A speed skater with a mass of 80 kg is travelling south at 6.0 ms^-1 when he collides with a se

step 1 Welcome back to Numrod. My name is Kevin Shrock. We have a situation where a 91 kilogram hockey

A speed skater with a mass of 80 kg is travelling south at...

A speed skater with a mass of 80 kg is travelling south at $6.0 \mathrm{~ms}^{-1}$ when he collides with a second skater, who has a mass of 70 kg and is travelling at $3.0 \mathrm{~ms}^{-1}$ in the same direction. After the collision the velocity of the first skater is $4.0 \mathrm{~ms}^{-1}$ south. a How fast does the second skater leave the collision? b Is this an elastic or inelastic collision?

A speed skater with a mass of 80 kg is travelling south at $6.0 \mathrm{~ms}^{-1}$ when he collides with a second skater, who has a mass of 70 kg and is travelling at $3.0 \mathrm{~ms}^{-1}$ in the same direction. After the collision the velocity of the first skater is $4.0 \mathrm{~ms}^{-1}$ south.
a How fast does the second skater leave the collision?
b Is this an elastic or inelastic collision?

Key Concepts

Conservation of Momentum

This principle states that in the absence of external forces, the total momentum of a system remains constant before and after an event such as a collision. It is a fundamental concept in physics, particularly in analyzing collisions, where the combined momentum of the colliding objects must equal the momentum of the system after the collision. In problems involving multiple bodies, momentum conservation is applied separately for each axis when dealing with two-dimensional scenarios, though many collision problems are simplified to one dimension.

Elastic vs Inelastic Collisions

Collisions are categorized based on whether kinetic energy is conserved. In an elastic collision, both momentum and kinetic energy are conserved, meaning no energy is lost to sound, heat, or deformation. In contrast, an inelastic collision is characterized by the loss of some kinetic energy due to factors such as friction, deformation, or heat generation. Identifying the type of collision involves comparing the kinetic energy before and after the impact.

Transcript

00:01 Welcome back to numrod.

00:01 My name is kevin shrock.

00:02 We have a situation where a 91 kilogram hockey player is skating on ice at 5 .5 meters per second.

00:09 Another hockey player of equal mass is moving at 8 .1 meters per second in the same direction hits him from behind and then they slide off together.

00:16 So let's draw a little picture here.

00:17 So we've got that one of these, one of these objects was moving.

00:23 The other object was moving as well.

00:25 There was some kind of collision that occurred and now they're moving off together.

00:31 Right now they both have this velocity that they're traveling with we're being asked what's the total energy and the momentum of the system before the collision for part a so let's start there total energy some of energy initial would be purely in kinetic states right so be the kinetic energy of the first person plus the kinetic energy of the second person which we can say is one half mass of the first person times the velocity of the first person squared plus one half mass of the second person plus the velocity of the second person squared that's then going to be one half times 91.

01:09 Velocity of first person would be at that 5 .5, so it'd be 5 .5 squared, plus one half mass of the second person, which does it provide, let's see, equal mass.

01:23 So that's actually going to be the same one, m2 here.

01:27 Equal mass.

01:27 So now, again, this 91 times the velocity two, which is 8 .1 squared.

01:35 All right, let's take a moment and throw that in the calculator.

01:36 So now we've got 0 .5 times 91.

01:41 Times 5 .5 times 5 .5 and that's going to equal 1376 .4 plus and we'll do the next one.

01:54 0 .5 times 91 times 8 .1 and times 8 .1 again.

02:03 So that'd be plus 2985 .0 .935.

02:08 Okay.

02:09 Combine both those together and we get 4 ,300.

02:19 161 .7 joules of energy.

02:22 So that'll be the sum of all the energy initial.