Chapter 10, Problem 7STP

To determine

To Choose: The correct option.

Answer to Problem 7STP

Option D

Explanation of Solution

Given:

Force applied on the box, $F=100.0\text{N}$

Height of the ramp, $h=3.0\text{m}$

Angle of the inclined plane, $\theta =30.0°$

Formula Used:

Work done: $W=F\cdot s$

Here, F is the applied force and s is the length of the ramp.

Trigonometric identity:

  $\sin \theta =\frac{P}{H}$

Where, P is the perpendicular and H is the hypotenuse.

Calculations:

First calculate the length of the ramp using trigonometric identity:

  $\begin{array}{l}\sin \theta =\frac{P}{H}=\frac{h}{s}\\ \Rightarrow s=\frac{h}{\sin \theta }\\ \Rightarrow s=\frac{3.0\text{m}}{\sin 30°}\\ \Rightarrow s=\frac{3.0\text{m}}{0.50}\\ \Rightarrow s=6.0\text{m}\end{array}$

Work done to move the ramp can be calculated as follows:

  $\begin{array}{c}W=F\cdot s\\ W=100.0\text{N}\cdot 6.0\text{m}\\ \text{=600}\text{J}\end{array}$

Conclusion:

Thus, correct option is D.