Question

Imagine you are ice skating with your BFF. Both of you are at rest in the middle of the ice, when you shove your BFF away from you. You have a mass of 70 kg and your BFF has a mass of 60kg. When you shove off, you are moving with a velocity of 2.5 m/s.
What should the total net momentum be after the push?

Answer 1

Answer:

The total net momentum after the push is 0.

   

Explanation:

The total net momentum is given by:

$p_{f} = p_{1_{f}} + p_{2_{f}} = m_{1}v_{1} + m_{2}v_{2}$

Where:

m₁: is the mass of 70 kg

m₂: is the mass of 60 kg

v₁: is the speed of 2.5 m/s

v₂:?

To find the final momentum first we need to find the speed v₂:

$m_{1}v_{1} + m_{2}v_{2} = p_{i}$  

Where $p_{i}$ is the initial momentum = 0 (they are at rest)          

$v_{2} = -\frac{m_{1}v_{1}}{m_{2}} = -\frac{70 kg*2.5 m/s}{60 kg} = -2.92 m/s$          

The minus sign is because the second person is moving in the opposite direction to the first person.

Now, the total net momentum is:

$p_{f} = m_{1}v_{1} + m_{2}v_{2} = 70 kg*2.5 m/s + 60 kg*(-2.92 m/s) = 0$

The final total momentum (after the push) should be zero because of momentum conservation.

Therefore, the total net momentum after the push is 0.

I hope it helps you!