Document Sharing Be sure to review Example 7.13 before...

Document Sharing Be sure to review Example 7.13 before attempting these problems. Part A A small box is released from rest at the top of a frictionless inclined plane as shown in (Figure 1). The horizontal surface at the base of the plane is rough and has a coefficient of kinetic friction $\mu_k = 0.5$. If $H = 30$ m, how far does the box slide on the rough surface before coming to rest, $d$? Express your answer with the appropriate units. Figure 1 of 1 d =

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00:01 Hello, we have the following problem.

00:03 Crate has a mass m and it starts at the rest at the top of the inclined plane with the height of 5 .7 meters.

00:18 It is inclined by the angle of 17 degrees.

00:22 And after letting the object go, it has a final speed v of 0 .45 meters per second.

00:37 Co -efficient of friction of the plane is 0 .1, coefficient of kinetic friction of the horizontal surface is 0 .2.

00:48 And in question a, we have to find speed of the bottom.

00:52 At the bottom, let's do this.

00:54 So let's make a quick sketch.

00:55 Here, gravity is acting downwards.

00:58 Normal reaction is perpendicular.

01:01 Let's show angle theta and friction force is acting as shown here.

01:05 That's why if you label lengths of this flat of this slope as l, then initial potential energy mgh plus work of the friction force equals to 5 kinetic energy at the bottom.

01:20 Then here is wf, work of the friction force is negative, mu kmg, cosine, theta, times l.

01:31 And this l is h 0 over, actually mgh over sine theta.

01:44 It means that this work is negative muk, mg, h, cotangent, theta.

01:52 And now we can express vb, that is square root of 2, g, h times 1, plus minus mu, muc, k cotangenteta...

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