Question

A lawn roller is pulled along a horizontal surface through a distance of 20 m by a rope with a force of 200 N. If the rope makes an angle of \[60{}^\circ \]with the horizontal while pulling, the amount of work done by the pulling force is:
A. 4000 J
B. 1000 J
C. \[2000\sqrt{3}\,\text{J}\]
D. 2000 J

Answer 1

Hint: This question can be easily solved by making use of the free body diagram of the system consisting of the lawn roller and the forces acting on it. The work done is the product of the force acting on the body and its displacement. Thus, we will multiply the horizontal component of the force with the displacement to obtain the value of the amount of work done by the pulling force.

Complete step by step solution:
The free-body diagram of the system consisting of the lawn roller and the forces acting on it is drawn as follows.

In this diagram, the horizontal component of the force is represented, as, when the lawn roller is pulled along a horizontal surface, the horizontal component of the force acts on it. The term ‘S’ represents the distance covered by the lawn roller when pulled by the rope.
Now, we will compute the work done by the pulling force for pulling the lawn roller horizontally. The equation for the same is given as follows.
\[W=F.S\]
The horizontal component of the force acts on the lawn roller. Thus, the above equation of the work done can be represented as follows.
\[W=F\cos \theta .S\]
Now, substitute the given values in the above equation.
\[\begin{align}
  & W=200\cos 60{}^\circ \times 20 \\
 & W=200\times \dfrac{1}{2}\times 20 \\
\end{align}\]
Continue the further calculation.
\[\begin{align}
  & W=100\times 1\times 20 \\
 & W=2000\, \\
\end{align}\]
\[\therefore \] The amount of work done by the pulling force is 2000 J.
As, the amount of work done by the pulling force equals the value of 2000 J, thus, option (D) is correct.

Note: This question is a direct one. But, we have made use of the free body diagram to get a clear understanding of the components of the force acting on the body. So, by solving the problems by drawing a free body diagram of the given system, we can understand the concept clearly. The units of the parameters should be taken care of.