1 Review Newton’s 3 rd Law 6 Momentum 7 Energy Review Questions

2 Forces and Interactions inter = between all forces are interactions between masses each mass feels same size force Newton’s 3rd Law of Motion: Whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first.

3 5 Newton’s Third Law

4 What is the net force on the boxed system? Explain with a diagram.

5

6 Force Diagram each object. Which has greater acceleration when released?

7 Vectors magnitude and direction represented by arrows examples: force, velocity, and displacement vector addition is done tail-to-head horizontal part is the “x component” vertical part is the “y component” Pythagorean theorem applies to x and y components, i.e.

8 Example: Vector Sum of 1 and 1 is the square root of 2.

9 Example: A 30N force + 40N force could be replaced with a single 50N force.

10 The x-component of the 50N force is 40N. The y-component of the 50N force is 30N.

11 6 Momentum

12 Impulse-Momentum Momentum = mv SI Unit: kg·m/s impulse = Ft SI Unit: N·s = kg·m/s Ft =  (mv)

13 Conservation of Momentum Momentum of a System is constant when the net external force on it is zero. This law is usefully applied in many situations

14 Conservation of Momentum

15 Conservation of Momentum

16 Conservation of Momentum

17 Bouncing Motion Dead stop:  (mv)= 0 – mv = – mv Bouncing:  (mv) = –mv – mv = – 2mv bouncing object exerts/feels twice the impulse as a dead stop

18 Collisions any brief interaction between masses inelastic (heat, sound, etc. are generated) elastic (no heat, sound, etc. is created) deformation is an important aspect of collisions, e.g. ball being hit by club or bat

19 7 Energy

20 Work W = Fd (F parallel to d) W = 0 (F perpendicular to d) Work is change in energy Energy is the capacity to do work Energy can be positional or motional

21 Energy Positional Energy is called Potential Energy, e.g. stretched spring Motional Energy is called Kinetic Energy SI Units for Work and Energy: J = Nm = kgm 2 /s 2

22 Work-Energy Theorem Work =  (KE) Examples: Positional-Motional Bow and Arrow Mass and Spring Inclined Plane Motor and Car

23 Conservation of Energy Energy cannot be created or destroyed; it may be transformed (by work) from one form into another, but the total amount of energy never changes. Energy Forms include: thermal, elastic, chemical, electromagnetic, nuclear, kinetic.

24 Machine A device that changes an applied force by increasing it, decreasing it, or changes its direction. Examples of Machines: pulley, lever, jack, inclined plane.

25 Efficiency The percent of the work put into a machine that is converted into useful work output. efficiency = (work output)/(energy input)

26 Review Questions

N, N, or 3. Zero? In the situation shown the scale reads What is different here if you held the scale from the right side? If the scale were attached to a wall?

28 scale reads 100. Nothing is different N, N, or 3. Zero?

29 1. A. 2. B. 3. Both the same. Two identical rubber bands connect masses A and B to a string over a frictionless pulley of negligible mass. The pulley is free and the masses are accelerating. The amount of stretch is greater in the band that connects

30 1. A. 2. B. 3. Both the same. pulley is free to turn does not affect size of interaction between A and B light frictionless pulley is perfect machine for redirecting a force without changing its size therefore 3 rd Law applies:

31 1. A. 2. B. 3. Both the same. Two identical rubber bands connect masses A and B to a string over a frictionless pulley of negligible mass. The pulley is held and the masses are motionless. The amount of stretch is greater in the band that connects?

32 1. A. 2. B. 3. Both the same. The pulley is held and the masses are motionless. The amount of stretch is greater in the band that connects The string is now interacting individually with each side of the pulley – they are independently hanging and each side holds the entire weight of each object.

33 Whenever an interaction occurs in a system, forces occur in equal and opposite pairs. Which of the following do not always occur in equal and opposite pairs? 1. Impulses. 2. Accelerations. 3. Momentum changes. 4. All of these occur in equal and opposite pairs. 5. None of these do.

34 1. Impulses. 2. Accelerations. 3. Momentum changes. 4. All of these occur in equal and opposite pairs. 5. None of these do. Whenever an interaction occurs in a system, forces occur in equal and opposite pairs. Which of the following do not always occur in equal and opposite pairs?

35 In which car will you be moving the fastest at the very bottom of the incline? 1. Front car 2. Middle car 3. Rear car 4. Other

36 1. Front car 2. Middle car 3. Rear car 4. Other In which car will you be moving the fastest at the very bottom of the incline?

37 Two smooth tracks of equal length have “bumps”—A up, and B down, both of the same curvature. If two balls start simultaneously with the same initial speed, the ball to complete the journey first is along 1. Track A.2. Track B.3. Same

38 1. Track A.2. Track B.3. Same Two smooth tracks of equal length have “bumps”—A up, and B down, both of the same curvature. If two balls start simultaneously with the same initial speed, the ball to complete the journey first is along

39 Three baseballs are thrown from the top of the cliff along paths A, B, and C. If their initial speeds are the same and air resistance is negligible, the ball that strikes the ground below with the greatest speed will follow path 1. A.2. B.3. C.4. Either A or C. 5. All strike with the same speed.

40 1. A.2. B.3. C.4. Either A or C. 5. All strike with the same speed. Three baseballs are thrown from the top of the cliff along paths A, B, and C. If their initial speeds are the same and air resistance is negligible, the ball that strikes the ground below with the greatest speed will follow path