Question

Cart C is moving to the right at 3 m/s toward cart D, which is at rest. The cart collide in an elastic collision, and after the collision cart D is moving to the right at 2.4 m/s. The mass of cart C is 2kg and the mass of cart D is a 3kg.

What is the total momentum of the cart C + cart D system before the collision?

What is the speed and direction of cart C after the collision?

What is the change in kinetic energy of the cart D and how much work was done on cart D by cart C during the collision?

If cart D moved a distance of 0.5 cm while cart C was in contact with it, what average force did cart C apply ti cart D while they were in contact?

Answer 1

here,

mass of cart C , mC = 2 kg

mass of cart D , mD = 3 kg

initial speed of cart C , uC = 3 m/s

final speed of cart D , vD = 2.4 m/s

the total momentum of the cart C + cart D system before the collision , Pi = mC * uC + mD * uD

Pi = 2 * 3 + 0 kg.m/s

Pi = 6 kg.m/s

let the speed of cart C after the collison be vC

using conservation of momentum

Pi = Pf

Pi = mC * vC + mD * vD

6 = 2 * vC + 3 * 2.4

vC = - 0.6 m/s

the speed of block C is 0.6 m/s and to the LEFT

the change in kinetic energy of the cart D , KEd = 0.5 * mD * ( vD^2 - uD^2)

KEd = 0.5 * 3 * ( 2.4^2 - 0) = 8.64 J

using Work energy theorm

the work done on cart D by cart C , Wd = KEd = 8.64 J

s = 0.5 cm = 0.005 m

the average force exerted , F = Wd /s

F = 8.64 /0.005 N = 1728 N