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An object was thrown at a certain angle to the ground moves in a curved path and falls back to the ground. The initial and the final points of the path of the object lie on the same horizontal line. What is the work done by the force of gravity on the object?
Given:
An object thrown at a certain angle to the ground moves in a curved path and falls back to the ground. The initial and the final points of the path of the object lie on the same horizontal line.
To do:
To calculate the work done by the force of gravity on the object.
Solution:
Before calculating the work done by the force of gravity on the object let us observe the path and the direction of the displacement of the object, and the direction of the force of gravity acting on the object.
Observation of the direction of displacement and the force of gravity:
As given that the object thrown at a certain angle to the ground moves in a curved path and falls back to the ground. the initial and the final points of the path of the object lie on the same horizontal line. So, the displacement of the object is in a horizontal line as shown in the figure below:
While the direction of the force of gravity on the object is vertically downward.
Hence, the angle between the force of gravity and displacement is $90^{\circ}$.
Based on the observation above let us calculate the work done by the force of gravity on the object:
Work done by the force of gravity:
Formula for the work done is:
$\boxed{W=Fd\cos\theta}$
Here, $\theta=90^{\circ}$
Therefore, work done by the force of gravity, $W=Fd\times \cos90^{\circ}$
$=Fd\times 0=0$
Hence, from the above calculation, we can conclude that the work done by the gravitational force on the object is zero.
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