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An ordinary pulley has an MA of 1; it only changes the direction of the force and not its magnitude. Combinations of pulleys, such as those illustrated in [link] , are used to multiply force. If the pulleys are friction-free, then the force output is approximately an integral multiple of the tension in the cable. The number of cables pulling directly upward on the system of interest, as illustrated in the figures given below, is approximately the MA of the pulley system. Since each attachment applies an external force in approximately the same direction as the others, they add, producing a total force that is nearly an integral multiple of the input force T .

In figure a, a rope over two pulleys is shown. One pulley is fixed at the roof and the other is hanging through the rope. A weight is hanging from the second pulley. The tensions T are shown at the two parts of hanging pulley and at the free end of the rope. The mechanical advantage of the system is two. In figure b, a set of three pulleys is shown. A pulley is fixed at the roof with another pulley below it. The third pulley is hanging through the rope with a weight hanging at it. The tensions on the rope are shown as vectors on the rope and at the end of the rope. In figure c, set of three pulleys is shown. One of the pulleys is fixed at the roof. Two connected pulleys are hanging through a rope over the first pulley. The directions of the tensions are marked on the ropes and at the end of the rope.
(a) The combination of pulleys is used to multiply force. The force is an integral multiple of tension if the pulleys are frictionless. This pulley system has two cables attached to its load, thus applying a force of approximately 2 T . This machine has MA 2 size 12{ ital "MA" approx 2} {} . (b) Three pulleys are used to lift a load in such a way that the mechanical advantage is about 3. Effectively, there are three cables attached to the load. (c) This pulley system applies a force of 4 T , so that it has MA 4 size 12{ ital "MA" approx 4} {} . Effectively, four cables are pulling on the system of interest.

Section summary

  • Simple machines are devices that can be used to multiply or augment a force that we apply – often at the expense of a distance through which we have to apply the force.
  • The ratio of output to input forces for any simple machine is called its mechanical advantage
  • A few simple machines are the lever, nail puller, wheelbarrow, crank, etc.

Conceptual questions

Scissors are like a double-lever system. Which of the simple machines in [link] and [link] is most analogous to scissors?

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Suppose you pull a nail at a constant rate using a nail puller as shown in [link] . Is the nail puller in equilibrium? What if you pull the nail with some acceleration – is the nail puller in equilibrium then? In which case is the force applied to the nail puller larger and why?

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Why are the forces exerted on the outside world by the limbs of our bodies usually much smaller than the forces exerted by muscles inside the body?

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Explain why the forces in our joints are several times larger than the forces we exert on the outside world with our limbs. Can these forces be even greater than muscle forces (see previous Question)?

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What is the mechanical advantage of a nail puller—similar to the one shown in [link] —where you exert a force 45 cm size 12{"45"`"cm"} {} from the pivot and the nail is 1.8 cm size 12{1 "." 8`"cm"} {} on the other side? What minimum force must you exert to apply a force of 1250 N size 12{"1250"`N} {} to the nail?


50 N

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Suppose you needed to raise a 250-kg mower a distance of 6.0 cm above the ground to change a tire. If you had a 2.0-m long lever, where would you place the fulcrum if your force was limited to 300 N?

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a) What is the mechanical advantage of a wheelbarrow, such as the one in [link] , if the center of gravity of the wheelbarrow and its load has a perpendicular lever arm of 5.50 cm, while the hands have a perpendicular lever arm of 1.02 m? (b) What upward force should you exert to support the wheelbarrow and its load if their combined mass is 55.0 kg? (c) What force does the wheel exert on the ground?

a) MA = 18 . 5 size 12{"MA"="18" "." 5} {}

b) F i = 29.1 N size 12{F rSub { size 8{i} } ="29" "." 1`N} {}

c) 510 N downward

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A typical car has an axle with 1 . 10 cm size 12{1 "." "10"`"cm"} {} radius driving a tire with a radius of 27 .5 cm size 12{"27" "." 5`"cm"} {} . What is its mechanical advantage assuming the very simplified model in [link] (b)?

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What force does the nail puller in [link] exert on the supporting surface? The nail puller has a mass of 2.10 kg.

1 . 3 × 10 3 N size 12{1 "." "30" times "10" rSup { size 8{3} } `N} {}

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If you used an ideal pulley of the type shown in [link] (a) to support a car engine of mass 115 kg size 12{"115"`"kg"} {} , (a) What would be the tension in the rope? (b) What force must the ceiling supply, assuming you pull straight down on the rope? Neglect the pulley system’s mass.

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Repeat [link] for the pulley shown in [link] (c), assuming you pull straight up on the rope. The pulley system’s mass is 7.00 kg size 12{7 "." "00"`"kg"} {} .

a) T = 299 N size 12{T="299"`N} {}

b) 897 N upward

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Questions & Answers

Calculate the work done by an 85.0-kg man who pushes a crate 4.00 m up along a ramp that makes an angle of 20.0º20.0º with the horizontal. (See [link] .) He exerts a force of 500 N on the crate parallel to the ramp and moves at a constant speed. Be certain to include the work he does on the crate an
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Practice Key Terms 1

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