If the weight piston has an area of 214 square inches and the power piston an area of 4 square inches, what power will be required to lift a weight of 760 pounds?

20. Penetration of Armor. The depth of penetration of armor by a projectile varies as the caliber of the gun.

If an 8-inch gun penetrates to a depth of 4 inches, compute the penetration of a 14-inch

gun in the same armor at the same distance.

21. Strength of the Current.

The current varies as the tangent of the angle of deflection (tan d).

The current from a battery deflects the needle of a tangent galvanometer 10°; with a second battery, the deflection is 25°.

Compute the ratio of the strengths of the two currents.

22. Law of the Lever. In a lever of whatever class the power is to the weight, as the weight's distance from the fulcrum is to the power's distance from the fulcrum.

FIG. 71.
Tangent Galvanometer.

A lever 8 feet long has the fulcrum 9 inches from one end. What force in pounds applied at the long end will balance a weight of 480 pounds, 2 inches from the short end?

23. Height in Communicating Tubes. The heights of liquids at equilibrium in a U-tube vary inversely as their densities.

The height of the water in one of two communicating tubes is 14 inches.

Compute the height of the mercury in the other tube, mercury being 13.6 times as heavy as water,

24. Weight of a Gun. The weight of a gun varies approximately as the cube of its caliber.

An 8-inch gun weighs 14.2 tons.

Determine the weight of a 12-inch gun of the same type.

25. Charles' Law. Under constant pressure, the volume of a gas varies as the absolute temperature.*

A gas with a volume of 90 cc. at 10° C. is heated to 35° C.

Compute its volume at the higher temperature, the pressure being the same at both temperatures.

26. Osmotic Pressure. The osmotic pressure O of a solution varies as the molecular mass M of the substance dissolved.

Solve the formula for M1.

27. A Falling Body. The distance through which a body falls from rest varies

as the square of the time during which it is falling.

A body falls 175.6 meters in 6 seconds.
How far will it fall in of a second?

28. The Lever. The distances from the fulcrum of a lever, of two weights which are in equilibrium, vary inversely as the weights; that is, the distance varies inversely as the weight.

At the ends of a lever 10 feet long are two weights of 120 and 84 pounds respectively.

At what distance from the center must the fulcrum be placed in order that the weights may balance?

See paragraph 37, problem 16.

29. Oscillation of a Pendulum.

The number of oscillations

of a pendulum per time unit varies inversely as the square root of its length.

*Absolute temperature =273°+the recorded temperature Centigrade.

The length of a pendulum which beats seconds at the sealevel, is 39.1 inches.

How long is a pendulum which oscillates 3 times a second?

30. Apparent Size. The apparent size of an object varies inversely as its distance.

Solve the formula for D1.

31. Flow of Gas in Pipes. The volume of gas discharged from a horizontal pipe under constant pressure and specific gravity, varies inversely as the square root of the length of the pipe.

The volume in 3

cubic feet?

hours from a pipe 600 feet long was 1750

Find the volume discharged per hour from a mile length of the same pipe.

32. Vibration of Strings. The number of vibrations per time unit, of a string under constant tension, varies inversely as the length of the string.

FIG. 73.

When the length is 4 feet 8 inches, the string vibrates 256 times per second.

What must be the length of a string of the same material and diameter, in order that the vibrations may be doubled?

33. Relation of Mass to Velocity. The velocity imparted to a body varies inversely as its mass.

A given force imparts a velocity of 75 feet per second to a body whose weight is 644 pounds.

What velocity will the same force impart to a body whose mass is 120?

34. Linear Velocity. Linear velocity varies directly as areal †

† Areal velocity equals the rate at which an area increases.

velocity and inversely as the distance from the center of force to the line of motion.

Solve the formula for D2.

35. Linear Velocity. The linear velocity of a particle per time unit varies directly as the radius of revolution and inversely as the time of one revolution. Solve the formula for R1.

36. Angular Velocity. The angular velocity (w) of any point in a revolving body varies directly as the areal velocity and inversely as the square of the radius vector (R). Solve for R2.

37. Centrifugal Force. The centrifugal force at any point in a revolving body varies as the square of the linear velocity.

Solve the formula for VL1.

38. Vibration of Light. The number of vibrations of light per second varies inversely as the wave length L. Solve the formula for L2.

39. Intensity of Heat. The intensity of heat H received from a radiating body varies inversely as the square of the distance from the source of heat.

Solve the formula for H2.

40. Boyle's Law. Under

constant temperature the vol

ume of a gas varies inversely as the pressure.

If a gas have a volume of 106 cubic inches under a pres

sure of 14.7 pounds, compute the volume when the pressure is 15.3 pounds more.

41. Bending of a Bar. The amount a bar will bend varies inversely as the width when the thickness and the length remain the same.

If a bar 3.5 inches wide bend through 5° under the application of a given force, compute the amount of bending of a bar 5.1 inches wide, of the same material, length, and thickness, under the same force.

42. Centrifugal Force. The centrifugal force at any point of a revolving body varies as the radius of revolution of the point. The centrifugal force is 900 pounds when the radius is 24 inches. Compute the force when the radius is 18 inches.

43. Density and Volume. The density of a given weight of a gas varies inversely as its volume.

If the density is .108 when the volume is 4.5 cubic feet, find the density when the volume is reduced by pressure to 3.8 cubic feet. 44. Internal Resistance of a Bat

tery. The total resistance varies as the cotangent of the angle of deflection. When the resistance is 9.8, the angle of deflection is 45°.

Find the resistance when the angle is 24°.

45. Area on a Globe. The area of a country on a terrestrial globe varies as the square of the diameter of the globe.

FIG. 75.

On a globe 28 inches in diameter, the area of a certain island is 2.6' square inches.

Compute the area of the same island on a globe 36 inches in diameter.

46. Period of a Pendulum. The time of vibration (period) of a pendulum varies inversely as the square root of the force causing it to vibrate.

Solve the formula for F1.

47. Force of a Moving Body. The force imparted by a moving body varies as the mass of the body times its acceleration.

Solve the formula for M2.