Problem Solving Strategy involving Newton’s Laws 1. Visualize the problem

Draw diagrams, identify what are given and what you need to find. Read the question, and decide whether the objects of interest are in stable EQM or in

acceleration. Isolate the objects of interest, identify the forces acting ON each of them, draw

FREE-BODY diagram for each of them. Indicate the direction of acceleration of the objects (if any) beside the free-body diagram.

2. Describe the problem in physics terms (physics description)

Choose a suitable coordinate system, preferably with one axis having no acceleration, the other one having acceleration.

3. Plan a solution

Invoke Newton’s 2nd law for each axis. Plan how to reach the unknown.

4. Execute the plan

Translate the plan into a series of appropriate mathematical actions: Solve simultaneous equations Substitute specific values into the expression to obtain an arithmetic solution. Apply calculus to solve problems if necessary.

5. Check and evaluate – Check units and magnitude, and whether the answer makes sense. Things to take note for Free-Body Diagram and Forces: ALWAYS box up the object of interest. NEVER EVER include forces that are NOT acting directly on the object. NEVER EVER include both action/reaction pair on the same object. NEVER ASSUME the value of normal contact force unless you are 100% sure. Static friction, , does not always equal to , it takes values in the range 0 .

PC1431 Problem Set 2 Question 1 Alice and Bob stand on a platform of negligible weight as shown in Figure 1. Bob weighs 500 N and Alice weighs 400 N. Alice is supporting some of her weight on the end of the rope she is holding. What downward force is she exerting on the platform?

Figure 1

Question 2 Two blocks that are connected by a massless cord passing over a small, frictionless pulley, are placed at rest on frictionless planes as shown in Figure 2. The inclined plane is fixed to the ground.

Figure 2

(a) Find the acceleration of the system, , if the block is sliding down the incline. (b) Find the tension in the cord. (c) Can you do the same analysis if the pulley is not frictionless and not massless? If not,

what else do you need to consider?

Question 3

A block with mass m is being pushed by a constant force F that makes an angle of with the horizontal, as shown in Figure 3.

Figure 3

The coefficient of kinetic friction between the block and the surface is k . If the block moves

with constant velocity on a level surface, which one of the following equations gives the correct magnitude of F? Question 4 In Figure 4, a cable pulls a skier up a hill inclined at 10° above the horizontal. The skier starts from rest and the cable exerts a tension T at an angle 30° above the surface of the hill. The mass of the skier is 60 kg and the effective coefficient of friction between the skier and the snow is 0.10. What is the maximum tension in the cable if the starting acceleration (along the slope) does not exceed 0.40 ?

Figure 4

Question 5 A slab of mass 40.0kg rests on a frictionless floor, and a block of mass 10.0kg rests on top of the slab as shown in Figure 5. Between the block and the slab, the coefficient of static friction is 0.600, and the coefficient of kinetic friction is 0.400. The block is pulled

by a horizontal force . Find the resulting accelerations of the block and the slab when the magnitude of the horizontal force is (a) 100 N, and (b) 60 N.

Figure 5

Question 6 Four blocks are arranged on a smooth horizontal surface as shown in Figure 6.

Figure 6

The masses of the blocks are 0.40kg and 0.85kg. A light rope connects the two top blocks. The coefficient of static friction between the top and the bottom blocks is 0.35. What is the maximum value of the horizontal force F, applied to one of the bottom blocks as shown in Figure 6, that makes all four blocks move with the same acceleration? Question 7 In Figure 7, a block of mass 0.50kg is on a wedge of mass 2.00kg. The wedge is subjected to a horizontal force F and slides on a frictionless surface. The coefficient of static friction between the block and wedge is 0.600. Take 40.0°. Find the range of values of F for which the block does not slide on the incline.

Figure 7

Question 8 A particle of mass m moves in one dimension with a velocity subject only to a resistive

force (b is a constant). Let 2.0s and the initial speed be 100ms .

(a) Write down the equation of motion in terms of v and t. (b) Solve the equation and determine the distance moved at 2.5s. (Answer: 49.7m)