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(PHYS111)[2009](sum)midterm~id-^_10539.pdf
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Physics 111 (Fall 2009) Midterm
28 October, 2009
Total: 60 marks, Time allowed: 75 minutes

Answer all questions. Take g = 9.8 ms.2 in your calculations. Answers should be given to 3 significant figures.

1) A car of mass M = 1500 kg is driven on a vertically curved section of a bridge, which can be approximated by a circle of radius R = 100 m.
(a) Calculate the normal reaction of the bridge on the car at the top of the bridge when its speed is 20 ms.1.
(b) Calculate the speed of the car if it loses contact with the bridge at the top of the bridge.
(c) When the speed of the car is 30 ms.1 on its way down the bridge, the car loses contact with the bridge when it is inclined at an angle with the horizontal direction. Calculate .


2) A small block of mass m = 1.5 kg is initially stationary at position A. It starts to slide down a rough slope of inclination = 45o. After sliding through a distance of a = 10 m, the block reaches the position B, where the slope changes inclination to = 15o. The block continues to slide through a distance b and reaches position C, where it comes to rest. The coefficient of kinetic friction between the block and both slopes is k = 0.4.
(a) Calculate the distance b.
(b) Calculate the work done against friction from A to C.
(c) Calculate the kinetic energy at position B.

Please turn over
A

3) A ball of mass m1 = 0.2 kg moves in the positive direction of an x axis at speed u1 = 3 ms.1. It collides with a stationary ball of mass m2 = 0.1 kg. After the collision the ball of mass m1 is deflected by an angle of = 30o. The ball of mass m2 moves at an angle of = 60o.
(a) Calculate the final velocity v2 of the target ball after the collision.
(b) Calculate the change in kinetic energy during the collision.
(c) If the time of contact between the two balls is 0.01 s, calculate the magnitude of the average force acting on the target ball from the incident ball.


4) A disk of mass M = 12 kg and radius R = 0.2 m is free to rotate on a horizontal axis. A string is fastened to the surface of the disk and a block of mass m = 6 kg hangs from the other end. An agent applies a force F = 33 N at right angle to a crank of length L = 0.4 m. The crank drives the disk to rotate in an anticlockwise direction, and the mass is lifted up. The rotational inertia of a disk about its center is I = MR2/2.
(a) Calculate the acceleration of the mass.
(b) Calculate the tension of the string.
(c) Calculate the time taken by the disk to rotate one cycle after it has started from rest.


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