# FIRST YEAR EXAMINATION in MECHANICS

A.A.E.   (F)   (48)
CRANWELL (1)
3

#### JANUARY, 1948

MECHANICS

Time allowed — Two hours

FIVE questions are to be attempted

1. State the conditions which must apply if a body is in equilibrium when three forces act on it.

A horizontal drawbridge, of span 12 ft., is hinged at one end and held by a chain at the other end. The chain makes an angle of 40° with the bridge and is also fixed to a wall at a point vertically above the bridge hinge. The centre of gravity of the bridge is 4 ft. from the hinge. If the bridge weighs 2 tons, find (by drawing or calculation) the tension in the chain and the hinge reaction.

2. A body of mass 50 lb. is held at rest on a smooth plane by a rope, which makes an angle of 15° above the plane. If the plane is inclined at an angle of 30° to the horizontal, find (by drawing or calculation) the tension in the rope and the reaction of the plane.

3. State Newton's Second Law of Motion.

A body of mass 50 lb. is moved over a rough horizontal surface with in acceleration of 5 ft. per sec.² by a force of 18½ lb. wt. Find the coefficient of friction between the body and surface under these conditions. Take g = 32 ft. per sec.²

4. A body starts from rest and, accelerating uniformly, in 3 sec. travels 36 ft. It is then brought to rest again in 12 ft. by a constant force. If the body has a mass of 20 lb., find the stopping force.

5. What is meant by the power of a machine ?

A press makes 100 working strokes per minute. The length of each stroke is 2 in. and the average force exerted during each stroke is 1,200 lb. wt. The press is driven by an electric motor and the overall efficiency of the system is 60 per cent. Find the power consumed by the motor (in kilowatts) if l h.p. = 746 watts.

6. Distinguish between:—
 (a) Mass and weight. (b) Kinetic energy and potential energy.

A bullet, of mass ½ oz., moving at 1,000 ft. per sec., penetrates a plank ½ in. thick, and in so doing, has its velocity reduced to 200 ft. per sec. Find the average value of the resistive force due to the wood.

7. A projectile is fired at an angle of 45° to the horizontal with an initial velocity of
800(SQR 2) ft. per sec. Find after what intervals of time it will lie 9,600 ft. above it's point of projection, and its distances horizontally in front of its point of projection at these times.