Chapter 10, Problem 52A

To determine

Work done by man.

Answer to Problem 52A

  $7.35\text{kJ}$

Explanation of Solution

Given:

Weight of piano, $mg=4200\text{N}$

Ramp length, $d=3.5\text{m}$

Ramp angle, $\theta ={30}^o$

Formula Used:

Work done is given by,

  $W=Fd$    …..    (1)

Where $W$ is work done, $F$ is applied force and $d$ is displacement.

Calculation:

  

Here, component of weight $mg$ along the plane is $mg\sin \theta$ as shown.

As the piano is moved slowly with constant velocity, it means there is no net force parallel to ramp on the piano.

So the force parallel to plane is

  $F=mg\sin \theta$

So, from (1)

  $\begin{array}{l}W=Fd=mg\sin \theta \times d\\ =4200\times \sin {30}^o\times 3.5\\ =7.35\text{kJ}\end{array}$

Conclusion:

Therefore, work done by man in moving the piano is $7.35\text{kJ}$ .