Without prefix: What is the maximum power and force output of a trolley motor?

In summary: The speed of the maximum power output and the speed of the maximum force exerted by the motor would be the same. In summary, the power output from the electric motor is maximum when the velocity is at zero.
  • #1
vu10758
96
0
The power output from a trolley motor depends upon velocity P(v) = av(b^2-v^2). The power is 0 for v^2>b and "a" and "b" are constants. Determine the speed of the maximum power output and the speed of the maximum force exerted by the motor.


How do I begin this problem? I don't know how to start.
 
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  • #2
In terms of the calculus, what do you know about power?
 
  • #3
It's the derivative of work with respect to time.
 
  • #4
Okay, good, but let's take it a step further. We know that [tex]P = \frac{dW}{dt} = \frac{\vec{F} \cdot \vec{ds}}{dt} = \vec{F} \cdot \frac{ \vec{ds}}{dt} = \vec{F} \cdot \vec{v} [/tex]. Does this give you a start or any ideas?
 
  • #5
vu10758 said:
The power output from a trolley motor depends upon velocity P(v) = av(b^2-v^2). The power is 0 for v^2>b and "a" and "b" are constants. Determine the speed of the maximum power output and the speed of the maximum force exerted by the motor.


How do I begin this problem? I don't know how to start.
The first part is a calculus maximization problem (or maybe a graphing calculator problem??). You are given P as a function of v and asked to maximize with respect to v.

I'm still thinking about the second part. The force is not constant here, so you cannot say P = Fv
 
Last edited:
  • #6
OlderDan said:
The first part is a calculus maximization problem (or maybe a graphing calculator problem??). You are given P as a function of v and asked to maximize with respect to v.

I'm still thinking about the second part. The force is not constant here, so you cannot say P = Fv
Oh, oops, I overlooked that, but you are right. The force is not constant and can't be taken out of the derivative. Hum, it would be easy to graph into mathematica or another graphical program to find the quantitative solution, but the analytical solution is tough. Yes, I will have to think about this some more too.
 
  • #7
Mindscrape said:
Oh, oops, I overlooked that, but you are right. The force is not constant and can't be taken out of the derivative. Hum, it would be easy to graph into mathematica or another graphical program to find the quantitative solution, but the analytical solution is tough. Yes, I will have to think about this some more too.
The more I think about it, the more I think you were right to begin with, at least for any physically reasonable force. The force related to an incremental displacement ds is not going to change while moving the distance ds. So it's not a product rule derivative when you write
dW = Fds
It's just dividing the incremental work by the incremental time

dW/dt = Fds/dt
P = Fv
F = P/v = a(b^2-v^2) is maximum when v = 0

That seems reasonable actually. I think electric motors typically have maximum torque at zero speed, so you would expect maximum force at zero speed.
 

What does "given power, find speed" mean?

"Given power, find speed" is a physics equation that represents the relationship between power and speed. It means that if you know the amount of power an object has, you can calculate its speed using this equation.

What is power?

Power is the rate at which work is done or energy is transferred. It is measured in watts (W) and is calculated by dividing work by time.

What is speed?

Speed is the rate at which an object moves. It is measured in units of distance per time, such as meters per second (m/s) or miles per hour (mph).

How do you calculate speed from power?

To calculate speed from power, you can use the equation: speed = power / force. This equation can be rearranged to solve for speed by multiplying power by the inverse of force.

What are some real-world applications of "given power, find speed"?

This equation is commonly used in physics and engineering to analyze the performance of machines and vehicles. It can also be applied in sports, such as calculating the speed of a baseball pitch based on the power of the pitcher's throw.

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