Question

A child is riding in a wagon. The wagon has a mass of 8.25 kg, and the child has a mass of 35.25 kg. The wagon (with the child in it) has a velocity of 2.5 m/s. What is the momentum of the system?
Assume that through science (or magic) that you have the ability to add a second, identical child to the child-wagon system. What would be the new velocity of the wagon and the two children?

Answer 1

Answer:

i) 108.75 kg.m/s

ii) 1.38 m/s (approx.)

Explanation:

Given:

• Velocity of the wagon (v) = 2.5 m/s

• Mass of the wagon = 8.25 kg

• Mass of the child = 35.25 kg

So, the combined mass of the child and the wagon (m) = 8.25 + 35.25 = 43.5 kg

To find:

i) Momentum of the system (p)

ii) Velocity of the wagon with 2 identical children

Method to find:

i) p = mv

⇒ p = 43.5 * 2.5

⇒ p = 108.75 kg.m/s

ii) Since there was no additional force applied, the momentum of the wagon will be the same as before, even with 1 additional child.

Mass of the new wagon (m) = 43.5 + 35.25 = 78.75 kg

Momentum of the new wagon (p) = same as before = 108.75 kg m/s

So, the velocity (v) of the new wagon will be:

p = mv

⇒ 108.75 = 78.75 * v

⇒ v = 108.75 / 78.75

⇒ v = 1.38095238095 ≈ 1.38 m/s

Hope it helps!