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7. Find all the trigonometric functions of (180° + y).
8. Give the formulas and state the process by which an oblique triangle is solved when two sides and the included angle are given.
1. DEFINE the terms Force, Weight, Mass.
2. If two forces acting perpendicularly on a straight lever in opposite directions and on the same side of the fulcrum balance each other, they are inversely as their distances from the fulcrum; and the pressure on the fulcrum is equal to the difference of the forces.
3. The pressure upon any particle of a fluid of uniform density is proportional to its depth below the surface of the fluid.
4. In 50 cubic yards of rock, whose average specific gravity is 142, there enter 32 cubic yards of a substance whose specific gravity is 124. Find the specific gravity of the remainder of the rock.
5. How would you graduate a hydrometer for ascertaining the strength of alcohol.
6. How do you change from Fahrenheit to Centigrade ?
1. How does the weight of a body differ from the mass ? How are forces represented ? If it be stated that two forces of 5 lbs. and 10 lbs. act upon a body, what more is wanting to enable us to determine the result ? 2. Prove the proposition, “If two forces, acting at any
, angles on the arm of any lever, balance each other, they are
inversely as the perpendiculars drawn from the fulcrum to the directions in which the forces act."
3. The direction of two forces, P and Q, which act on a bent lever and keep it at rest, make equal angles with the arms of the lever, which are at 6 and 8 inches respectively. Find the ratio of Q to P.
4. Find the centre of gravity of a triangle. One half of a given triangle is cut off by a straight line parallel to the base: find the centre of gravity of the remaining trapezium.
5. Prove the proposition, “When a body of uniform density floats on a fluid, the part immersed: the whole body :: the specific gravity of the body: the specific gravity of the fluid.”
6. If the difference of readings of a thermometer, which is graduated both according to Fahrenheit's and the Centigrade scale, be 40, find the temperature in each scale.
1. PROVE the law of the parallelogram of forces.
2. Find the centre of gravity of any number of heavy points.
3. Deduce the law of the equilibrium of movable pulleys, taking the weight of the pulleys into account.
4. Find the relation of P's velocity to that of W on an inclined plane.
5. Prove the equality of fluid pressures. Explain the Hydrostatic Paradox.
6. If the volume of the receiver of a condensing pump is five times that of the barrel, find the pressure on the valve after ten strokes.
1. Define Force; Weight; Mass; and Density. How are forces represented ?
2. Give the axioms of the lever. Assuming the properties of the straight lever, prove the laws of the bent lever.
3. Can the resultant of two forces, in any case, be equal to one of the components ? If so, what are the conditions ?
4. A string passing round a smooth peg is pulled at each end by a force equal to the strain upon the peg. Find the angle between the two parts of the string.
5. Deduce the laws of the inclined plane, both when the body on the plane is at rest, and when it is in motion.
6. Prove that when a body of uniform density floats on a fluid, the part immersed : the whole body:: the specific gravity of the body: the specific gravity of the fluid.
7. Prove that the elastic force of air at a given temperature varies as the density. A barometer is sunk to the depth of twenty feet in a lake, find the consequent rise in the mercurial column. (Specific gravity of mercury = 13.57.)
III. 1. Describe the different kinds of levers, giving examples of each kind.
2. Enunciate the Parallelogram of Forces. Assuming it to be true for the direction of the resultant, prove it for the magnitude of the resultant.
3. A string passing around a smooth peg is pulled at each end by a force equal to the strain on the peg. Find the angle between the two parts of the string.
4. On the inclined plane when the power acts parallel to the plane, prove that the power : the weight :: height of the plane : length of the plane.
5. In the leaning tower of Pisa the top overhangs the base by 12 feet; why does it not fall ?
6. Prove that when a body of uniform density floats on a fluid, the part immersed : the whole body :: the specific gravity of the body : the specific gravity of the fluid.
7. A piece of iron weighs 12 pounds in water; and when a piece of wood which weighs 5 pounds is attached to it, the two together weigh 9 pounds in water. Find the specific gravity of the wood.