two carts of unequal mass (ma>mb) move on fictionless tracks. Both strat from re

Question

two carts of unequal mass (ma>mb) move on fictionless tracks. Both strat from rest and have the same sonstant force exerted on them untill they reach the finish line. The force begines to be exerted on cart A first. the force starts acting on cart B only as cart A passes it.Both carts reach the finish line at the same time. At the finish, cart B is moving faster cart A. (a) at an instant when both carts have the force exerted on them is, the acceleration of cart A greater than, less than, or equal to the acceleration of cart B?(b) Is the magnitude of the final momentum of cat A greater than, less than or equal to the final momentum of cart B? (c) in the final kinetic energy of cart A greater than, less than, or equal to the final kinetic energy of cart B? Please explain your reasoning.

Explanation / Answer

a)

Force, F = mass(m) * acceleration(a)

So, a = F/m

So, as same force acts on both, so the body which has less mass will have greater acceleration.

As ma > mb , acceleration of A < acceleration of B <-------answer

b)

At finish speed of B (vB) > speed of A (vA)

Now, Force = change of momentum/ time

F = m*v/t <----- as initial momentum = 0

So, mv = F*t

So, final momentum = force*time traveled

As A travels for more time than B under the same force, so final momentum of A > final momentum of B

c)

From Work Energy principle,

Work done = change in Kinetic energy

Now, Work done = F*s

where s = distance traveled

So, change in kinetic enrgy = F*s

Now,distance traveled by A is greater than that of B.

So, final Kinetic energy of A is greater than that of B <---------answer

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