Question

An ant sits on the back of a mouse. The mouse carries the ant across the floor for a distance of 10 m. Was there work done by the mouse? Explain

Answer 1

Here we need to tell about the work done. Remember work is a scalar quantity and it is given as the dot product of the force acting on the body and the displacement of the body during the course of time.

Step by step answer: Given ant sits on the back of the mouse. The mouse walks. The only force acting on the ant is the gravitational force of the earth which acts in the downward direction and the displacement of the ant is in the horizontal direction.
Dot product or scalar product of two vectors is given by $\overrightarrow{A}.\overrightarrow{B}=AB\cos \alpha$
Where $\alpha$ is the angle between the two vectors. Here the angle between the force and the displacement is equal to $90{}^\circ$.
If both the vectors are not equal to zero then the only way that the dot product of two vectors is equal to zero is making cos$\alpha$equal to zero.
We know the value of cos for this angle is zero and hence the dot product comes out to be zero. As work is a dot product of force and displacement and in this case the angle between them is 90 degree. So, the work done is equal to zero.

Note: While taking either dot product or cross product we have to keep in mind we have to take the angle between the two original vectors. The work is a scalar quantity because the dot product gives a scalar result.