Chapter 4.1, Problem 7PP

To determine

To calculate: the efficiency of the ramp.

Answer to Problem 7PP

The efficiency of the ramp is $\underset{\_}{50\%}$ .

Explanation of Solution

Given data:

Input work on the crate, $W_{in}=8000\text{ J}$

Weight of crate, $F=2000\text{ N}$

Height of the ramp, $d=2\text{ m}$

Formula used:

• Work Equation:

  $W=Fd$

Where $W$ is work in joules, $F$ is the applied force in newton and $d$ is the distance moved by the object in meters

• Efficiency Equation:

  $e=\frac{W_{out}}{W_{in}}\times 100$

Where $e$ is efficiency of machine (as percentage), $W_{in}$ is the input work in joules and $W_{out}$ is the output work in joules.

Calculation:

As per the problem,

Weight of crate, $F=2000\text{ N}$

Height of the ramp, $d=2\text{ m}$

To calculate the output work, substitute the values of force and distance in the work equation:

  $\begin{array}{l}{W}_{out}=Fd\\ W_{out}=(2000\text{ N)(2 m)}\\ W_{out}=4000\text{ J}\end{array}$

Now, $W_{in}=8000\text{ J}$

Substitute the values of input and output work in the efficiency equation:

  $\begin{array}{l}e=\frac{W_{out}}{W_{in}}\times 100\\ e=\frac{4000\text{ J}}{8000\text{ J}}\times 100\\ e=50\%\end{array}$

Conclusion:

The efficiency of the ramp is $\underset{\_}{50\%}$ .