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

Sliding down snow and ice covered hills on plastic sheets is a popular recreation during the winter. The first step is to provide an initial velocity to the sled, which can be done with a little push. The acceleration of the person on the sled is dependent on the angle of the incline, not on the mass of the rider as most would assume.

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.

Credit: Flickr: Eden, Janine and Jim
Source: http://www.flickr.com/photos/10485077@N06/5294837172

Sliding down hills with a greater incline will result in a greater acceleration [Figure2]

• Since the person on the sled is on an incline, his normal force is mgcosθ\begin{align*}mg \cos \theta\end{align*} not  mg\begin{align*}mg\end{align*}. 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 only the materials that are interacting, it can easily be seen that no mass term is present in the equation. Next time when you are going on a sledding trip, remember to minimize the coefficient of friction and look for a hill with the greatest incline for the greatest acceleration.

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 inclined plane 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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