Question

# A 2.9-kg cart is rolling across a frictionless, horizontal track toward a 1.4-kg cart that is...

A 2.9-kg cart is rolling across a frictionless, horizontal track toward a 1.4-kg cart that is held initially at rest. The carts are loaded with strong magnets that cause them to attract one another. Thus, the speed of each cart increases. At a certain instant before the carts collide, the first cart's velocity is +4.3 m/s, and the second cart's velocity is −1.9 m/s.

(a) What is the total momentum of the system of the two carts at this instant?
kg · m/s

(b) What was the velocity of the first cart when the second cart was still at rest?
m/s

here,

mass of cart 1 , m1 = 2.9 kg

mass of cart 2 , m2 = 1.4 kg

intial speed of 1 , u1 = 4.3 m/s

initial speed of 2 , u2 = - 1.9 m/s

a)

the total momentum of the system of the two carts at this instant , Pi = m1 * u1 + m2 * u2

Pi = 2.9 * 4.3 - 1.4 * 1.9 kg.m/s

Pi = 9.81 kg.m/s

b)

let the final speed of cart 1 after the collison be v1

using conservation of momentum

Pi = Pf

9.81 = 2.9 * v1

solving for v1

v1 = 3.38 m/s

the final speed of cart 1 after the collison is 3.38 m/s

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