4.40: Efficiency
This man is pushing heavy boxes on a dolly. If he were to push the boxes across the ground without the dolly, it would take a lot more force because he would have to overcome the sliding friction between the boxes and the ground. Using a dolly reduces the friction because rolling friction between the wheels and the ground is much less than sliding friction.
Machines and Friction
A dolly is a machine because it changes a force to make work easier. What is work? In physics, work is defined as the use of force to move an object over a distance. It is represented by the equation:
Work = Force x Distance
All machines make work easier, but they don’t increase the amount of work that is done. You can never get more work out of a machine than you put into it. In fact, a machine always does less work on an object than the user does on the machine. That’s because a machine must use some of the work put into it to overcome friction. Friction is the force that opposes motion between any surfaces that are touching. All machines involve motion, so they all have friction. How much work is needed to overcome friction in a machine depends on the machine’s efficiency.
Machine Efficiency
Efficiency is the percent of work put into a machine by the user (input work) that becomes work done by the machine (output work). The output work is always less than the input work because some of the input work is used to overcome friction. Therefore, efficiency is always less than 100 percent. The closer to 100 percent a machine’s efficiency is, the better it is at reducing friction. Look at the ramp in the Figure below. A ramp is a type of simple machine called an inclined plane. It is easier to push the heavy piece of furniture up the ramp to the truck than to lift it straight up off the ground, but 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 with the ramp.
Q: Why would it be more efficient to use a dolly to roll the furniture up the ramp?
A: There would be less friction to overcome if you used a dolly because of the wheels. So the efficiency of the ramp would be greater with the dolly.
Calculating Efficiency
Efficiency can be calculated with the equation:
\begin{align*}\mathrm{Efficiency=\frac{Output\;work}{Input\;work}*100\%}\end{align*}
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:
\begin{align*}\mathrm{\frac{6000J}{8000J}*100\%=75\%}\end{align*}
Q: Rani puts 7500 joules of work into pushing a box up a ramp, but only 6700 joules of work actually go into moving the box. The rest of the work overcomes friction between the box and the ramp. What is the efficiency of the ramp?
A: The efficiency of the ramp is:
\begin{align*}\mathrm{\frac{6700J}{7500J}*100\%=90\%}\end{align*}
For an animated ramp and its efficiency, go to this URL:
http://www.leydenscience.org/physics/work/effic.htm
Summary
- A machine always does less work on an object than the user does on the machine, because the machine must use some of the work to overcome friction.
- Efficiency is the percent of work put into a machine by the user (input work) that becomes work done by the machine (output work). It is a measure of how well a machine reduces friction.
- You can calculate the efficiency of a machine with this equation: \begin{align*}\mathrm{Efficiency=\frac{Output\;work}{Input\;work}*100\%}\end{align*}
Efficiency=OutputworkInputwork∗100%
Vocabulary
- efficiency: Measure of how well a machine reduces friction; calculated as the percent of input work that becomes output work.
Practice
At the following URL, review efficiency and how to calculate it. Then do the problems at the bottom of the Web page. Check the correct answers and the explanations for them.
http://equalrightsforall.net/classical_mechanics/energy/023_Machines.html
Review
- Why is the output work of a machine always less than the input work done on the machine?
- What is the efficiency of a machine?
- If a machine requires an input of 5000 joules of work to put out 4000 joules of work, what is the machine’s efficiency?
Image Attributions
- Explain why all machines must overcome friction.
- Define the efficiency of a machine.
- Show how to calculate the efficiency of a machine.