a man m is at rest on a stationary flat car. the car can move without friction along horizontal rails. The man starts walking with velocity v relative to the car, work done by him is
To find the work done by the man, we first need to understand the concept of work.
Work is defined as the product of force and displacement, both of which are vectors. Mathematically, work (W) is given by the equation:
W = F ⋅ d,
where F is the force applied and d is the displacement vector.
In this case, the man is walking with a velocity v relative to the car. Since velocity is a vector quantity, we can represent it as v in the direction of the man's motion.
Now, when a person walks, their motion is the result of the force exerted by their legs against the ground. This force is equal in magnitude but opposite in direction to the frictional force between the person's feet and the ground. Thus, the force exerted by the man can be represented as F = -f (negative sign indicates the opposite direction to the motion).
Since the man is walking on the stationary car, there is no external force acting on him apart from friction. Therefore, the force exerted by the man balances the frictional force, resulting in zero net force.
Since there is no net force, the displacement of the man (d) is also zero. Hence, the work done by the man is given by:
W = F ⋅ d = (-f) ⋅ (0) = 0.
Thus, the work done by the man in this scenario is zero.