# The Pamphlet Collection of Sir Robert Stout: Volume 50

# University of New Zealand. — Examination for Matriculation, December, 1885. — Mechanics

## University of New Zealand.

## Examination for Matriculation, December, 1885.

## Mechanics.

1. Explain the terms *acceleration, foot-pound, specific gravity*. Distinguish between the *mass* of a body and its *weight*. Is a *pound* a unit of mass or of weight?

2. State the second law of motion.

A ferry-boat has to go straight across an estuary where the tide is running at the rate of 5 miles an hour. If the boat can steam 10 miles an hour, shew on a diagram the direction in which she should be steered.

3. If a body start from rest under the influence of a constant force, find the space described in a given time.

A body starting from rest is observed to pass over 162 feet in 6 seconds; what is the acceleration, supposed constant?

4. In what time will a falling body acquire the velocity of 20 miles an hour?

5. A 321b. cannon-ball is moving with a velocity of 1000 feet per second; find in foot-pounds the work it is capable of performing.

6. Define the *centre of gravity* of a body.

Two heavy particles, weighing respectively 4 and 9 ounces, are attached to the ends of a straight weightless rod 12 inches long; find the position of their centre of gravity.

7. What is meant by the *moment* of a force? How is its magnitude measured?

A uniform straight lever is 6 feet long and weighs 10lbs.

If weights of 20 and 301bs. be suspended from its extremities, find the position of the fulcrum on which it will balance.

8. Make a diagram of the system of pulleys in which each string is attached to the weight.

If there are three moveable pulleys find what power will sustain a weight of 2801bs.

9. Shew that if two liquids, that do not mix, meet in a bent tube open at both ends, the heights of their upper surfaces above their common surface will be inversely proportional to their densities.

10. A piece of metal weighs 120grs. in air and 105grs. when suspended in water; find its specific gravity.