Jogging Jake runs along a train flatcar that moves at the velocities shown. In each case, Jake's

Jogging Jake runs along a train flatcar that moves at the...

Key Concepts

Relative Velocity

Relative velocity is the velocity of an object as observed from a particular reference frame, which may itself be moving. When calculating momentum in different frames, it is crucial to account for the fact that the measured velocity of an object depends on the observer’s frame, so the velocity relative to the moving flatcar is combined with the flatcar's velocity relative to the ground to determine the actual velocity observed from the ground.

Galilean Transformation

Galilean transformation refers to the method used in classical mechanics to relate the coordinates and velocities measured in one inertial frame to those measured in another moving with a constant velocity relative to the first. This concept is applied here to transform Jake's velocity from the flatcar frame to the ground frame, illustrating how the momentum is affected by the relative motion between these frames.

Momentum

Momentum is the product of an object's mass and its velocity. In physics, it is a measure of the motion of an object and is conserved in isolated systems. Here, it is important to understand that while momentum is conserved in closed systems, its value can differ depending on the reference frame from which it is measured.

Reference Frames

A reference frame is the perspective or coordinate system from which an observer measures physical quantities like position, velocity, and momentum. In this problem, different reference frames are considered—the flatcar and the ground—highlighting how the perceived momentum of the same moving object can vary with the observer's frame of reference.

Transcript

00:01 So on this problem, we're going to see jake running on a moving train flight car, and we're going to rank the magnitude of the momentum from greatest to smallest.

00:12 On part a, we're going to do this ranking relative to an observer on the flat car, and on par b, we're going to do it relative to an stationary observer on the ground.

00:24 So let's start with part a, and let's call the momentum.

00:32 For situation one, momentum, 1a over here.

00:47 And we're going to say that the positive side is pointing towards the right.

00:57 So let's start with momentum 1a over here.

00:59 We see that jake is running to the left, so he has a negative velocity.

01:04 Therefore, for an observer on the flat car, all that he sees on jake is his velocity toward his four, meters per second velocity.

01:14 Therefore, the magnitude that is observing is minus 4 mj.

01:22 Since the formula for the momentum is mass times velocity.

01:26 So mj is mass of jake and velocity is minus 4.

01:30 For situation 2, we're going to do momentum momentum to a and we see that jake is moving towards the right, which is the positive side.

01:47 So he has a 6 meter per second velocity therefore the momentum is going to be 6 mj so six times which is the velocity times the mass of jake on part three is again moving towards the right so the velocity is positive once again so the momentum here momentum 3a is going to be 4 meters per second towards the right times the mass of jake for mj.

02:36 And then on the last case over here, we have jake moving towards the left at 6 meters per second.

02:41 So since he's moving towards the left, the velocity is negative.

02:46 The momentum is going to be momentum for a is going to be the mass of jake times minus 6 meters per second, minus 6 mj.

03:10 So now let's do the ranking over here for part a.

03:15 We have the biggest momentum is for 2a, which is 6 times the mass of jake.

03:23 But since we care only about the magnitude of the momentum, we're going to say that for part 2a and for part 4a, we have the same magnitude, which is 6mj.

03:35 So we have 2a is equal to 4a and then these two are both going to be greater than the 4mj magnitude for part 1 and 3.

03:58 So bigger than 1a which is equal to 3a.

04:07 Now for part b, we're going to see a relative to the stationary observer on the ground.

04:13 So the stationary observer over here, he's going to see jake moving to the left at 4 meters per second, but the cart is moving to the right at 8 meters per second.

04:24 So from his point of view, he's going to see jake moving towards the right at 4 meters per second.

04:31 Since it's the 8 meters per second moving towards the right, subtracted by the 4 meters per second of jake moving to the left.

04:41 So then we get momentum 1b is going to be equal to.

04:55 So 8 to the right, 4 to the left, 8 minus 4.

05:00 We get 4.

05:02 So positive for mj.

05:07 Here on part 2, we write the momentum, momentum 2b.

05:18 The observer is going to see jake moving towards the right at 6 meters per second and the cart moving towards the left at 10 meters per second...

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