- #1
In summary: Take a look at the second drawing. In this drawing the pivot has been moved to the middle of the pulley. This changes the lever ratio because now the distance from fulcrum to contact point is different for each end of the contact.If B moves slowly what happes to A ?In summary, the tension in A is greater than the tension in B in position 1 because A seems more stretched. In position 2, the tension is the same. However, there is no answer like that.
- #2
berkeman
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NA19 said:
Welcome to the PF.
In problems like this, it is generally best to start by drawing a free body diagram (FBD) showing the tensions...
- #3
NA19
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I tried that, but I am not sure how the pulleys and the arrow would affect the forces acting on the strings. My initial instinct was that the tension in A is greater than the tension in B in position 1 because A seems more stretched.
Then, I thought that the tension is the same in position 2 which seems like a rest position.
However, there is no answer like that.
Then, I thought that the tension is the same in position 2 which seems like a rest position.
However, there is no answer like that.
- #4
CWatters
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Take a look at the top pulley. Ignore everything else. The pivot is not in the middle.
So..
Q1) The pulley isn't moving so what does that say about the total torque on the pulley?
Q2) Given the answer to Q1... If one force (B) is applied close to the pivot and the other (A) is applied further away from the pivot what does that mean for the forces?
So..
Q1) The pulley isn't moving so what does that say about the total torque on the pulley?
Q2) Given the answer to Q1... If one force (B) is applied close to the pivot and the other (A) is applied further away from the pivot what does that mean for the forces?
- #5
NA19
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Why isn't the pivot in the middle?
Why isn't the pulley moving?
Why isn't the pulley moving?
- #6
CWatters
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- #7
NA19
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Q1) The total toque on the pulley is zero.
Q2) Forces farther away are less than when they are close.
I kind of understand what is happening right now, but a few more questions:
How do you determine that this is a lever question instead of a pulley question? I don't really understand how this system acts as a system of levers.
Isn't B farther away from the pivot point than A?
Q2) Forces farther away are less than when they are close.
I kind of understand what is happening right now, but a few more questions:
How do you determine that this is a lever question instead of a pulley question? I don't really understand how this system acts as a system of levers.
Isn't B farther away from the pivot point than A?
- #8
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A pulley can be thought of as a lever, at any given instant. A centrally mounted pulley isn't a very interesting lever because it's 1:1; the distance from fulcrum to contact point is the same for both ends of the contact. If the pulley is eccentrically mounted (and sufficiently frictional that the string does not slide) then it will behave like a lever, except that as the pulley turns the lever ratio will change.NA19 said:
To see this, cut out all parts of the pulley except the two radii to the two ends of the contact.
- #9
NA19
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Okay, but...
Isn't B farther away from the pivot point than A in position 1?
Why are we ignoring everything but the top pulley.
Isn't B farther away from the pivot point than A in position 1?
Why are we ignoring everything but the top pulley.
- #10
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No. The pivot point is the dot, yes? In position 1, string B extent is closer to the dot where it reaches the pulley than is string extent A.NA19 said:
Bottom pulley is the same, by symmetry. Only the pulleys separating extent A from extent B are relevant.
- #11
CWatters
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NA19 said:
Levers also change velocities. If B moves slowly what happes to A ?
In case it helps.. The string doesn't slip on the pulley so (for small angles of rotation) you can replace the pulley with lever arms like this. In practice the pulley rotates through quite large angles so levers aren't used but the principle is the same..
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FAQ: How do lever arms affect the velocity of objects?
What is a pulley?
A pulley is a simple machine consisting of a grooved wheel and a rope or cable. It is used to change the direction of a force and make it easier to lift or lower objects.
How do pulleys work?
Pulleys work by distributing the weight of an object over multiple ropes or cables, reducing the amount of force needed to lift the object. They also change the direction of the force, making it easier to lift objects straight up rather than at an angle.
What are the different types of pulleys?
There are three main types of pulleys: fixed, movable, and compound. Fixed pulleys have a stationary axle and can only change the direction of the force. Movable pulleys have a moving axle and can also reduce the amount of force needed. Compound pulleys combine fixed and movable pulleys to provide a mechanical advantage for lifting heavy objects.
How are pulleys used in everyday life?
Pulleys are used in various everyday activities, such as raising and lowering flags, lifting weights in a gym, and operating elevators. They are also used in construction and transportation industries, such as cranes and pulley systems in cars for opening and closing windows.
What is a lever arm?
A lever arm is a rigid bar that rotates around a fixed point, called the fulcrum. It is used to transmit and amplify force, making it easier to lift or move objects. The longer the lever arm, the greater the mechanical advantage.