duced to 14 cm. by 10 cm., what force will be required at the same pressure?

XXXIII. WORK AND ENERGY.

DEFINITIONS.-Work; unit of work; foot-pound; kilogram-meter; foot-poundal; erg; energy; potential energy; kinetic energy; activity; horse-power; watt.

NOTE.-The student is referred to §§ 15 and 16 for table of units of force and work.

1. How much work is done in lifting 100 lbs. 1 ft.? how much in lifting it 3 ft.? How much in lifting 200 lbs. 4 ft. ?

2. A man pulls a car weighing 300 lbs. up a track till it is 10 ft. higher than it was at first. How much work has he done?

3. A rope 12 ft. long sustains a mass of 150 lbs. How much work is it performing?

4. A mass of 8 kgm. is lifted to the top of a tower 50 m. high. How much work is done upon it?

5. How much work will a mass of 70 kgm. do in falling from a height of four meters?

6. Through what height must a gram be lifted in order that 2 kilogram-meters of work may be done upon it?

7. A cart moves on a road when a force of 700 lbs. is applied to it. How much work does a horse do in drawing the cart a quarter of a mile?

8. If the force of one poundal acts through 15 ft., how many units of work are done?

9. If a force of 20 dynes acts through 5.2 m., how much work is done?

10. A certain force lifts a mass of 50 gm. 30 cm. against gravity. Express the value of the work done in gm.-cm. and also in ergs.

11. A block whose weight is 2 kgm. is drawn 10 cm.

along a horizontal surface when the coefficient of friction is. Find the force in dynes required and the work performed in ergs.

12. A body weighing 96 kgm. rests on an incline. How much work must be done in drawing the body 250 cm. up the incline when the vertical ascent is 1 meter and the coefficient of friction?

13. A rectangular block of metal weighing 500 lbs. has its centre of gravityfoot above the surface on which it rests when the block rests on a side. When the block rests on an end the centre of gravity is 34 ft. above the surface. Find the work done in changing from one position to the other.

14. A force of 7 smooth incline 2 m.

kgm. is needed to draw a car up a long when the force is applied in a line parallel to the incline. If the force is applied horizontally it must be equal to 8 kgm. Compare the work done in the two cases.

15. Find the ratio of the base of the incline (in Prob. 14) to the length of the slope.

16. Find the weight of the car.

(Prob. 14.)

17. A machine lifts 100 kgm. of grain 3 meters in a minute. How much work is done in an hour?

18. 1200 ergs of work are available. resisted through 6 meters?

19. Reduce 30 ergs to kilogram-meters.

20. Reduce 20 ft.-lbs. to ft.-poundals.

What force can be

21. A wheel to which a force is applied, tending to turn it, can be held still by a force of 20 lbs. applied tangentially at its rim. The wheel is 3 ft. in diameter. Find the work done in 10 revolutions of the wheel.

22. How many ergs of work will a weight of 2 kgm. do in falling from a height of 10 meters?

23. A car weighing 100 lbs. is drawn up an incline which rises 3 ft. for every 15 ft. of track. If the coefficient of

friction is, find the work done in moving the car 20 ft. along the track.

24. A body consists of two masses weighing respectively 40 and 100 gm., connected by a straight weightless rod one meter long. Find the work done in tilting the rod from a horizontal to a vertical position. (The masses are sup posed to be concentrated at the extremities of the rod.)

25. A uniform rectangular block weighs 360 gm. and measures 10 by 12 by 30 cm. Find the work done in tilting it from a position of resting on one of its smallest surfaces to resting on one of its largest surfaces.

26. Which is doing the most work-a man who carries a ton of coal to a height of 30 ft. in an hour, or a man who carries half a ton up 120 ft. in two hours?

27. How much energy and of what kind has a mass of 100 lbs. at a height of 2 ft.?

28. A stone weighing 5 kgm. is thrown with a velocity of 4 meters per second. Express its kinetic energy both in ergs and in gravitation units.

29. How many units of kinetic energy does a mass of 1 gm. acquire by falling one second?

30. A stone weighing 5 kgm. is thrown upwards with a velocity of 980 cm. per second. Find (a) how long it will rise; (b) how far it will rise; (c) what its energy is at starting; (d) what its energy is half-way up; (e) what its energy is at highest point; (ƒ) what its energy is half-way down.

31. A hammer weighing 90 lbs. strikes an anvil with a velocity of 10 ft. per second. How many pounds weight would the blow raise through 15 ft. if none of the energy of the blow were lost in heat and other unavailable forms?

32. A cannon-ball weighing 80 kgm. is moving at the rate of 750 meters per second. How much energy does it possess?

33. How far will it compress a spring which requires a force of 900 kgm. to shorten it 1 cm. ?

34. Express clearly the difference of meaning between energy and activity, and illustrate your answer by the case of a man lifting a weight.

35. What is the activity per second of a motive power which can do 33,000 ft.-lbs. of work in one minute? (Note. This particular activity is called "a horsepower.")

36. If "one horse-power" is the ability to lift 550 lbs. 1 ft. in one second, what is the horse-power of a hoistingengine which can draw a weight of 1200 lbs. to a height of 30 ft. in 4 seconds?

37. If a watt is the activity manifested by doing 10 million ergs of work per second, of how many watts is an electric motor which can raise 2000 kgm. 3 meters in 24 seconds?

38. A force of 2000 dynes acting through a space of 120 cm. in one second furnishes an activity of how many ergs per second ?-of how many watts ?

39. Through how many cm. per second must a force of 500,000 dynes act to furnish an activity of 4 watts?

40. In what time must 1000 ft.-lbs. of work be performed to furnish an activity of horse-power?

XXXIV. SIMPLE MACHINES.

DEFINITIONS. Machine; lever; compound lever; wheel and axle; pulley; inclined plane; wedge; screw; "mechanical advantage."

Levers: Simple and Compound.-1. The arms of a lever on opposite sides of the fulcrum are 1 ft. and 2 ft. long respectively. What force at the end of the longer arm will balance a force of 20 lbs. at the end of the shorter arm?

If a force just sufficient to produce motion be applied at the end of the longer arm and move that end one inch, how far will the 20 lbs. weight be moved?

2. In an ordinary wheelbarrow, suppose the centre of gravity of the load to be 2 ft. from the axle of the wheel, and the hands of the user 4 ft. from the axle. How great a load can a man lift by this arrangement if he can exert a force of 175 lbs. ?

3. A lever is arranged so that one end works a ratchetwheel when the other is moved back and forth. How great a force can be exerted on the wheel by a man who pulls the other end of the lever with a force of 40 kgm. if the power-arm is five times as long as the resistancearm?

4. Draw a diagram to show

(a) The relation existing in the case of a simple lever between the magnitudes of power-arm, resistance-arm, power, and weight.

(b) The distance the power moves and the distance the weight moves.

5. Draw a diagram to show how a simple lever may be used to exert ten times the pressure at one end that is applied to the other end.

6. In a certain machine a force of 20 kgm. moving 5 cm. is found to be able to move a weight 25 cm. How great

is the weight moved?

7. How heavy a stone could a man who could push down with a force of 150 lbs. lift with a crowbar six feet long if the fulcrum were one foot from the stone?

8. It is found that when a force of just 10 kgm. is applied to one end of an equal-armed lever hung on a pivot it will lift a weight of 9.75 kgm. at the other end. plain how this is possible.

Ex

9. A compound lever has arms as follows: AB = 2 ft.,