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# Simple Machines

## Calculate ideal and actual mechanical advantage of the six simple machines

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Mass Doesn't Matter

### Mass Doesn’t Matter

Credit: Pierce Martin
Source: http://www.flickr.com/photos/pierce-martin/6718574081/

Every year parents and kids around the United States slide down snow and ice covered hills on plastic or metal sheets. Usually starting with little more than a push, the acceleration of the person on the sled is more dependent upon the angle than the mass of the rider.

#### Amazing But True

• When sliding down an incline, the two forces that are acting on you are those parallel to the incline and those that are perpendicular to the surface of the incline. The forces that are parallel to the surface are: the horizontal component of the force due to gravity pulling you down the incline and the frictional force that is opposing your motion. Perpendicular to the surface is the normal force and the vertical component of the gravitational force.
• Since the person on the sled is on an incline, their normal force is not the standard mg\begin{align*}mg\end{align*}, but mgcosθ\begin{align*}mg \cos \theta\end{align*} instead. Solving for the acceleration of the person on the incline gives the following:

a=g(sinθμcosθ)\begin{align*}a=g(\sin \theta - \mu \cos \theta)\end{align*}

• since the coefficient of friction only depends on the materials that are interacting, it can easily be seen that no mass term is present in the equation. So the next time you are going on a sledding trip, to achieve the greatest acceleration, look to minimize the coefficient of friction or look for a hill with the greatest incline.

#### What Do You Think

Using the information provided above, answer the following questions.

1. How can you prove the above equation for the acceleration is down an incline plain is valid?
2. Why does the normal force on an inclined plane usually only act along one axis while the gravitational force acts along both the x\begin{align*}x\end{align*} and y\begin{align*}y\end{align*} axis?
3. Would the acceleration down an inclined plane be increased or decreased if you were able to decrease the coefficient of kinetic friction?

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