Question
Question: A lawn roller is pulled along a horizontal surface through a distance of 20 m by a rope with a force...
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∘with the horizontal while pulling, the amount of work done by the pulling force is:
A. 4000 J
B. 1000 J
C. 20003J
D. 2000 J
Solution
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=Fcosθ.S
Now, substitute the given values in the above equation.