# A person lifts a 950\ \mathrm{N} box by pushing it up an incline. If the person exerts a force of...

## Question:

A person lifts a {eq}950\ \mathrm{N} {/eq} box by pushing it up an incline. If the person exerts a force of {eq}350\ \mathrm{N} {/eq} along the incline, what is the mechanical advantage of the incline?

## Mechanical Advantage:

Mechanical advantage is a dimensionless quantity that can gauge the efficiency of a machine in terms of force. The mechanical advantage is a ratio between the input force applied to a lever or gear, to the output force produced by the machine itself. For gears, in particular, mechanical advantage can also be expressed as the ratio of the angular velocity of the input gear to the angular velocity of the output gear.

## Answer and Explanation:

Given:

- {eq}\displaystyle \rm F_{out} = 950\ N {/eq} is the output force of the push, since the box is being pushed

- {eq}\displaystyle \rm F_{in} = 350\ N {/eq} is the input force

The mechanical advantage is simply the ratio between the output force and the input force:

{eq}\displaystyle \rm MA = \frac{F_{out}}{F_{in}} {/eq}

We substitute our values:

{eq}\displaystyle \rm MA = \frac{950\ N}{350\ N} {/eq}

We will get:

{eq}\displaystyle \rm \boxed{\rm MA = 2.71} {/eq}

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from Middle School Physical Science: Tutoring Solution

Chapter 1 / Lesson 13