Torque, the mass that can be lifted, and speed it rises

[katamoria]

Homework Statement

a. compute the torque developed by an industrial motor whose output is 225kW at an angular speed of 4000rpm.
b. a drum with negligible mass and .4m 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 life at constant speed?
c. at what constant speed will the weight rise?

Homework Equations

rpm x 2pi/60s = rad/s angular speed (w) = 418 rad/s
1Kw = 3.6x10^6J
Power = (torque)(angular speed)?
V = Rw

The Attempt at a Solution

i changed the w from rpm to rad/s
I converted kW to J and got 81x10^8J
I'm not sure that's right, that seems really big to me.
and if Power = (torque)(angular velocity) then i rearranged and solved for torque and got 19.4x10^6, which seems high to me
I have no idea what to do with part B
I know that tension in the rope equals the weight of the object tied to it.

 

[jbsteele]

and I'm guessing that the "constant speed" in part c would just be the angular velocity, 418 rad/s, right?

 

[kerimek]

Torque is a measure of the rotational force applied to an object. In this case, the torque developed by the industrial motor is 19.4x10^6 Nm (Newton-meters). This is a significant amount of torque and indicates that the motor is powerful and capable of lifting heavy loads.
In part B, the weight that can be lifted by the motor at constant speed depends on the diameter of the drum and the power output of the motor. Using the equation P = T*w (power = torque * angular speed), we can calculate the maximum weight that the motor can lift at constant speed. However, since the mass of the drum is negligible, we can assume that all the power is used to lift the weight. Therefore, the maximum weight that the motor can lift is 19.4x10^6 N divided by the speed at which the drum rises (V), which can be calculated using the equation V = R*w (velocity = radius of drum * angular speed). The speed at which the weight rises, or the velocity of the drum, will be determined by the weight of the object and the tension in the rope.
In part C, we can use the formula V = R*w to calculate the speed at which the weight will rise. This will depend on the weight of the object and the tension in the rope. Once we know the speed, we can determine the angular speed (w) using the formula w = V/R. This will give us the constant speed at which the weight will rise.
Overall, the key factors that determine the weight that can be lifted and the speed at which it rises are the torque developed by the motor, the power output of the motor, and the weight and tension of the object being lifted.