ROYAL MILITARY COLLEGE,

SANDHURST.

JUNE 1858.

MECHANICS.

1. Define force. How is statical pressure estimated? How are forces represented geometrically in magnitude and direction? What do you understand by a material body? Why are bodies sometimes considered as material particles? What is the advantage of so considering them? When are bodies said to be in equilibrium? How must two forces act upon a particle to be in equilibrium? How must three equal forces act upon a particle to keep it at rest? Could the forces 5, 7, 13, be so arranged as to be in equilibrium on a particle?

2. If P and Q are two forces acting at any angle 0, find the resultant of P and Q, and give values to the angle 0, so that the resultant may be, (1) greatest, (2) least.

D

Two pressures of 10 lbs. each act at an angle of 120°, find the magnitude and direction of the resultant.. Compare this resultant with

10

No3

the

resultant of two forces each lbs. acting at an angle of 60°.

3. What is meant by the moment of a force? If a force P act upon a rigid body at a distance (a) from a fulcrum in the rigid body, how must the force act that the moment may, (1) greatest, (2)

zero.

If any number of forces act upon a body in the same plane round a fixed point in the body, express the condition of equilibrium. Will this condition be sufficient if no point in the body be fixed? Weights of 4 lbs., 74 lbs. balance on a lever 12 inches long, where must the fulcrum be placed (1) when the lever is without weight, (2) when it weighs half-a-pound?

4. Find the centre of gravity of a triangle.

If G be the centre of gravity of the triangle ABC, and if GA, GB, GC, represent forces acting on a particle at G, they will keep the particle at

rest.

5. What is meant by the mechanical advantage of a machine? Is there always a mechanical advantage in the use, (1) of a lever, (2) of a pully? In the case of the screw describe its construction, and find the relation between the power and the weight when there is equilibrium. What must be the length of a lever at the extremity of which a force of 1 lb. acts, and supports on a screw 1000 lbs., the distance between the two contiguous threads being three-quarters of an inch?

6. State the laws of statical friction, as ascer

tained by experiment; show how to determine the coefficient of friction for a given substance.

A weight (W) is just prevented from sliding on an inclined plane by a force (P) parallel to the plane, find (P) when the coefficient of friction is , and the angle of the plane a.

7. What do you understand by "labouring force?" What is meant by the "unit of work?" How is horse-power estimated?

How many horse-powers would it take to raise 100 tons of coal per hour from a pit 110 yards deep.

8. How is velocity estimated, (1) when uniform, (2) when variable? In the case of uniform velocity obtain an equation for determining the time in which a given space is described with a given velocity. A railroad train travels one quarter of a-mile in eighteen seconds, find the time in which it will describe 120 miles.

9. A body is projected perpendicularly upwards, with a velocity (V), find the space it will describe in (t) seconds. A body is projected perpendicularly upwards, with a velocity of 966 feet in a second, find the space it describes in 6 seconds. Find also the time in which it will describe 2753.1 feet, and explain the double answer.

10. Show how the second law of motion is applicable to the theory of projectiles: find the range and time of flight of a projectile in vacuo.

Three balls are projected together at the same instant from the same point with given velocities and given angles of projection: find the height of their common centre of gravity above the horizontal plane passing through the point of projection, after (t) seconds.

11. How is force measured when the mass of the moving body is taken into account. If W-M g, what is the unit of weight referred to.

A weight of six ounces raises a weight of four ounces by means of a fixed pulley: find the accelerating force and the tension of the string.

pact.

12. Distinguish between direct and oblique im

If two elastic balls, moving in opposite directions, impinge directly upon each other, find the velocity of each after impact.

Two balls, whose modulus of elasticity is, move in opposite directions with velocities of 25 and 16 feet in a second respectively: find the distance between them, 4 seconds after their direct impact.

EUCLID.

1. Define a "straight line," and "parallel straight lines."

State any axioms of Euclid that relate specifically to straight lines and parallel straight lines. Enunciate the proposition in Euclid's First Book, in the proof of which the 12th axiom is used.

2. If two triangles have two sides of the one equal to two sides of the other, each to each, but the angle contained by the two sides of the one greater than the angle contained by the two sides equal to them of the other, the base of that which has the greater angle shall be greater than the base of the other.

If the angle between two sides of a parallelogram is diminished, the diagonal of the parallelogram passing through that angle is increased.

3. If the square described upon one of the sides. of a triangle is equal to the squares described upon the other two sides of it, the angle contained by those sides is a right angle.

If the two exterior angles at the base of a triangle are bisected by two straight lines which are produced to meet each other, the line which joins the vertical angle of the triangle and the point of intersection will bisect the vertical angle.

4. If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the parts and to twice the rectangle contained by the parts.

Explain how a rectangle is represented arithmetically, pointing out the unit of area referred to. What is the area of the rectangle whose sides are 3 feet and 16 inches respectively?

5. If one circle touch another internally at any point, the straight line which joins their centres being produced shall pass through that point of

contact.

Show that any straight line drawn through the point of contact will cut off similar segments from the two circles.

6. Draw a tangent to a given circle from a given point without it.

Given two points in the circumference of a circle, show how to draw another circle through these points, such that at either point of intersection the tangent to each circle shall pass through the centre of the other.

7. In a given circle inscribe an equilateral and equiangular pentagon.

In the construction for this proposition show