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(PHYS111)[2010](f)midterm~=tkk933^_39354.pdf
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Physics 111 (Fall 2010) Midterm
27 October, 2010
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) Yao Ming (height = 2.29 m!) is trying to shoot a basketball from the mid-court at a distance L = 13 m from the basket. As shown in the figure, the basket is H = 0.3 m above the level of his hands which shoot the ball. Suppose he shoots the ball with an initial velocity of v0 = 11.5 ms.1 at an angle . = 50o.
(a)
Calculate the time that the ball travels in the air.

(b)
When the ball hits the backboard, is it above or below the basket? Calculate the distance of the ball from the basket.

(c)
Calculate the magnitude and direction of the velocity of the ball when it hits the backboard.

(d)
The mass of a basketball is m = 0.624 kg. Ming shoots the ball in 0.1 s, that is, the time from starting to move the ball from stationary position to the time the ball leaves his hands is 0.1 s. Calculate the magnitude of the average force acting on the ball.


basket backboard

2) As shown in the figure, a ball of mass m = 0.1 kg is released at rest from a height h along the frictionless track. Part of the track is a loop of radius R = 0.3 m.
(a)
If h = 3R, what is the velocity of the ball at the top of the loop?

(b)
In (a), what is the normal reaction between the ball and the loop?

(c)
If h is set to a different value, the ball will lose contact with the loop when . = 60o. What is the value of h that this takes place?



Please turn over
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3) In an inelastic collision, a white ball of mass m and initial velocity u is incident on a stationary black ball of mass 3m along the x axis. During the collision, 1/8 of the kinetic energy of the white ball is converted to internal energy of the black ball. After the collision, the motion of the balls remains on the x axis, but the white ball has not penetrated the black ball.
(a)
Calculate the final velocity v1 of the white ball after the collision.

(b)
Calculate the final velocity v2 of the black ball after the collision.

4) As shown in the figure, a block of mass m = 0.8 kg is connected to a string that passes over a pulley of mass M = 1.2 kg and radius R = 0.1 m free to rotate on a horizontal axis. The string is then tied to a spring of spring constant k = 80 Nm.1 that has one end fixed. The block is released from rest with the spring relaxed.

(a)
Using the conservation of energy or otherwise, calculate the velocity of the block when it has fallen d = 0.1 m.

(b)
What maximum distance does the block fall before it stops momentarily?

(c)
Using Newtons second law or otherwise, calculate the magnitude and direction of


the acceleration of the block when it has fallen d = 0.1 m. Remark: The rotational inertia of the pulley about an axis perpendicular to the disk and through its centre is I = MR2/2.
k M

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