Consider two bodies, A and B, moving in the same direction with the same kinetic energy. A has a mass twice that of B. If the same retarding force is applied to each, how will the stopping distances of the bodies compare?
(Force)*(stopping distance)
= (work done against the force)
= (initial kinetic energy)
Since the kinetic energies and forces are the same for the two different masses, the stopping distances are the same.
To determine how the stopping distances of bodies A and B compare, we need to understand the relationship between mass, force, and stopping distance.
According to Newton's second law of motion, force is directly proportional to mass and acceleration. In this scenario, both bodies (A and B) experience the same retarding force, so we can assume that the force acting on each body is equal.
The stopping distance of a moving object is affected by two factors: the initial velocity and the deceleration caused by the force opposing its motion. Since both bodies have the same kinetic energy, we can assume they have the same initial velocity.
Therefore, the only difference between bodies A and B is their mass. Since mass is directly proportional to force and acceleration, and the retarding force is the same for both bodies, the only difference in their motion will be the deceleration.
Since body A has twice the mass of body B, it will experience half the acceleration (a = F/m). As a result, body A will take a longer time to come to a stop compared to body B. Since the stopping distance is directly related to the time it takes to come to a stop, body A will have a longer stopping distance than body B.
In conclusion, when the same retarding force is applied to bodies A and B, the stopping distance of body A will be longer than that of body B because of its higher mass.