Question

A 500 kg train car (Car 1) is traveling at 25 m/s when it hits and attaches to another 750 kg train car (Car 2) that is at rest. Find (1) the resulting velocity of both train cars after they hit and (2) the momentum of the train cars before and after they attach.

Answer 1

(1) The resulting velocity of both train cars after they hit is 10 m/s.

(2) The momentum of the first train before and after collision is 12,500 kgm/s and 5,000 kgm/s respectively.

• The momentum of the second train before and after collision is 0 kgm/s and 7,500 kgm/s respectively.

The given parameters;

• mass of the first train, m₁ = 500 kg

• initial velocity of the train, u₁ = 25 m/s

• mass of the second the train, m₂ = 750 kg

• initial velocity of the second train, u₂ = 0

(1)

The final velocity of the both trains after the collision is obtained  by applying the principle of conservation of linear momentum for inelastic collision.

m₁u₁ + m₂u₂ = v(m₁ + m₂)

where;

v is the final velocity of the two trains after collision.

The resulting velocity of both train cars after they hit is calculated as

(500 x 25) + (750 x 0) = v(500 + 750)

12500 = 1250v

$v = \frac{12500}{1250} \\\\v = 10 \ m/s$

(2)

The momentum of the first train before collision;

$P_1 = m_1 u_1\\\\P_1 = 500 \times 25\\\\P_1 = 12500 \ kg.m/s$

The momentum of the first train after collision;

$P_1_f = m_1 v\\\\P_1_f = 500 \times 10\\\\P_1_f = 5,000 \ kg.m/s$

The momentum of the second train before collision;

$P_2 = m_2 u_2\\\\P_2 = 750 \times 0\\\\P_2 = 0 \ kg.m/s$

The momentum of the second train after collision;

$P_2_f = m_2 v\\\\P_2_f = 750 \times 10\\\\P_2_f = 7,500 \ kg.m/s$

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