A mass of 10 kg is at a point A on a table. It is moved to a point B. If the line joining A and B is horizontal, what is the work done on the object by the gravitational force? Explain your answer.
Given:
A mass of 10 kg is at point A on a table. It is moved to point B.
To do:
To find out the work done on the object by the gravitational force if the line joining A and B is horizontal.
Solution:
Let us know a little about the work done and its formula before finding out the work done on the given object to move from A to bB horizontally from A to B by the gravitational force:
Work done:
When a force acts upon an object and the object is moved in a certain direction, it is said to be the work done by the force.
Formula for the work done:
$\boxed{W=Fd\cos\theta}$
Here, $W\rightarrow$ work done
$F\rightarrow$ Force acted upon the object
$d\rightarrow$ displacement of the object
$\theta$ Angle between the force and the displacement
Work done by the gravitational force to move the object:
It can be seen clearly in the diagram given below that a mass of $10\ kg$ is placed over a table and it is moved from point A to point B. The joining line AB is horizontal and the weight or gravitational force$(mgh)$ is vertical.
The gravitational force and displacement are perpendicular to each other.
Therefore, the angle between the gravitational force and the displacement, $\theta=90^{\circ}$
Therefore, work done $W=Fd\cos\theta$
Or $W=mgh\times AB\times \cos90^{\circ}$
Or $W=0$ [$\because \cos90^{\circ}=0$]
Therefore, the work done by the gravitational force is zero.
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