Increasing Torque, Force, and Work: Increasing crank Length (L)

AI Thread Summary
Doubling the crank length (L) allows for pulling up double the amount of water with the same force due to the relationship between torque and distance. The torque increases because torque is calculated as the product of force and distance, and with the crank length doubled, the same force generates double the torque. This means that the system can lift a greater weight (double the water) without needing to exert additional force. The incorrect options discussed highlight misunderstandings about the relationship between torque, work, and the mechanics of the crank system. Overall, the key takeaway is that increasing the crank length effectively enhances the lifting capacity while maintaining the same force applied.
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Homework Statement



You are pulling water with a constant velocity from a well using a crank of length L. If the length of the crank was doubled, you could ...

Homework Equations


Work = Torque*angular distance
Torque = I*angular acceleration
Torque=F*d*sin(angle)
It looks like the force is being applied to the lever at 90 degrees


The Attempt at a Solution


The answer is "pull up double the amount of water with the same force", however I can't work out why this is the correct answer.

Maybe working backwards...
Double the amount of water has double the weight, (force of gravity)
So The torque from the crank wheel would then need to be double (?)
Torque = F*D*sin(90 degrees)
And if D is us doubled, then the same force does twice the Torque.
Is this right?

Also, I couldn't convince myself why these other options were wrong:
Incorrect: pull up the pail with half the number of revolutions
Incorrect: exert double the torque while pulling up the pail with half the work
Incorrect: exert four times the torque while pulling up the pail with the same work
Incorrect: pull up double the amount of water with the same work
Incorrect: pull up the pail with half the work and half the force

Thanks!
 
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Oh, sorry, I should have been more clear. The "crank" is a circular pulley sort of crank that winds up a rope with a bucket attached to the end.
Does this affect your answer?
 
It still has a shaft (that the rope winds round before going down the well).
 

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