Chapter SH, Problem 4.7APP

To determine

To calculate: Efficiency of a ramp.

Answer to Problem 4.7APP

Efficiency of the ramp is approximately $\underset{\_}{82\%}$ .

Explanation of Solution

Given:

Length of the ramp = $3\text{ m}$

Height of the ramp = $\text{1 m}$ .

Mass of the box = $\text{20 kg}$

Input force = $\text{80 N}$

Formula used:

Efficiency is given by,

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

Where $W_{\text{out}}$ is output work and $W_{\text{in}}$ is input work.

Force is given by,

  $F=mg$

Where m is mass and $g=9.8\text{ N/kg}$ is acceleration due to gravity.

Work done is given by,

  $W=Fd$

Where F is force and d is distance.

Calculation:

Output force is calculated as:

  $\begin{array}{l}{F}_{\text{out}}=mg\\ F_{\text{out}}=\left(20\text{ kg}\right)\left(9.8\text{ N/kg}\right)\\ F_{\text{out}}=196\text{ N}\end{array}$

Output work calculated as:

  $\begin{array}{l}{W}_{\text{out}}=F_{\text{out}}d\\ W_{\text{out}}=\left(196\text{ N}\right)\left(\text{1 m}\right)\\ W_{\text{out}}=196\text{ J}\end{array}$

Input work is calculated as:

  $\begin{array}{l}{W}_{\text{in}}=F_{\text{in}}d\\ W_{\text{in}}=\left(\text{80 N}\right)\left(3\text{ m}\right)\\ W_{\text{in}}=240\text{ J}\end{array}$

Efficiency is calculated as:

  $\begin{array}{l}e=\frac{W_{\text{out}}}{W_{\text{in}}}\times 100\\ e=\frac{196\text{ J}}{240\text{ J}}\times 100\\ e\approx 82\%\end{array}$

Conclusion:

Efficiency of the ramp is approximately $\underset{\_}{82\%}$ .