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(PHYS111)[1998](f)midterm~=tkk933^_24086.pdf
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Physics 111
1st Midterm, 8 October, 1998

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

1. A ball is thrown with an initial velocity of 20 ms-1 and makes an angle of 30o with the horizontal. Besides gravitational acceleration, it is subject to wind forces which cause a horizontal acceleration of 2 ms-2 in the reverse direction.

(a) What are the times taken by the ball to reach a vertical height of 3 m?

(b) What is the magnitude and direction of the velocity 0.5 seconds after the ball is thrown?

(c) What is the time of flight when the ball hits the ground again?

(d) What is the horizontal range? [20]



2. As shown in the figure, two blocks each of mass m = 10 kg are placed on inclined planes which make angles of .1 = 30o and .2 = 45o with the horizontal respectively. They are connected by a taut, massless cord around a frictionless, massless pulley. The coefficient of kinetic friction between the sliding blocks and the inclined plane is .k = 0.1.
(a) What is the acceleration of the blocks?

(b) What is the tension in the connecting cord?

(c) After the blocks start from rest for a displacement of 1 m, what is their speed?

(d) What is the work done by friction for this displacement? [20]



3. As shown in the figure, a ball of mass m = 1 kg is placed at the top of a smooth hemisphere of radius r = 0.3 m and is released from rest.

(a) What is the kinetic energy of the ball when it makes an angle . with the vertical?

(b) What is the normal reaction between the ball and the hemisphere at this position?

(c) What is the angle . when the ball begins to lose contact with the hemisphere?

(d) If the hemisphere is not smooth, and the coefficient of kinetic friction is .k = 0.2, what is the work done by friction after the ball has moved to an angle . with the vertical? [Hint: the friction changes with the angle . , and a small displacement is dx = r d..] [20]