Peoples Physics Concepts

8.8. Mechanical Advantage http://www.ck12.org

8.8 Mechanical Advantage

• Define mechanical advantage and calculate it for various tools.

Students will learn about mechanical advantage and how to find the mechanical advantage of various tools.

Key Equations

Mechanical Advantage (MA)

MA=dd 21 =FFoutin

d1 is the distance of effort and d2 is the distance the object is moved

Guidance

• Mechanical Advantage is the ability to lift or move objects with great force while utilizing only a little force.
  The trade-off is that you must operate the smaller input force for a large distance. This is all seen through the
  work Equation. Work equals force times distance. Energy is conserved. Thus one can get a large force for a
  small distance equal to a small force for a large distance.


• Mechanical advantage equals the distance of effort divided by the distance the object moves. It is also equal
  to the output force divided by the input force.

Example 1

You need to push a 500 kg grand piano onto a stage that is 3 m above the ground. If you can only apply a maximum
force of 1000 N, what is the minimum distance from the stage that you should begin building your ramp?

Solution

We should start this problem by determining the mechanical advantage required to move the piano based on the

weight of the piano and the force you can apply. We’ll defineFoutto be the force it would take to lift the piano

straight up andFinto be the force you can apply.

MA=

Fout

Fin

MA=

500 kg∗ 9 .8 m/s^2

1000 N

MA=

4900 N

1000 N

MA= 4. 9

Now we can use this to find how long the ramp needs to be.