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Phys011 / Fall 2005

Mid-term Examination (13 Oct 2005)

Answer ALL questions.

1. Three blocks are in contact with each other on a frictionless, horizontal surface, as shown on the right. A horizontal force F is applied to m1. If m1 = 2.00 kg, m2 = 3.00 kg, m3 = 4.00 kg, and F = 18.0 N, draw a separate free-body diagram for each block and find

(a) the acceleration of the blocks,
(b) the resultant force on each block, and
(c) the magnitudes of the contact forces between the blocks.
(d) You are working on a construction project. A coworker is nailing up plasterboard on one side of a light partition, and you are on the opposite side, providing backing by leaning against the wall with your back pushing on it. Every blow makes your back sting. The supervisor helps you to put a heavy block of wood between the wall and your back. Using the situation analyzed in parts (a), (b), and (c) as a model, explain how this works to make your job more comfortable.




2. (a) A 1.0 kg block moves along the x-axis. It passes x = 0.0 with a velocity of 2.0 m/s. It is then subjected to the force shown in the graph.

(i) Find the work done when the block moves from x = 0.0 to x = 5.0 m.

(ii) Calculate the speed of the block at x = 5.0 m.




(b) Two blocks are accelerated up an incline of angle by a force F as shown. The force acts on the bottom larger block. The coefficient of static friction between the two blocks is , but there is no friction between larger block M and the incline. Draw a separate free-body diagram for each block and find the maximum value of F such that the smaller block will not slip.
What happens when is increased from 0 0to 900? Is your answer valid for = 900?






1

2

4

5

x/ m

0

2

-2

F/ N

M

m



F

3 (a) A 1500 kg car moving on a flat, horizontal road negotiates a curve. If the radius of curve is 50.0 m and the coefficient of static friction is 0.50, find the maximum speed the car can have and still make the turn successfully. Identify all the forces acting on the car and shown them in a free-body diagram.
(b) The car in (a) is now on a curved ramp of the same radius and banked at an angle to the horizontal. Show all the forces acting on the car in a free-body diagram. Find the angle of the ramp if the car does not have to rely on friction to round the curve without skidding.



(c) Now friction is also taken into account on the banked curve ramp, show all the forces acting on the car in a free-body diagram. Write down the equation of motion for the top speed of the car rounding the curve without skidding. Without solving the equation, comment on the top speed in this case. How can you be sure that your equation is correct?
(d) You are sitting in contact with right-hand door of the car in (c) making a left turn. Which of the following is correct about horizontal forces act