The figure is a graph of the kinetic energy K of an asteroid...

Name: The figure is a graph of the kinetic energy K of an asteroid versus its distance r from Earth's center, as the asteroid falls directly in toward that center. (a) What is the (approximate) mass of the asteroid? (b) What is its speed at r = 1.945 x 10^7 m? K (10^9 J) 3 2 1 1.75 1.85 1.95 r (10^7 m)
Uploaded: 2022-12-12T20:34:37-08:00
Duration: 8 min 39 s
Channel: Krystal K
Description: The figure is a graph of the kinetic energy K of an asteroid versus its distance r from Earth's center, as the asteroid falls directly in toward that center. (a) What is the (approximate) mass of the asteroid? (b) What is its speed at r = 1.945 x 10^7 m? K (10^9 J) 3 2 1 1.75 1.85 1.95 r (10^7 m)

The figure is a graph of the kinetic energy K of an asteroid versus its distance r from Earth's center, as the asteroid falls directly in toward that center. (a) What is the (approximate) mass of the asteroid? (b) What is its speed at r = 1.945 x 10^7 m? K (10^9 J) 3 2 1 1.75 1.85 1.95 r (10^7 m)

Transcript

00:01 Okay, so you're given a graph of kinetic energy versus the distance to the earth, so to the center of the earth, of an asteroid.

00:10 So at any given distance, there is a certain amount of kinetic energy in the asteroid.

00:17 And so in the first part of the problem, they want us to find the mass based on this information.

00:25 And so you can look at conservation of energy where the kinetic energy at one point plus the gravitational potential energy at one point.

00:41 It's going to be equal to the kinetic energy at another point plus the gravitational energy at that point.

00:53 And so gravitational energy is given by negative g mass of the earth times the mass of the asteroid over the distance.

01:05 So from this graph, we can get two different values of kinetic energy and the corresponding distances.

01:16 So normally kinetic energy is going to be 1 .5 mv squared, but we just have the actual value of the kinetic energy here.

01:25 So first let's choose two different points.

01:30 So we'll say r1 at 1 .85 times 10 of the 7 meters.

01:41 So we'll use that one in the corresponding kinetic energy at that point is going to be 2 .21 approximately times 10 to the 9 joules.

02:01 So for this graph you have some number, right? and so we've got 1 .85 here.

02:17 And we're saying this corresponds to about 2 .21 times, then you have to multiply by times 10 to the 9.

02:24 And the jules is the units.

02:26 Okay.

02:27 And so that's our first point.

02:30 And then the second point we'll say r2.

02:35 And you can do this at any 2.

02:36 Points, it doesn't actually matter, as long as you have the correct corresponding kinetic energies and distances.

02:44 So we'll say at 1 .75 times 10 to the 7 meters, corresponding kinetic energy at that point, this was supposed to be 75.

03:02 So at that point, just going straight up, and we get, on the actual graph, we get something like 3 .41 times 10 to the 9 joules.

03:25 So this graph i have drawn is not exactly to scale, but looking at the actual graph, that's the, about the number that you get.

03:34 Okay, and so we can plug in what we have here.

03:36 And first let's get our kinetic energies on one side and our potential energies on one side.

03:46 So just plugging in the actual equations here.

03:57 So this is g mass of earth times mass of the asteroid over r1 minus.

04:07 This goes we added this one to this side.

04:10 And then minus g m -e -m -a over r2.

04:17 Okay, so now we can plug in the actual values here...

Question

The figure is a graph of the kinetic energy K of an asteroid versus its distance r from Earth's center, as the asteroid falls directly in toward that center. (a) What is the (approximate) mass of the asteroid? (b) What is its speed at r = 1.945 x 10^7 m? K (10^9 J) 3 2 1 1.75 1.85 1.95 r (10^7 m)

Please give Ace some feedback