You are designing a simple elevator system for an old...

You are designing a simple elevator system for an old warehouse that is being converted to loft apartments. A 22,500-N elevator is to be accelerated upward by connecting it to a counterweight by means of a light (but strong!) cable passing over a solid uniform disk-shaped pulley. The cable does not slip where it is in contact with the surface of the pulley. There is no appreciable friction at the axle of the pulley, but its mass is 875 kg and it is 1.50 m in diameter. (a) What mass should the counterweight have so that it will accelerate the elevator upward through 6.75 m in the first 3.00 s, starting from rest? (b) What is the tension in the cable on each side of the pulley?

You are designing a simple elevator system for an old warehouse that is being converted to loft apartments. A 22,500-N elevator is to be accelerated upward by connecting it to a counterweight
by means of a light (but strong!) cable passing over a solid uniform disk-shaped pulley. The cable does not slip where it is in contact with the surface of the pulley. There is no appreciable friction at the axle of the pulley, but its mass is 875 kg and it is 1.50 m in diameter. (a) What mass should the counterweight
have so that it will accelerate the elevator upward through 6.75 m in the first 3.00 s, starting from rest? (b) What is the tension in the cable on each side of the pulley?

Transcript

00:01 Well, we're designing a simple elevator system for an old warehouse, apparently.

00:05 It's being converted to loft apartments.

00:08 So we have a elevator that weighs 22 ,500 newtons.

00:15 And we want to be accelerated upward by connecting to a counterweight.

00:24 So we have a counterweight over here, so we have a pulley up here.

00:29 They say a light, strong cable.

00:30 So we're going to necklick of the mass and the cable, but assume that it doesn't stretch at all and doesn't break, of course, and it's connected to a counterweight over here.

00:41 I'm assuming that this is a uniformed disc, but assuming that there's no slipping here, and there's no appreciable friction here, so there's no drag on their bearings.

00:53 Let's see, but the mass of this pulley is 875 kilograms, and it is a radius of 1 .5 meters.

01:04 So we draw free by diagram.

01:06 She is the elevator.

01:07 We have the weight of the elevator, the tension in the cable, connecting the elevator up to the pulley, an equal and opposite tension from onto the pulley.

01:17 The tension over here is not the same as over here because this has this angular, there's inertia here because we have this is accelerating, so we have some rate of change of inertia.

01:32 So we have a different tension over here in this cable.

01:35 And then we have the weight and with free by diagram of here says that this tension and this tension we cut the cable has to be equal and opposite and then we have the mass of the counterweight.

01:46 So let's see here...

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