# machines

## increasing distance

Examples of machines that increase the distance over which force is applied are paddles and hammers. Figure 16.9 explains how these machines work. In each case, the machine increases the distance over which the force is applied, but it reduces the strength of the applied force.

## increasing force

Examples of machines that increase force are doorknobs and nutcrackers. Figure 16.8 explains how these machines work. In each case, the force applied by the user is less than the force applied by the machine, but the machine applies the force over a shorter distance.

## how machines help us do work

A machine is any device that makes work easier by changing a force. When you use a machine, you apply force to the machine. This force is called the input force. The machine, in turn, applies force to an object. This force is called the output force. Recall that work equals force multiplied by distance: Work = Force Distance The force you apply to a machine is applied over a given distance, called the input distance. The force applied by the machine to the object is also applied over a distance, called the output distance. The output distance may or may not be the same as the input distance. Machines make work easier by increasing the amount of force that is applied, increasing the distance over which the force is applied, or changing the direction in which the force is applied. Contrary to popular belief, machines do not increase the amount of work that is done. They just change how the work is done. So if a machine increases the force applied, it must apply the force over a shorter distance. Similarly, if a machine increases the distance over which the force is applied, it must apply less force.

## an example efficiency of a ramp

Consider the ramp in Figure 16.11. Its easier to push the heavy piece of furniture up the ramp to the truck than to lift it straight up off the ground. However, pushing the furniture over the surface of the ramp creates a lot of friction. Some of the force applied to moving the furniture must be used to overcome the friction. It would be more efficient to use a dolly on wheels to roll the furniture up the ramp. Thats because rolling friction is much less than sliding friction. As a result, the efficiency of the ramp would be greater with a dolly.

Another measure of the effectiveness of a machine is its mechanical advantage. Mechanical advantage is the number of times a machine multiplies the input force. It can be calculated with the equation: Mechanical Advantage = Output force Input force This equation computes the actual mechanical advantage of a machine. It takes into account the reduction in output force that is due to friction. It shows how much a machine actually multiplies force when it used in the real world.

It can be difficult to measure the input and output forces needed to calculate actual mechanical advantage. Its usually much easier to measure the input and output distances. These measurements can then be used to calculate the ideal mechanical advantage. The ideal mechanical advantage represents the multiplication of input force that would be achieved in the absence of friction. Therefore, it is greater than the actual mechanical advantage because all machines use up some work in overcoming friction. Ideal mechanical advantage is calculated with the equation: Ideal Mechanical Advantage = Input distance Output distance Compare this equation with the equation above for actual mechanical advantage. Notice how the input and output values are switched. This makes sense when you recall that when a machine increases force, it decreases distance and vice versa. You can watch a video about actual and ideal mechanical advantage at this link: http://video.goo Consider the simple ramp in Figure 16.12. A ramp can be used to raise an object up off the ground. The input distance is the length of the sloped surface of the ramp. The output distance is the height of the ramp, or the vertical distance the object is raised. Therefore, the ideal mechanical advantage of the ramp is: Ideal Mechanical Advantage = 6m =3 2m An ideal mechanical advantage of 3 means that the ramp ideally (in the absence of friction) multiplies the output force by a factor of 3.

## calculating efficiency

Efficiency can be calculated with the equation: Efficiency = Output work 100% Input work Consider a machine that puts out 6000 joules of work. To produce that much work from the machine requires the user to put in 8000 joules of work. To find the efficiency of the machine, substitute these values into the equation for efficiency: Efficiency = 6000 J 100% = 75% 8000 J You Try It! Problem: Rani puts 10,000 joules of work into a car jack. The car jack, in turn, puts out 7000 joules of work to raise up the car. What is the efficiency of the jack?

## mechanical advantage and type of machine

As you read above, some machines increase the force put into the machine, while other machines increase the distance over which the force is applied. Still other machines change only the direction of the force. Which way a machine works affects its mechanical advantage. For machines that increase force including ramps, doorknobs, and nutcrackers the output force is greater than the input force. Therefore, the mechanical advantage is greater than 1. For machines that increase the distance over which force is applied, such as paddles and hammers, the output force is less than the input force. Therefore, the mechanical advantage is less than 1. For machines that change only the direction of the force, such as the rope systems on flagpoles, the output force is the same as the input force. Therefore, the mechanical advantage is equal to 1.

## efficiency of machines

You read above that machines do not increase the work done on an object. In other words, you cant get more work out of a machine than you put into it. In fact, machines always do less work on the object than the user does on the machine. Thats because all machines must use some of the work put into them to overcome friction. How much work? It depends on the efficiency of the machine. Efficiency is the percent of input work that becomes output work. It is a measure of how well a machine reduces friction.

## kqed exoskeletons walk forward

An exoskeleton suit may seem like science fiction, turning ordinary humans into super heroes. But wearable robots are moving forward into reality. And for paraplegics, the ability to stand and walk that these machines provide is a super power. QUEST meets Austin Whitney and Tamara Mena, two "Exoskeleton Test Pilots" who are now putting this new technology through its paces. For more information on exoskeleton suits, see http://science.kqed.org/ques MEDIA Click image to the left or use the URL below. URL:

## changing the direction of force

Some machines change the direction of the force applied by the user. They may or may not also change the strength of the force or the distance over which it is applied. Two examples of machines that work in this way are claw hammers and the rope systems (pulleys) that raise or lower flags on flagpoles. Figure 16.10 explains how these machines work. In each case, the direction of the force applied by the user is reversed by the machine. How does this make it easier to do the job?

## instructional diagrams

No diagram descriptions associated with this lesson

## questions

Machines that increase the distance over which force is applied include

``````-->  a. hammers.

b. doorknobs.

c. nutcrackers.

d. pry bars.
``````

Ways that machines make work easier include

``````-->  a. increasing force.

b. increasing work.

c. increasing efficiency.

d. all of the above
``````

If you apply 20 N of force to the handle end of a canoe paddle, how much force might the paddle end apply to the water?

``````a. 40 N

b. 30 N

c. 20 N

-->  d. 10 N
``````

If the output work of a machine is 3000 J and the input work is 4000 J, what is the efficiency of the machine?

``````a. 133%

b. 100%

-->  c. 75%

d. 66%
``````

If the ideal mechanical advantage of a machine equals 1, then the actual mechanical advantage of the machine must be

``````a. greater than 1.

b. equal to 1.

-->  c. less than 1.

d. less than zero.
``````

The output distance of a machine is always greater than the input distance.

``````a. true

-->  b. false
``````

Using a machine increases the amount of work that is done for a given amount of force.

``````a. true

-->  b. false
``````

A machine increases the applied force by increasing the distance over which the force is applied.

``````a. true

-->  b. false
``````

The output force of a machine is always less than the input force.

``````a. true

-->  b. false
``````

The force you apply to a doorknob is less than the force applied by the doorknob to open the door.

``````-->  a. true

b. false
``````

All machines that change the strength of the force also change the distance over which the force is applied.

``````-->  a. true

b. false
``````

A machine changes the way that work is done.

``````-->  a. true

b. false
``````

The actual mechanical advantage of a machine is always greater than its ideal mechanical advantage.

``````a. true

-->  b. false
``````

All machines change the direction in which force is applied.

``````a. true

-->  b. false
``````

A machine that applies force over a longer distance also increases the strength of the force.

``````a. true

-->  b. false
``````

If a machines output distance is greater than the input distance, the ideal mechanical advantage is less than

``````-->  a. true

b. false
``````

A pry bar changes the strength, distance, and direction of the input force.

``````-->  a. true

b. false
``````

If a machine changes only the direction of force, its mechanical advantage is equal to 1.

``````-->  a. true

b. false
``````

A lever is a machine that changes the direction of the force that is applied to it.

``````a. true

-->  b. false
``````

number of times a machine multiplies the input force

``````a. efficiency

b. input force

c. output force

e. input distance

f. output distance

g. machine
``````

distance over which force is applied to a machine

``````a. efficiency

b. input force

c. output force

-->  e. input distance

f. output distance

g. machine
``````

percent of input work that becomes output work

``````-->  a. efficiency

b. input force

c. output force

e. input distance

f. output distance

g. machine
``````

force applied to a machine

``````a. efficiency

-->  b. input force

c. output force

e. input distance

f. output distance

g. machine
``````

any device that makes work easier by changing a force

``````a. efficiency

b. input force

c. output force

e. input distance

f. output distance

-->  g. machine
``````

distance over which a machine applies force

``````a. efficiency

b. input force

c. output force

e. input distance

-->  f. output distance

g. machine
``````

force applied by a machine

``````a. efficiency

b. input force

-->  c. output force

e. input distance

f. output distance

g. machine
``````

A machine can make work easier by

``````a. increasing the amount of force that is applied.

b. increasing the distance over which force is applied.

c. changing the direction in which force is applied.

-->  d. any of the above
``````

Examples of machines that increase force include

``````-->  a. doorknobs.

b. hammers.

d. two of the above
``````

How does a nutcracker change the force applied to it?

``````-->  a. It increases the force that is applied.

b. It increases the distance over which force is applied.

c. It changes the direction in which force is applied.

d. two of the above
``````

A machine that increases the applied force and also changes its direction is a

``````a. hammer.

-->  c. pry bar.

d. doorknob.
``````

Which of the following could be the efficiency of a machine?

``````a. 200%

b. 150%

c. 100%

-->  d. 75%
``````

What is the mechanical advantage of a machine that increases the distance over which force is applied?

``````-->  a. less than 1

b. equal to 1

c. greater than 1

d. greater than 2
``````

If the output force of a machine is greater than input force, the mechanical advantage of the machine is

``````-->  a. greater than 1.

b. equal to 1.

c. less than 1.

d. any of the above
``````

## diagram questions

No diagram questions associated with this lesson