Question

A larger, faster-moving 20 kg mass strikes a slower, smaller moving mass, having a momentum of 99 kg m/s, from behind and then slows to 4 m/s and while the smaller mass now has a momentum of 47 kg m/s. What was the original velocity of the larger mass?

Answer 1

The original velocity of the larger mass was 1.4 m/s. This was calculated using the law of conservation of momentum by equating the total initial momentum with the final total momentum, and solving for the unknown initial velocity.

Step-by-step explanation:

To determine the original velocity of the larger mass in this physics problem, we can use the law of conservation of momentum. According to this law, the total momentum before the collision must equal the total momentum after the collision, assuming no external forces act on the system. We have a system of two objects where the first object (larger mass) has an unknown initial velocity and a mass of 20 kg; the second object (smaller mass) has a momentum of 99 kg·m/s.

Let's denote the initial velocity of the larger mass as V1,i and its final velocity after the collision as V1,f. We know V1,f is 4 m/s. The momentum of the smaller mass after the collision is given as 47 kg·m/s.

Using the conservation of momentum:

• Initial total momentum = Final total momentum
• (20 kg × V1,i) + 99 kg·m/s = (20 kg × 4 m/s) + 47 kg·m/s
• 20 kg·V1,i = 80 kg·m/s + 47 kg·m/s - 99 kg·m/s
• 20 kg·V1,i = 28 kg·m/s
• V1,i = (28 kg·m/s) / 20 kg
• V1,i = 1.4 m/s

So, the original velocity of the larger mass was 1.4 m/s.