Chapter 9, Problem 2A

Work is required to lift a barbell. How many times more work is required to lift the bar-bell three times as high?

To determine

The amount of work done compared to initial case.

Answer to Problem 2A

Three times more work has to be done.

Explanation of Solution

Given :

Height in first case is, $h_1=h$

Height in second case is, $h_2=3h$

Formula used :

According to work energy theorem wok done is equal to change in potential energy.

  $W=mgh$

Where, W is work done, m is mass and h is vertical distance.

Calculation :

Let the mass of barbell is m .

Acceleration due to gravity, $g=9.8{\text{ m/s}}^2$

Now, in first case substituting the value of m , g and h and solve.

  $\begin{array}{l}{W}_1=m\times 9.8\times h\\ =9.8mh\text{ J}\end{array}$

Now, in second case substituting the value of m , g and h and solve.

  $\begin{array}{l}{W}_2=m\times 9.8\times 3h\\ =3\times 9.8mh\text{ J}\\ \text{=3}{W}_1\text{ J}\end{array}$

Conclusion :

Therefore, to lift the barbell three times high, 3 times more work has to be done.