Simple Machines & Mechanical Advantage Cheat Sheet

A printable reference covering simple machines, mechanical advantage, efficiency, work, force, and distance tradeoffs for grades 5-7.

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Simple machines help people do work by changing the size or direction of a force. This cheat sheet covers levers, pulleys, wheels and axles, inclined planes, wedges, and screws. Students need these ideas to understand how tools make lifting, moving, cutting, and fastening easier. It is useful for solving force, distance, work, mechanical advantage, and efficiency problems. The most important idea is that machines do not create energy. A simple machine often lets you use a smaller input force over a longer distance. Mechanical advantage compares output force to input force, while efficiency compares useful output work to input work. In real machines, friction reduces efficiency, so actual mechanical advantage is usually less than ideal mechanical advantage.

Key Facts

Work is calculated with $W = Fd$ , where $W$ is work, $F$ is force, and $d$ is distance in the direction of the force.
Mechanical advantage is calculated with $\text{MA} = \frac{F_{\text{out}}}{F_{\text{in}}}$ , so a larger value means the machine multiplies force more.
Ideal mechanical advantage is calculated with $\text{IMA} = \frac{d_{\text{in}}}{d_{\text{out}}}$ when distance measurements are known.
Efficiency is calculated with $\text{Efficiency} = \frac{W_{\text{out}}}{W_{\text{in}}} \times 100\%$ , and real machines always have efficiency less than $100\%$ .
For a lever, ideal mechanical advantage can be found with $\text{IMA} = \frac{d_{\text{effort}}}{d_{\text{load}}}$ , using distances from the fulcrum.
For an inclined plane, ideal mechanical advantage is $\text{IMA} = \frac{L}{h}$ , where $L$ is ramp length and $h$ is vertical height.
For a pulley system, ideal mechanical advantage is $\text{IMA} = n$ , where $n$ is the number of rope sections supporting the load.
Simple machines trade force for distance, so decreasing the input force usually means increasing the input distance.

Vocabulary

Simple machine: A basic device that makes work easier by changing the size or direction of a force.
Effort force: The input force a person or motor applies to a machine to make it move.
Load: The object or resistance that a machine is trying to move, lift, cut, or hold.
Fulcrum: The fixed pivot point around which a lever rotates.
Mechanical advantage: A comparison of output force to input force, calculated as $\text{MA} = \frac{F_{\text{out}}}{F_{\text{in}}}$ .
Efficiency: The percent of input work that becomes useful output work, calculated as $\text{Efficiency} = \frac{W_{\text{out}}}{W_{\text{in}}} \times 100\%$ .

Common Mistakes to Avoid

Confusing input force with output force, which reverses the ratio for $\text{MA} = \frac{F_{\text{out}}}{F_{\text{in}}}$ . The output force is what the machine applies to the load, not what you push or pull with.
Forgetting that distance matters in work problems, which leads to using force alone. Work must use $W = Fd$ , and the distance must be in the same direction as the force.
Assuming a machine reduces both force and distance, which violates the force distance tradeoff. If a machine lowers the needed force, the effort usually moves through a greater distance.
Treating ideal mechanical advantage and actual mechanical advantage as the same, which ignores friction. Real machines lose some energy as heat and sound, so $\text{AMA} < \text{IMA}$ in most cases.
Counting the wrong rope sections in a pulley system, which gives the wrong $\text{IMA}$ . Only count rope sections that directly support the load.

Practice Questions

1 A student uses a ramp that is $6\ \text{m}$ long to raise a box to a height of $1.5\ \text{m}$ . What is the ramp's ideal mechanical advantage using $\text{IMA} = \frac{L}{h}$ ?
2 A lever lifts a $240\ \text{N}$ load when a student applies an effort force of $60\ \text{N}$ . What is the mechanical advantage using $\text{MA} = \frac{F_{\text{out}}}{F_{\text{in}}}$ ?
3 A machine has $W_{\text{in}} = 500\ \text{J}$ and $W_{\text{out}} = 400\ \text{J}$ . What is its efficiency using $\text{Efficiency} = \frac{W_{\text{out}}}{W_{\text{in}}} \times 100\%$ ?
4 A long ramp and a short ramp both lift the same box to the same height. Explain which ramp needs less force and why the work is not made to disappear.