Physics doubt - Work

Question

The work is 0 when force acts in the perpendicular direction, because F . S cos 90 = 0. But WHY is it so?? What is the reason? Say, for instance a ball is rolling and I put my leg on it to stop it and apply the force in the perpendicular direction, so does it mean the rolling ball wont stop regardless of my foot on it?

Answer 1

If the ball was frictionless with your foot and the floor - you would have no effect on the ball if you push perpendicular to the floor and the ball's motion. If there is friction, than there will be a force (proportional to the force you exert downwards) that will act opposite to the direction of motion of the ball and negative work will be done (the ball will lose kinetic energy).

It is a definition of work that it is force acting in the direction of the displacement of the body times that displacement. This is largely because the net work will cause a change in kinetic energy. There is no net work when there is no net force, no displacement, or force perpendicular to the displacement. The best example of the last condition is circular orbits where the gravitational force turns the body, but does not increase its speed (kinetic energy) because the force is always perpendicular to the direction of motion.

Answer 2

You

 

TUTOR

 When you stop a moving ball in the way you describe, it isn't the perpendicular component of the force of your foot that stops it - it's the force of friction from the floor and also sideways (parallel) friction from the sole of your shoe. The perpendicular component of the force from your shoe simply increases the amount of normal force between the ball and the floor, increasing the friction from the floor and producing sideways friction from your shoe. These frictions produce torques that almost instantly stop the ball from rolling - and when the ball stops rolling it stops moving forward.