Question

Two carts are on an air-track where friction is negligible. The Incident Cart is moving at an initial velocity of 0.44374 m/s, the target cart is at rest. The Incident cart has a mass of 490.3 g and the target cart has a mass of 497.4 g. The final velocity of the incident cart is 0.043994 m/s and the final velocity of the target cart is 0.001001 m/s. The collision is elastic.

a) What is the Initial Momentum of the carts?

b) What is the Final Momentum of the carts?

c) What is the Initial Kinetic Energy of the carts?

d) What is the Final Kinetic Energy of the carts?

Please show the formula used.

Answer 1

here,

mass of incident car , m1 = 490.3 g = 0.4903 kg

mass of target cart , m2 = 497.4 g = 0.4974 kg

initial speed of incident cart , u1 =0.44374 m/s

final speed of incident cart , v1 = 0.043994 m/s

final speed of target cart , v2 = 0.001001 m/s

a)

the Initial Momentum of the carts , Pi = m1 * u1

Pi = 0.4903 * 0.44374 Kg.m/s = 0.22 kg.m/s

b)

the final momentum of carts , Pf = m1 * v1 + m2 * v2

Pf = 0.4903 * 0.043994 + 0.4974 * 0.001001 kg.m/s = 0.022 kg.m/s

c)

the initial kinetic energy , KEi = 0.5 * m1 * u1^2

KEi = 0.5 * 0.4903 * 0.44374^2 = 0.049 J

d)

the final kientic energy , KEf = 0.5 * m1 * v1^2 + 0.5 * m2 * v2^2

Kef = 0.5 * 0.4903 * 0.043994^2 + 0.5 * 0.4974 * 0.001001^2 = 4.75 * 10^-4 J