Question

A car and a large truck traveling at the same speed collide head-on and stick together. Which vehicle experiences the larger change in the magnitude of its momentum

Answer 1

Answer:

Both vehicles experience the same change in momentum

Explanation:

Let m represent the mass of the vehicle, and 2m represent the mass of the large truck, and let v represent their initial speed, we have;

The total initial momentum, $p_i$ given as follows;

$p_i$ = 2·m·v - m·v = m·v

The total final momentum, $p_f$ = (2·m + m) × $v_f$

By the principle of conservation of linear momentum, the total initial momentum = The total final momentum

m·v = (2·m + m) × $v_f$

m·v = 3·m·$v_f$

∴ v = 3 × $v_f$

$v_f$ = v/3

The change in the momentum for the large truck = 2·m·v - 2·m·$v_f$

Therefore;

The change in the momentum for the large truck = 2·m·v - 2·m·v/3 = 2·m·(v - v/3)

The change in the momentum for the large truck = 2·m·(v - v/3) = 2·m·2·v/3 =  4·m·v/3

The change in the momentum for the car = m·v - m·(-$v_f$) = m·v - m·(-v)/3 = m·v + m·(v)/3 = 4·m·v/3

Therefore, the change in the momentum for the large truck = The change in the momentum for the car and both vehicles experience the same change in momentum.