Question

A student is playing marbles. They shoot a 0.05 kg marble at 2 m/s to the right at a 0.02 kg marble that is stationary. They don't move off together, but they both do move off to the right. If the velocity of the larger marble is 1.0 m/s after the collision, what will be the velocity and direction of the smaller marble?

Answer 1

By applying the law of conservation of momentum, we have calculated that the smaller marble's final velocity after the collision is 2.5 m/s to the right.

Step-by-step explanation:

We can find the velocity of the smaller marble after the collision using the law of conservation of momentum, which states that the total momentum before the collision is equal to the total momentum after the collision, assuming no external forces are acting on the system.

Let's denote:

m1 = mass of the larger marble (0.05 kg)

v1 = initial velocity of the larger marble (2 m/s)

m2 = mass of the smaller marble (0.02 kg)

v2 = initial velocity of the smaller marble (0 m/s)

v1' = final velocity of the larger marble (1.0 m/s)

v2' = final velocity of the smaller marble

Using the conservation of momentum:

1. Momentum before collision: (m1 × v1) + (m2 × v2)
2. Momentum after collision: (m1 × v1') + (m2 × v2')
3. Set the total momentum before equal to the total momentum after and solve for v2':
   
   (m1 × v1) + (m2 × v2) = (m1 × v1') + (m2 × v2')
   
   Substitute the known values:
   
   (0.05 kg × 2 m/s) + (0.02 kg × 0 m/s) = (0.05 kg × 1.0 m/s) + (0.02 kg × v2')
   
   Calculate v2':
   
   v2' = ((m1 × v1) - (m1 × v1')) / m2
   
   v2' = ((0.05 kg × 2 m/s) - (0.05 kg × 1.0 m/s)) / 0.02 kg
   
   v2' = (0.1 kg⋅m/s - 0.05 kg⋅m/s) / 0.02 kg
   
   v2' = 2.5 m/s

The smaller marble's final velocity v2' is 2.5 m/s to the right.