The mass of the blue puck in Figure P9.34 is 20.0% greater than the mass of the green puck. Befo

The mass of the blue puck in Figure P9.34 is 20.0% greater...

Key Concepts

Inelastic Collisions

An inelastic collision is one in which kinetic energy is not conserved, even though total momentum remains conserved. In these events, some of the kinetic energy is transformed into other forms of energy, such as internal energy (heat, sound, or deformation), which is critical when analyzing systems where energy loss influences the post-collision speed values.

Kinetic Energy Transformation

In collision analysis, understanding how kinetic energy is transformed during the event is crucial. Not all collisions conserve kinetic energy; in many practical scenarios, a portion of the kinetic energy is converted into other forms of energy, which affects the speeds of the colliding objects post-interaction. This concept helps in identifying the nature of the collision and the resulting energy balance.

Conservation of Linear Momentum

This principle states that in an isolated system, the total linear momentum remains constant before and after any collision, regardless of how the kinetic energy is transformed. It is fundamental in analyzing collisions since it allows one to relate the velocities and masses of objects before and after impact without considering the details of the forces during the collision.

Transcript

00:01 Okay, so here you have one mass moving to the left, let's say, and then another mass that's moving in the opposite direction.

00:15 And you're told, so let's call this mass b, let's call this mass g, because one is blue, one is green, and you're given some sets of information that you can essentially make use of here.

00:33 First thing is that they tell you that the blue mass is 20 % larger than the green mass.

00:39 So we already know that the mass of the blue compared to the mass of the green will give you 1 .2.

00:47 So this is because if this is 20 % larger, it means it's essentially the mass of the green plus 0 .2 mass of the green, which will give you 1 .2 mass of the green.

01:03 So the ratio with their masses is going to be this right here.

01:09 And they tell you that half the kinetic energy that you had before is converted to internal energy.

01:15 So we're not worried about the half that's compared to internal energy.

01:18 We're just going to worry about the half that stays kinetic energy.

01:22 So you know now that ki is equal to 2kf.

01:28 Because if you keep half the kinetic energy to get the initial just multiple about it.

01:32 So that's the second bit of information you have.

01:37 Third bit is that again, actually this vgi is 10 meters per second.

01:44 So that's the third bit of information that you have.

01:47 And then the other, what the other thing they tell you is that their momentum, momentum are equal in magnitude but opposite direction.

01:57 So you can actually immediately start by you looking at that fact.

02:02 So we know that pi always has to be equal to pf.

02:09 We're always going to use that.

02:10 So we'll get us right here.

02:12 But in this case, pi, you're told, since these momentum are the same, but in opposite directions, what that tells you is that pi, which is mbv -b -i plus mgv -g -g -g -i, since these two are the same in magnitude, but you know that the velocity of g is in the opposite direction, which means this value here is actually negative, which would make that negative.

02:45 So if you add these two equal values, you should get zero.

02:51 So this means that pi is actually zero, which means that pf should also be zero.

02:59 So already now you can see where this is going.

03:04 So mbvbf plus mbvgmvgvgf is actually also equal to zero.

03:19 So this is just moving that down here.

03:22 So this can be your equation one essentially to keep that.

03:28 So we have two unknowns here.

03:30 So clearly we need two equations for the velocities in order to find these two unknowns.

03:37 So the next step is to now account for the kinetic energy of the system.

03:44 So we can further simplify this if we want because we know what the ratio of the masses is.

03:51 So we know this is mb, this is mg, that's zero over there.

03:55 So anyway, so if we divide throughout by mg, what we get is, that 1 .2 vbf minus or you can just keep it as a plus in this case because we don't know what direction it's going to go this is going to be vgf and that's equal to zero so this i've used that fact now here to simplify that equation so this is just the same so you can't now go back and plug it in here because the same equation i just simplify a little bit.

04:36 So now let's look at the kinetic energy.

04:38 So you know that this is going to be the governing rule for the energies.

04:43 So essentially you can now calculate ki...

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