A block of mass m 05 kg starts to slide from rest at the top...

A block of mass m = 0.5 kg starts to slide from rest at the top A of a curved track at a height h = 4 m. There is no friction between the block and the track between points A and B. Then the block slides along the 4.0 m horizontal surface a distance d before coming to rest at C. The coefficient of kinetic friction on the horizontal surface between points B and C is Î¼ = 0.3 (g = 10 m/s^2). 1- Calculate the total energy of the block at point A. 2- Determine the speed of the block at point B. 3- Find the distance d between the points B and C.

Transcript

00:01 All right, hello, in this question we're given this setup.

00:02 We have a block sitting on top of a ramp that is four meters tall and is a frictionless ramp that it can slide down and it gets to the bottom at point b.

00:10 And then it hits a rough patch with a coefficient of friction of 0 .3 and it's going to travel four meters before coming to a stop.

00:16 We're asked various things about this.

00:17 The first is calculate the total energy of the block at point a.

00:20 So my energy at point a, well, i'm told that it's not moving.

00:24 It starts from rest.

00:25 So i know all i'm going to have is gravitational potential and i know that's going to be mgh.

00:30 In this case, i have all those values so i can go ahead and plug them in.

00:35 If i do that, i'm going to get that i have a total energy of 20 joules at point a.

00:40 Part two says determine the speed of the block at point b.

00:45 So when it gets down here to point b, it's going to be moving to the right with some speed, vb.

00:50 We're going to figure out what that is.

00:51 Well, i know that my energy at a is going to equal my energy at b because there's no friction involved.

00:57 It's just conservative forces.

00:58 Just have a conservation of energy question.

01:01 Well, my energy at a i found before and i know that my energy at b is going to be all kinetic energy because it's at the bottom.

01:08 So it's going to be one half m times vb squared.

01:11 So vb is going to be two times my energy divided by my mass and i want to take the square root of that.

01:18 Go ahead and plug in those values and i'll get that my speed at point b is going to be 8 .94 meters per second.

01:26 We're then told, i drew this a little incorrectly.

01:29 We're then told that the block slides along this four meter long thing, but at some point in there it is going to come to rest at point c before it hits the end of that four meters.

01:41 So we want to figure out once it hits this rough patch, what is the distance d, i'll call it big d, that it needs to travel before it comes to a stop.

01:50 So in order to do this, we have a couple options.

01:52 I'm going to opt to use work here...

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