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(PHYS111)[2008](f)midterm~id-^_10538.pdf
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Physics 111 (Fall 2008) Midterm
31 October, 2008
Total: 75 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 fighter airplane releases a bomb when it is flying at h = 1 km above the ground with a velocity of v0 = 300 km/h. Its path is heading towards a target T at a downward angle of = 30o with the horizontal direction. Assume that air resistance is negligible.


(a)
What is the time taken by the bomb to reach the ground?


(b)
What are the direction and the magnitude of the velocity of the bomb when it reaches the ground?


(c)
What is the distance d between the target T and the landing point P of the bomb?






2.
A flat highway curve is banked at an angle of = 10o. The curve has a radius of R = 200 m. The coefficient of static friction between the road and the wheels of a car is s = 0.5.


(a)
What is the speed of the car when it does not require friction to prevent sliding?


(b)
What is the speed of the car when it is about to slide up the bank?








Please turn over

3.
Two blocks, of masses m1 = 0.8 kg and m2 = 1.2 kg, are connected to a spring of spring constant k = 80 Nm.1 that has one end fixed, as shown in the figure. Between the sliding block and the horizontal surface, the force of sliding friction is 2 N. The pulley has negligible mass and is frictionless. The blocks are released from rest with the spring relaxed.


(a)
What is the spring potential energy when the hanging block has fallen d = 0.1 m?


(b)
What is the combined kinetic energy of the blocks when the hanging block has fallen d?


(c)
What is the work done against friction when the hanging block has fallen d?


(d)
What is the power of the gravitational force on the system when the hanging block has fallen d?


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






4.
A thin uniform rod of mass M = 0.2 kg and length L = 0.8 m is freely hinged at a pivot point 0.3 m from the center. (The rotational inertia of a rod about its center is ML2/12.) A mud ball of mass m = 0.05 kg and velocity u = 6 ms.1 hits the rod 0.2 m below the center of the rod at an angle = 70o with the upward vertical direction. The mud ball sticks on the rod and both swing together about the hinge after the impact.


(a)
What is the rotational inertia of the rod about the pivot point?


(b)
What is the initial angular momentum of the mud ball about the pivot point?


(c)
What is the angular velocity of the rod and the mud ball immediately after the impact?


(d)
How much energy is lost during the impact?


(e)
What is the maximum angular displacement of the rod after the impact?






THE END