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Physics – The Foundational Science
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Chapter 11 – Work and Machines
Key Equations
𝑊 = 𝐹𝑑
𝑃=
𝑊
𝑡
𝑃 = 𝐹𝑣
𝐼𝑀𝐴 =
𝐼𝑀𝐴 =
𝐼𝑀𝐴 =
𝑑𝑖
𝑑𝑜
𝑟𝑖
𝑟𝑜
2𝜋𝑟
𝑝
𝐴𝑀𝐴 =
𝐴𝑀𝐴 =
1
𝑠𝑖𝑛Ө+ 𝜇𝑘 𝑐𝑜𝑠Ө
𝐹𝑜
𝐹𝑖
𝑊
ŋ = (𝑊𝑜 ) (100%)
𝑖
𝐴𝑀𝐴
ŋ = ( 𝐼𝑀𝐴 ) (100%)
𝐹𝑖 𝑟𝑖 = 𝐹𝑜 𝑟𝑜
Questions
1. (a) What is the definition of work? (b) What is the basic work equation?
a.
b.
2. What are the units of work in the SI and U.S. customary system?
3. How is the component of force in the direction of motion determined?
4. How is total work computed when individual contributions are known?
Unit 2 ♦ Mechanics ♦ Chapter 11 – Work and Machines
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5. What is the difference between negative work and net work?
6. What energy is acquired by an object lifted into the air?
7. State the definition of average power both in words and in an equation.
8. How does our everyday use of the word “power” differ from the scientific use?
9. What are the three major units of power?
a.
b.
c.
Unit 2 ♦ Mechanics ♦ Chapter 11 – Work and Machines
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10. What did horsepower originally mean? What is the conversion between horsepower and the
SI unit of power?
11. How may work and energy be found when power is given?
12. List the simple machines.
13. State the law of levers in words and in an equation.
14. Distinguish IMA from AMA and tell how each is measured.
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15. Describe each class of levers.
16. (a) If the IMA of a lever is 6, what do you know about the structure of the lever? (b) How
do the input distances and forces relate to the output distances and forces? (c) For what two
reasons will the actual gain in force be less than six-fold? (d) What index shows the actual gain
in force?
a.
b.
c.
d.
17. What is the input force for an inclined plane without friction? With friction?
18. What is the IMA of a screw? Identify each variable.
Unit 2 ♦ Mechanics ♦ Chapter 11 – Work and Machines
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19. How is the IMA of a pulley determined?
20. What is the IMA of a wheel and axle? Identify each variable.
21. Design a block and tackle with an IMA of 7. Draw a sketch.
22. Which simple machines usually operate with the greatest friction? With the least?
23. State two equations for efficiency.
a.
b.
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Problems
1. A locomotive is pushing a 2.20 x 105-N boxcar exactly 3.20 km up a 30.0° slope at a constant
speed of 15.6 m/s. How much work is the locomotive doing? Ignore the effects of friction.
2. (a) Calculate the work done in raising 480 N to a height of 5.00 m. (b) Find the work done in
raising 250 g a distance of 215 cm at a constant velocity.
a.
b.
3. How much work is required to carry a 180-N sack up to the third floor of an apartment
building if the vertical distance between floors is 3.5 m?
4. How much work is done in pushing a 75-kg box a horizontal distance of 7.35 m if the speed is
constant and the coefficient of kinetic friction is 0.35?
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5. How much work is done in #4 if the box is accelerated at 0.94 m/s2 (a) on a flat surface, and
(b) down a ramp raised 20.° above the horizontal?
a.
b.
6. An airplane weighing 11,000 N climbs to a height of 1.6 km in 9.8 minutes. Calculate the
accomplished power in horsepower.
7. The hopper of a concrete hoist weights 3100 N when half loaded. If this hopper is raised 55
m in 6.0 s, find the power required in (a) W, and (b) hp.
a.
b.
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8. An elevator car with 6 passengers weighs 5600 N. (a) Calculate the power required to raise
this car at 1.8 m/s. (b) If the cables holding the car run over pulleys to a total counterbalancing
weight of 2400 N, what power is required from the elevator’s motor?
a.
b.
9. A farmer is prying a stump with a 1.6-m iron rod. The rod rests on a rock 0.30 m from the
lower end. If the farmer can exert a downward force of 180 lb on the upper end of the rod, how
much upward force does the rod exert on the stump?
10. A loaded crate weighing 1250 N is pushed up a plank onto a platform. If the plane in
inclined at 10.0° to the horizontal and μk is 0.420, calculate (a) the IMA, (b) the amount of force
required to push the crate upward, (c) the AMA, and (d) the efficiency.
a.
b.
c.
d.
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11. A screw jack has a handle of radius 1.0 m and a thread pitch of 6.4 mm. Calculate the IMA
of the jack.
12. A wheel and axle have diameters of 0.50 m and 3.8 cm, respectively. A force of 280 N is
necessary to raise a load of 2400 N. Calculate (a) the IMA, (b) the AMA, and (c) the efficiency.
a.
b.
c.
13. A force of 55 N exerted through 0.35 m on the input side of a lever raises a load of 106 N a
distance of 0.16 m. What is the efficiency of the lever?
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