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

In summary, the question asks if doubling the length of a crank would allow for pulling up double the amount of water with the same force. By using the equation work = torque * angular distance, it is determined that doubling the length of the crank would result in double the torque. Therefore, the answer is correct and other options such as exerting double the torque with half the work or pulling up half the amount of water with the same work are not feasible. This is due to the fact that the force of gravity increases with double the amount of water, requiring double the torque to pull it up.
  • #1
Femme37706
2
0

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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  • #3
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?
 
  • #4
It still has a shaft (that the rope winds round before going down the well).
 
  • #5


Increasing the length of the crank will indeed allow for more water to be pulled up with the same force. This is due to the relationship between torque, force, and distance. Doubling the crank length will double the distance from the center of rotation to the point where the force is applied, resulting in a doubling of the torque. This increased torque allows for more force to be applied to the water, resulting in a greater amount of water being pulled up with the same amount of work.

To understand why the other options are incorrect, it is important to consider the equations for torque and work. Torque is directly proportional to both force and distance, meaning that increasing the force or distance will result in an increase in torque. Work, on the other hand, is directly proportional to force and distance, but also takes into account the angle at which the force is applied. In this scenario, the force is being applied at a 90 degree angle, resulting in a simplified equation of work = force * distance. Doubling the distance will double the work, but doubling the force will result in a quadrupling of the work. Therefore, the incorrect options either do not take into account the effect of distance on torque, or they do not take into account the effect of angle on work.
 

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

How does increasing crank length affect torque?

Increasing crank length increases the lever arm, which in turn increases the torque. This is because the longer distance from the center of rotation to the point of application of force increases the moment arm, resulting in a greater torque output.

Does increasing crank length also increase force?

Yes, increasing crank length increases both torque and force. Torque is the product of force and lever arm, so as the lever arm increases, so does the force.

What is the relationship between crank length and work?

Crank length has a direct relationship with work. As crank length increases, the distance traveled by the point of application of force also increases, resulting in more work being done.

Is there a limit to how much torque can be increased by increasing crank length?

Yes, there is a limit to how much torque can be increased by increasing crank length. This is because as the crank length increases, the pedal speed decreases, resulting in a decrease in the number of rotations per minute and a decrease in power output.

Are there any potential risks or downsides to increasing crank length?

One potential risk of increasing crank length is that it can put more strain on the knee joint, potentially leading to injury. It may also require a readjustment of the bike fit and can affect the rider's pedaling technique. Additionally, increasing crank length may not always result in a proportional increase in torque and power output, as there are other factors at play such as muscle strength and efficiency.

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