Question

1. an ant sits on the back of a mouse. the mouse carries the ant across the floor for 10 meters. was there any work done by the mouse?

yes, because distance was covered
no, because the force was vertical and the motion was horizontal
yes, because the mouse exerted a vertical force
no, because the ant has no weight

Explanation:

Step1: Recall the work formula

Work \(W = F\times d\times\cos\theta\), where \(F\) is the force, \(d\) is the displacement, and \(\theta\) is the angle between the force and the displacement.

Step2: Analyze the forces and motion

The mouse is carrying the ant horizontally. The force exerted by the mouse to support the ant's weight is vertical (\(F = mg\), acting upward). The displacement \(d = 10\space m\) is horizontal. So, \(\theta=90^{\circ}\) and \(\cos\theta=\cos90^{\circ} = 0\).

Step3: Calculate the work

Substituting into the work formula \(W = F\times d\times\cos\theta\), we get \(W = F\times10\times0=0\).

Answer:

No, because the force was vertical and the motion was horizontal.