Acceleration of two pulleys help

In summary, the relation between the accelerations of m1 and m2 is a1 = 2*a2. This can be visualized by using a string or shoe lace around a coffee cup, where pulling one end of the string up a distance x will result in the cup moving x/2.
  • #1
bcmb146
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Homework Statement



If a1 and a2 are the accelerations of m1 and m2, respectively, what is the relation between these accelerations?

Homework Equations



Link to the diagram :
http://www.webassign.net/serpop/p4-38.gif

The Attempt at a Solution



The answer is a1 = 2*a2, but I'm having trouble visualizing/understanding how it was gotten. Is there a specific way to do this?
 
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  • #2
Get a string or shoe lace and wrap it around a coffee cup. Hold one end of the string still and pull the other end of the string up some distance x, the coffee cup will move x/2.
 

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  • #3
I get it now; thanks a lot! I can't believe I didn't even see that in the first place.
 

What is the concept of acceleration in relation to two pulleys?

The acceleration of two pulleys refers to the rate of change of velocity of the pulleys in a system. It is a measure of how quickly the pulleys are speeding up or slowing down.

How is the acceleration of two pulleys calculated?

The acceleration of two pulleys can be calculated using the formula a = (v2 - v1) / t, where a is the acceleration, v2 is the final velocity, v1 is the initial velocity, and t is the time taken.

What factors affect the acceleration of two pulleys?

The acceleration of two pulleys is affected by the mass of the pulleys, the tension in the ropes or belts connecting the pulleys, and the friction between the pulleys and the ropes or belts.

Can the acceleration of two pulleys be negative?

Yes, the acceleration of two pulleys can be negative if the pulleys are slowing down. This is indicated by a negative value in the acceleration formula.

How does the acceleration of two pulleys affect the speed of rotation?

The acceleration of two pulleys affects the speed of rotation by determining how quickly the pulleys will speed up or slow down. A higher acceleration will result in a faster change in speed, while a lower acceleration will result in a slower change in speed.

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