Chapter 4, Problem 5STP

To determine

To Choose: The correct option.

Answer to Problem 5STP

The height by which the box should be raised is $\underset{\_}{3.5\text{ m}}$ , so option A is the correct answer.

Explanation of Solution

Given data:

Mass of the box, $m=10\text{ kg}$

Gravitational potential energy, $GPE\text{=350}\text{J}$

Gravity, $g\text{ = 9}\text{.8}\text{}\text{}\text{ N/kg}$

Formula used:

Gravitational Potential Energy Equation:

  $GPE=mgh$

Where $GPE$ is the gravitational potential energy of the object in joules, $m$ is the mass of the object in $\text{kg}$ and $h$ is the height of the object in meters from the ground.

Calculation:

As per the problem,

  $\begin{array}{l}m=10\text{ kg}\\ g\text{= 9}\text{.8}\text{}\text{}\text{ N/kg}\\ GPE\text{=350}\text{J}\end{array}$

Substitute the values of mass, gravity and gravitational potential energy in the rearranged gravitational potential energy equation to get height:

  $\begin{array}{l}GPE=mgh\\ h=\frac{GPE}{mg}\\ h=\frac{350\text{ J}}{(10\text{ kg)(9}\text{.8 N/kg)}}\\ h=3.57\text{ m}\approx \text{3}\text{.5 m}\end{array}$

Conclusion:

The height by which the box should be raised is $\underset{\_}{3.5\text{ m}}$ , so option A is the correct answer.