. Zero net work?Constant speed.

18. A 90.0-kg biker (bike and person) approaches a 10-% hill at a speed of 10.0 m/s. After 60.0 m uphill, his speed is 4.00 m/s. Neglect friction. a)Work of gravity? b)Work of biker? c)Average driving force of the biker?

19. A 50.0-kg child drops off a ladder onto a thick spring mattress. The top of the ladder is 2.50 m above the surface of the mattress. If the mattress springs have an effective force constant of 50 kN/m, what is the maximum depression of the mattress?

20. A particle starts from rest at x = 0 and moves to x = L under the action of a variable force F(x), which is shown in the figure. What is the particle's kinetic energy at x=L/2 and at x=L? a) Fmax L/2, FmaxL b) Fmax L/4, 0 c) Fmax L, 0 d) Fmax L/4, Fmax L/2 e) Fmax L/2, Fmax L/4

21. Two marbles, one twice as heavy as the other, are dropped to the ground from the roof of a building. Just before hitting the ground, the heavier marble has 1.as much kinetic energy as the lighter one. 2.twice as much kinetic energy as the lighter one. 3.half as much kinetic energy as the lighter one. 4.four times as much kinetic energy as the lighter one. 5.impossible to determine