How to Calculate the Mass of the Second Skater in a Skating Duo?

[Workout]

Homework Statement

A 62-kg ice skater pushes off his partner and accelerates backwards at 1.8m/s2. If the partner accelerates in the opposite direction at 2.1m/s2, what is the mass of the other skater? Assume that frictional forces are negligible.

Homework Equations

F=ma

The Attempt at a Solution

Okay so I found the force the 62kg ice skater exerted. I subtracted the two accelerations and arrived at a -0.3 m/s^2 acceleration from the 62kg ice skater. So I plugged in:

F = (62kg)(-0.3m/s^2)
So the force exerted by the 62kg person is -18.6N. I don't really know where to go from there? I played around with the equation a bit but I can't seem to get anything remotely close to figuring the mass out of the second skater.

Like I'll put the equation as F+18.6N = (m)(0.3m/s^2) But then I'll have two unknowns but not two equations so it just doesn't work out.

 

[Weissritter]

In this case, the same quantity of force applies to both guys. In different direction, tough. This works like Pascal's principle, or the sum of kinetic and potential energy of an object.
So, right here, only considering the quantities of force, F₁=F₂. You can break force into mass and acceleration both as scalar magnitudes. Try it from here.

 

[howie8594]

Since both skaters are at rest before they push each other, the net force equals 0.

net F=ma.

You can set the forces equal to each other in terms of mass and acceleration and you should only have one unknown, the mass of the second skater.

 

[Workout]

Thank you Howie!

 

[Nickie]

I would first confirm that your calculations for the force exerted by the 62kg skater are correct. It seems like you may have made a calculation error, as the force should be positive since the skater is pushing in the opposite direction of their acceleration.

Assuming that the force is actually 18.6N, we can use Newton's Second Law (F=ma) to solve for the mass of the other skater. Since we know the acceleration and force applied, we can rearrange the equation to solve for mass:

m = F/a
m = 18.6N / 2.1m/s^2
m = 8.86 kg

Therefore, the mass of the other skater is approximately 8.86 kg. This makes sense, as the other skater is accelerating at a faster rate than the 62kg skater, indicating that they likely have a smaller mass.