Maximum Torque / Evenly Spread across a lever.

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SUMMARY

The maximum torque on a lever is calculated to be 1.5 x 10^6 Newtons, with a lever length of 20 meters. To determine how many individuals weighing 750N can stand evenly spaced on this lever, the equation T = FR is applied. The solution involves setting up the integral of the force over the lever's length, leading to the equation 1.5 x 10^6 N = (integral from 0-20) 750X dL. The next step is to divide by 750 and integrate, confirming that X, the number of people, can be treated as a constant during integration.

PREREQUISITES
  • Understanding of torque and its calculation using the equation T = FR
  • Familiarity with integral calculus, specifically definite integrals
  • Knowledge of weight calculation using W = mg
  • Basic principles of equilibrium in physics
NEXT STEPS
  • Study the concept of torque and its applications in physics
  • Learn about definite integrals and their use in calculating areas under curves
  • Explore the principles of static equilibrium and how forces interact on levers
  • Investigate alternative methods for solving torque problems without integration
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Students studying physics, particularly those focusing on mechanics and torque, as well as educators looking for effective teaching methods for these concepts.

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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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Is there an easier way than integrating?
 

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