Review of Mechanics

1. Review of Mechanics

2. Force and Motion Newton’s 1st Law of Motion An object at rest remains at rest and an object in motion remains in a uniform motion in a straight line unless acted on by an unbalanced external force. If an object is in non-uniform motion and/or in a motion not in a straight line, then there must be an unbalanced external force acting on the object. If an object remains at rest or in a uniform motion in a straight line even when an external force is applied on that object, there must be an extra force acting on the object with equal strength and in the opposite direction

3. Ex Which of the following trajectories would the ball most closely follow after it is released at P during the circular motion on a frictionless table top? (4) (3) P (1) O (2)

4. FN f mg Ex A 1-kg block is resting on a p/6 inclined plain. What forces are acting on the block. Indicate all the forces acting on the block. How big is the friction? f = 4.9 N FN = 8.49 N 30

5. Ex A 5-kg mass is hanging on a string as shown in the figure. What are the magnitudes of the tensions on two strings, A and B? A B FA = 25.4 N FB = 35.9 N 60 45 5 kg

6. Newton’s 2nd Law of Motion The first law says that an unbalanced external force causes change in motion. Using the second law, you can quantitatively understand how its motion changes. Once you know acceleration, game over!

7. Ex Consider the following trajectory of an object. The velocity of the object at the given points P and Q are represented by two vectors. Which of the following vectors represent the direction of the average acceleration between two points? (1) (2) (3) (4) (5) need to know time Q P

8. Ex A 9-kg block is pulled with a 24 N force as shown in the figure. Katie found the block moving with an acceleration of 2.0 m/s2. From this observation, can you tell if there is friction between the block and the table surface? If there is, what is the Magnitude of the friction? If no friction, a = 2.67 m/s2. a = 2.0 m/s2 f = 6 N (opposite direction) 24 N

9. Ex A 5-kg block (1) rests on a frictionless table top. A cord attached to it is connected to a 1.28 kg mass (2) over a frictionless pulley. The system accelerates at x m/s2. Both mass 1 and 2 accelerate at the same rate. What external force causes the mass 1 accelerate? What forces cause the mass 2 accelerate? (1) Write down eq. of motion for 1 and 2 separately. Both 1 and 2 are moving together and should have the same accel. 1 x = 2.0 m/s2 2

10. Constant Speed Circular Motion acceleration (constant magnitude) toward the center of the circle centripetal acceleration (ac) F = mac: centripetal force ac = v2/r Fc = mv2/r

11. Newton’s 3rd Law of Motion Action and Reaction Whenever an object exerts a force on a second object, the second object exerts a force on the first one with the same strength but in the opposite direction Key to understand net external force!

12. Same color vectors are action-reaction pair. Pay attention to the acting points of these vectors. Assume that the ceiling and the posts have no mass.

13. Energy, Work, & Conservation Energy || Ability to Work For work to be done, (1) there must be an applied force (2) the force must act through a distance (displacement) (3) the force must have a component along the displacement.

14. W = (Fcosq)·S force component along the displacement Ex How much work is done by a 20 N force in pulling the block as shown in the figure a distance 10 m? W = 173 Nm = 173 J 20 N 30 10 m q: angle made by F and S

15. Ex Who did the most work? John pushed a 20 lb box horizontally with a 200 N force for 20 m. Julia pulled a 40 lb box horizontally with 200 N force for 20 m. Eddie lifted up a 100 lb box and walked horizontally for 20 m. Kathy pushed a 10 lb box horizontally with 150 N for 30 m. (1) John (2) Julia (3) Eddie (4) Kathy (5) I have to know how large the frictional force is.

16. F f S Energy || Ability to Work Conversely, if a force did work on an object, it added to the object an amount of energy equal to the work done!! F did positive work on the block  increased energy f did negative work on the block  decreased energy (dissipation)

17. Potential Energy Position or Condition MECHANICAL ENERGY Kinetic Energy Motion(mv2/2) Work-Energy Theorem The work of a net external force on an object is equal to the change in kinetic energy.

18. h2 h3 m P.E. = mgh1 h1 P.E. = mgh2 P.E. = mgh3 Only difference in P.E. is meaningful. However, one can set a reference point.

19. mg h Work done by mg = (mg) x h = mgh v = 0 height h m Change in kinetic energy = mgh = (K.E.)f – (K.E.)i = (1/2)mvf2 - 0 vf = (2gh)1/2

20. F 12 cm Ex What average force F is necessary to stop a 16-g bullet traveling at 260 m/s as it penetrates into a wood block for a distance of 12 cm? F = 4510 N (see fig. for direction)

21. F S f Q A block was pulled by applying a force F on a rough surface for a certain distance S. During this process the block was moving with a constant speed. Choose a wrong statement. (1) f = F (2) F did positive work on the block. (3) f did negative work on the block. (4) As a result, energy of the block has increased. (5) There is no change in kinetic energy.

22. 470 kg F = 5.6 x 10-2 N vf = ?? vi = 275 m/s S = 2.42 x 109 m Ex Space probe Deep Space I was launched on Oct 24, 1998. It uses a type of engine called an IPD (Ion Propulsion Drive) which can put out a thrust force 5.6 x 10-2 N. The probe (470 kg) started the engine when the speed was 275 m/s and has been propelled for 2.42 x 106 km so far. What is the speed of the probe now? vf = 804 m/s

23. Work, Energy, and Conservation We = DK.E. + DP.E. DP.E. = -Wc We: work done by any forces other than conservative force such as lifting force, friction, contact force,… Wc: work done by conservative forces such as electrostatic force, gravitational force