# The Pamphlet Collection of Sir Robert Stout: Volume 50

# University of New Zealand. — Mathematics. — Paper c. Elementary Mechanics and Hydrostatics

## University of New Zealand.

## Mathematics.

##
Paper *c*. Elementary Mechanics and Hydrostatics.

1. Explain how a force may be resolved into two forces whose directions are specified. Also state and prove the triangle of forces.

A door, whose height is 12 feet and breadth 5, turns about two hinges, one at the foot and the other (which is a smooth vertical bolt passing through a horizontal ring) halfway up, the door-post being vertical, and the weight of the door 120 lbs. Draw the actions at the hinges, and prove that they are respectively 50 lbs. and 130 lbs.

2. Find the resultant of two unequal parallel forces.

Three weights, 2, 3, 4, are placed at three angles of a square; find where it must be suspended from a hook on one of the sides, that this side may be horizontal.

3. Find the condition that a body of any shape may rest when placed on a horizontal plane.

A triangle ABC, obtuse-angled at C, is placed with AB in contact with a horizontal plane, and CD is drawn perpendicular on AB produced; prove that equilibrium will be possible or impossible according as BD is less or greater than AB.

page 24. State the conditions to be observed in constructing a good balance. How is it possible to weigh accurately with an imperfect balance?

5. State the laws of motion, and examine briefly the evidence for them.

6. Explain the symbols *u*, *g*, in the equation of motion of a rising body *s*=*ut*—½*gt*^{2} and prove the equation.

A man drops a stone over a bridge into a stream beneath, and three seconds afterwards hears the splash; assuming that sound travels at the rate of 1090 feet per second, find the height of the bridge.

7. Find the resultant pressure on a body either wholly or partially immersed in water.

8. Explain the use of Nicholson's hydrometer in finding the specific gravity of heavy fragments.

In weighing some fragments whose specific gravity is 8.8 in the hydrometer, 240 grains and 370 grains respectively have to be added: find the weight of the fragments.

9. Describe the air condenser, and find the pressure in the receiver after *n* strokes.