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Chapter 2: Problem 96

Cassie uses a ramp to load a heavy box from the street into a truck. The bed of the truck is \(1.26 \mathrm{~m}\) above the street. If the ramp is \(5.3 \mathrm{~m}\) long, what is the mechanical advantage of the ramp (ignoring friction)? Round your answer to the nearest tenth:

Short Answer

Expert verified
The mechanical advantage of the ramp is 4.2

Step by step solution

01

- Identify Given Values

First, identify the given values. The height of the truck bed above the street is 1.26 meters, and the length of the ramp is 5.3 meters.
02

- Understand Mechanical Advantage Formula

The formula for mechanical advantage (MA) of an inclined plane (ramp) is given by \[ MA = \frac{length \ of \ the \ ramp}{height \ of \ the \ ramp} \]
03

- Substitute the Values

Substitute the given values into the mechanical advantage formula: \[ MA = \frac{5.3 \mathrm{~m}}{1.26 \mathrm{~m}} \]
04

- Calculate the Mechanical Advantage

Divide the length of the ramp by the height of the ramp to find the mechanical advantage: \[ MA = \frac{5.3}{1.26} \approx 4.2 \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

inclined plane
An inclined plane is a flat surface set at an angle to a horizontal surface. It helps move objects up or down with less effort. This concept is central to understanding how ramps work.
Key Points:
  • Reduces the required force to move an object vertically
  • Changes the direction of the effort force
  • Mechanical advantage makes moving heavy objects easier
simple machines
Simple machines are devices that make work easier by changing the direction or magnitude of a force. There are six types of simple machines: the inclined plane, lever, pulley, wheel and axle, screw, and wedge.
Ramps are a prime example of an inclined plane, one of the six simple machines. They help reduce the effort needed to lift objects by extending the distance over which the effort is applied.
  • Reduces the input force needed
  • Uses mechanical advantage to provide an easier way to perform tasks
  • Key in everyday tools and devices
physics calculations
Physics calculations often involve understanding relationships between different physical quantities. In this exercise, we dealt with mechanical advantage.
The mechanical advantage (MA) of an inclined plane is calculated as:
  • Formulated by dividing the ramp length by its height: \[ MA = \frac{length \ of \ the \ ramp}{height \ of \ the \ ramp} \]
  • For a ramp 5.3 meters long and 1.26 meters high, the MA is: \[ MA = \frac{5.3}{1.26} \approx 4.2 \]
This means the ramp makes lifting the box 4.2 times easier.

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