Question

The table summarizes the known values for a completely elastic collision. Given the information, what is the mass of ball 27 Ball 1 Ball 2 4.3 ? mass (kg) initial velocity (m/s) final velocity (m/s) 2.0 -5.0 0.11 -6.91 7.49 kg

Answer 1

Given,

mass of Ball 1, m₁ = 4.3 kg

initial velocity of Ball 1, u₁ = 2.0 m/s

final velocity of Ball 1, v₁ = –6.91m/s

mass of Ball 2, m₂ = ?

initial velocity of Ball 2, u₂ = –5.0 m/s

final velocity of Ball 2, v₂ = 0.11m/s

In elastic collision, law of conservation of momentum and law of conservation of energy hold.

In elastic collision, final velocities after collision, are v₁ = [ (m₁ – m₂) / (m₁ + m₂) ]u₁ + [ 2m₂ / (m₁ + m₂)] u₂

and v₂ = [ 2m₁ / (m₁ + m₂)] u₁ + [ (m₂ – m₁) / (m₁ + m₂) ]u₂

Let us substitute the given values in the first formula for v₁.

–6.91 = [(4.3 – m₂) / (4.3 + m₂) ]x2 + [ 2m₂ / (4.3 + m₂)]x (–5)

–6.91 = [((4.3 – m₂)x2 – 10m₂ ] / (4.3 + m₂)

–6.91x  (4.3 + m₂) = 8.6 – 2m₂ – 10m₂

  –29.71 – 6.91m₂ = 8.6 – 12m₂

    – 6.91m₂ +12m₂ = 8.6 + 29.71

5.09m₂ = 38.31

m₂ = 7.52 kg

So, the mass of Ball 2 is 7.52 kg