Boxes are transported from one location to another in a...

Boxes are transported from one location to another in a warehouse by means of a conveyor belt that moves with a constant speed of 0.50 $\mathrm{m} / \mathrm{s}$ At a certain location the conveyor belt moves for 2.0 $\mathrm{m}$ up an incline that makes an angle of $10^{\circ}$ with the horizontal, then for 2.0 $\mathrm{m}$ horizontally, and finally for 2.0 $\mathrm{m}$ down an incline that makes an angle of $10^{\circ}$ with the horizontal. Assume that a 2.0 $\mathrm{kg}$ box rides on the belt without slipping. At what rate is the force of the conveyor belt doing work on the box as the box moves (a) up the $10^{\circ}$ incline, (b) horizontally, and (c) down the $10^{\circ}$ incline?

Transcript

00:01 All right, so let's say we have a conveyor belt that moves objects up and incline at 10 degrees, and then it travels horizontally, and then goes back down the same sort of incline at 10 degrees.

00:15 And each of these distances are two meters.

00:23 And so we're told that the speed that the conveyor belt moves is half a meter per second.

00:28 Part a, we want to know basically what's the power of the conveyor.

00:31 Your belt does if an object that it's moving has a mass of two kilograms so what's the power done as it moves up the incline so the power is just going to be like the change in potential energy over time and another way of writing this is like the force in the vertical direction times the velocity and so the the force that has to counteract even though it was it a constant velocity of the force of basically the force of gravity times or you know dot product with the velocity times the cosine of the angle between them which will really be like 10 degrees because the the force of gravity is going this way our velocity is going this way so sorry it's going to be the sign of 10 degrees because it's 90 10 degrees plus 90 so it's the sign of 10 so anyway, if we compute this, this is going to be two kilograms times 9 .8 meters per second squared.

01:35 That's the weight and then times the sine of or sorry, times the velocity, so times half a meter per second, and then times the sign of 10.

01:51 And so if we plug those numbers in, we just have 9 .8 times the sign of 10 degrees.

01:57 So this is about 1 .7 watts.

02:02 Part b on the horizontal section, the power is going to be zero because it's not changing the energy...

Question

Please give Ace some feedback