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(a) Compute the torque developed by an industrial motor whose output is 150 $\mathrm{kW}$ at an angular speed of 4000.0 rev/min. (b) A drum with negligible mass and 0.400 $\mathrm{m}$ in diameter is attached to the motor shaft, and the power output of the motor is used to raise a weight hanging from a rope wrapped around the drum. How heavy a weight can the motor lift at constant speed? (c) At what constant speed will the weight rise?

a) 358 $\mathrm{N.m}$b) $1.79 \times 10^{3} \mathrm{N}$c) 83.8 $\mathrm{m} / \mathrm{s}$

Physics 101 Mechanics

Chapter 10

Dynamics of Rotational Motion

Newton's Laws of Motion

Rotation of Rigid Bodies

Equilibrium and Elasticity

Hope College

University of Sheffield

University of Winnipeg

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problem. Number 21 deals with a industrial motor who provides a power. Ah, 150 Killer wants. That's 150 into the third wants. And it gives you an angular speed. Ah, for 8000 rpm. Yeah. And now we gotta convert that to radiance per second, which gives us a 418.9 radian per seconds. Matter question, eh? And that's what's the torque provided by this matter. You know, that definition of power is torque times angular speed. Someone in here we get 1 50 into the third gives us a torque value. 358 Noon. Peters it Herbie tells me that I have a drum and that iss attached to this motor shop so that a circular drunk attached to his motor shaft and it is lifting. Hey, there's a a weight hanging from a rope. We want to know what's the largest? Wait, what is our largest wait that this motor can left. We got two things here. First off, we know, um, that this wait would be equal to the tension in the rope by Newton's law. And we know that the motor provides that torque bands that torque is due to the tension times the liver prudently. We solved that torque to be 3 58 We're looking for that tension, which we know is also the weight in the level R is the radius of that drum, which is 0.2. So attention is just our weight is 17 90 news and finally part. See, uh, that what is the speed at which this wait will rise? Well, we do know that, um, we were looking for the tan gentle speed. You know, that's related through the angular speed by the radius. We do know that angular speed is given to us. It is for 18.9 and our radius is 0.2, which gives us a velocity of 83 0.8 leaders per second. Thank you for learning.

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