A 4,000 \text{ kg} empty railcar is rolling along a straight, level track at a velocity of… — Armed Services Vocational Aptitude Battery (ASVAB)

A $4,000 \text{ kg}$ empty railcar is rolling along a straight, level track at a velocity of $6 \text{ m/s}$ . It collides and automatically couples with a stationary loaded railcar that has a mass of $8,000 \text{ kg}$ . Assuming no external friction is acting on the railcars, what is the final velocity of the two coupled railcars immediately after the impact?

$2 \text{ m/s}$ Cevap
B
$3 \text{ m/s}$
C
$6 \text{ m/s}$
D
$19.6 \text{ m/s}$

Cevap

The final velocity is

2 \text{ m/s}

By the law of conservation of momentum, the total momentum before the collision equals the total momentum after. The initial momentum is

4,000 \text{ kg} \times 6 \text{ m/s} = 24,000 \text{ kg}\cdot\text{m/s}

. After the railcars couple, the new total mass is

12,000 \text{ kg}

. Dividing the total momentum by the total mass gives a final velocity of

2 \text{ m/s}

Adım Adım Çözüm

Calculate the total initial momentum of the system.

p_{initial} = 4,000 \text{ kg} \times 6 \text{ m/s} = 24,000 \text{ kg}\cdot\text{m/s}

Because momentum is conserved in the collision, finding the total momentum before impact is required.

Determine the total mass of the coupled railcars.

m_{total} = 4,000 \text{ kg} + 8,000 \text{ kg} = 12,000 \text{ kg}

In an inelastic collision where objects couple together, they move as a single combined mass after impact.

Calculate the final velocity using the conserved momentum and total mass.

v_{final} = \frac{24,000 \text{ kg}\cdot\text{m/s}}{12,000 \text{ kg}} = 2 \text{ m/s}

Dividing the total conserved momentum by the new total mass isolates the final velocity of the combined system.

Anahtar Kavram

Conservation of Momentum in Inelastic Collisions

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