Maximum Torque / Evenly Spread across a lever.

AI Thread Summary
The maximum torque on a lever is 1.5 x 10^6 Newtons, and the lever is 20 meters long. To determine how many people weighing 750N can stand evenly spaced on the lever, the torque equation T=FR is applied. The discussion involves integrating the force over the length of the lever, but there is confusion about treating the number of people as a constant during integration. Participants are seeking clarification on the integration method and whether there is a simpler approach to solve the problem. Understanding the torque distribution and the integration process is essential for finding the solution.
Cyclopssummers
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Homework Statement


The maximum torque on a lever is 1.5 x 10^6 Newtons. How many people of weight 750N can stand evenly spaced on this lever, which has a length of 20 meters?

Homework Equations


T=FR
Weight=mg
W=Fd
X = Number of people

The Attempt at a Solution


I have set 1.5x10^6 N = (integral from 0-20) 750X dL.
I understand that the correct next step is to divide out the 750, and to integrate the length over the interval 0 to 20. However, I do not quite understand how this method works. Can we assume that X, the number of people, is a constant when integrating?
 
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