Question

Suppose Mitch Marner (mass=80kg) and Zdano Chara (mass=116kg) collide head-on at the blue line when Marner is skating 10m/s and Chara is standing still. Whose velocity would change more and Why?

Answer 1

Answer:

1) The person whose velocity changes more is Marner

2) The change in velocity of Marner is more than the change in velocity of Chara because Chara has more mass than Marner

Explanation:

The given information are

The mass of Mitch Marner = 80 kg

The mass of Zdano Chara = 116 kg

Marner's skating speed before the collision = 10 m/s

From the principle of conservation of linear momentum, we have;

Total initial momentum before the collision = Total final momentum after the collision

m₁×u₁ + m₂×u₂ = m₁×v₁ + m₂×v₂

Where;

m₁ = The mass of Mitch Marner = 80 kg

m₂ = The mass of Zdano Chara = 116 kg

u₁ = The initial velocity of Mitch Marner = 10 m/s

u₂ = The initial velocity of Zdano Chara = 0 m/s

v₁ = The final velocity of Mitch Marner

v₂ = The final velocity of Zdano Chara

Given that the collision is head on, they can be assumed to have an equal instantaneous velocity immediately after collision, therefore;

v₁ = v₂ = v

We have;

m₁×u₁ + m₂×u₂ = (m₁ + m₂) × v₂

By substituting the values, we have;

80 × 10 + 110 × 0 = (80 + 110) × v = 190 × v

Which gives;

80 × 10 + 110 × 0 = 190 × v

800 = 190 × v

v = 800/190 =  80/19 = $4\frac{4}{19} \ m/s$

Therefore the instantaneous final velocity of both Marner and Chara is $4\frac{4}{19} \ m/s$

The change in velocity of Marner = $10 - 4\frac{4}{19} = 5\frac{15}{19} \ m/s$

The change in velocity of Chara = $4\frac{4}{19} - 0 = 4\frac{4}{19} \ m/s$

Therefore;

1) The person whose velocity changes more is Marner

2) The reason is because the ratio of her mass to the combined mass of both of them is less than the ratio of the Chara;s mass to the combined mass of them both

Which means that the change in velocity of Marner is more than the change in velocity of Chara because Chara has more mass than Marner.