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(PHYS111)[1999](f)midterm1~=tkk933^_14304.pdf
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Physics 111 1st Midterm, 7 October, 1999
Answer all questions. Take g = 9.8 ms-2 in your calculations. Answers should be given to 3 significant figures.
1. A rocket with mass m = 1000 kg is fired from the ground. The motor of the rocket creates a force of F = 3 . 104 N at a constant angle of 30o with the horizontal. Assume that the mass of the fuel consumed by the rocket is negligible, and that air resistance is negligible.
(a)
What is the magnitude and direction of the acceleration of the rocket?

(b)
What is the magnitude and direction of the velocity of the rocket after 30 s?

(c)
What is the vertical height of the rocket after 30 s?

(d)
What is the horizontal displacement of the rocket after 30 s? [20]


2. As shown in the figure, two blocks each of mass m = 10 kg are connected by a taut, massless cord around a frictionless, massless pulley. Block A is placed on a rough inclined plane which makes an angle of . = 30o with the horizontal. The coefficient of kinetic friction between block A and the inclined plane is .k = 0.3. Block B is hung vertically.
(a)
What is the acceleration of the blocks?

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

(c)
From the moment when the system starts from rest to the moment when block A acquires a velocity of v = 0.5 ms-1, how far has it dropped?

(d)
At the moment when block A acquires a velocity of v = 0.5 ms-1, what is the power due to the frictional force? [20]


3. 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 = 2R, the ball will lose contact with the loop before it reaches the top. What is the height that this takes place?

(d)
If h = 2R and the ball is pushed forward by an external force F = mg for a distance d along the track, what is the value of d so that the ball can just pass over the top of the loop? [20]