Question

A 2.8-kg cart is rolling along a frictionless, horizontal track towards a 1.2-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 +4.6 m/s, and the second cart's velocity is -2.7 m/s. (a) What is the total momentum of the system of the two carts at this instant? (b) What was the velocity of the first cart when the second cart was still at rest?

Answer 1

Answer with Explanation:

We are given that

Mass of one cart,$m_1=2.8 kg$

Mass of second cart,$m_2=1.2 kg$

Initial velocity of one cart,$u_1=4.6m/s$

Initial velocity of second cart,$u_2=-2.7 m/s$

a.Total momentum,$P=m_1u_1+m_2u_2=2.8(4.6)+1.2(-2.7)$

$P=9.64 kgm/s$

b.Velocity of second cart,$v_2$=0

According to law of conservation of momentum

Initial momentum=Final momentum

$9.64=2.8v_1+1.2\times 0$

$v_1=\frac{9.64}{2.8}$

$v_1=3.44m/s$