The 50-lb crate slides down the curved path in the vertical...

The 50-lb crate slides down the curved path in the vertical plane. If the crate has a velocity of 6.2 ft/sec down the incline at A and a velocity of 30.2 ft/sec at B, compute the work $U_f$ done on the crate by friction during the motion from A to B.

Transcript

00:02 Okay, a little vector application here in problem number 41.

00:08 Basically, what we want to do is figure out how much work is required to drag that cart 30 or that crate 30 feet as you see it in the diagram there.

00:22 Now, it's, imagine it's like pulling a wagon, right? the you're walking along pulling a wagon the handle is angled towards the wagon yet the wagon is rolling horizontally same kind of thing here okay we're applying 50 pounds of force and dragging that crate however it's in an upward angle of 30 degrees what we need to compute the work is we need the horizontal force components because that's the direction that the crate is being dragged.

01:01 So we need to figure out the magnitude of that vector there that you just, that you see in yellow.

01:09 And that's easy enough to do because we're very graciously given a 30 degree angle.

01:15 And we can just use our knowledge of the 30, 60, 90 right triangle to come up with that horizontal component.

01:24 And then, of course, when we're ready to compute it, work is just a force times distance.

01:31 And we have the distance.

01:33 It's 30 feet.

01:34 We just need to get that horizontal component for the force, which is easy enough to do again.

01:40 Let's just look at it like this.

01:42 Let's call it a 30, 6090 right triangle where the hypotenuse is 50.

01:48 We know that the short leg is half of the hypotenuse...

Question

The 50-lb crate slides down the curved path in the vertical plane. If the crate has a velocity of 6.2 ft/sec down the incline at A and a velocity of 30.2 ft/sec at B, compute the work $U_f$ done on the crate by friction during the motion from A to B.

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