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Imagine a movable massless pulley with a rope around it (no friction). One end of the rope is fixed to the ground, and the other hangs a mass. If I accelerate the movable pulley up, then the object will also accelerate up. What is the relationship between the two accelerations? (of the pulley and of the object)

2006-10-15 15:44:46 · 3 answers · asked by Leon L 1 in Science & Mathematics Physics

3 answers

So, we get to do you homework for you....better check the answer for correctness.

Make a sketch:
...|.......<-a
...O...
..|..|...
..|..m.....<--b
..X

O is the pulley, m is the mass, x is the fixed ground
At point a the pulley moves up a distance d
then the mass at point b moves 1/2(d) because the string is a constant length and the movement d=1/2(one string movement)+(1/2)(othe string movement).

The Force (F) at point a is equal to mass times acceleration:
F=ma. SInce the one end is fixed, the other rope has the whole mass and the acceleration is d/t**2. Therefore:
F=ma
F=m(d)/t**2

at point b
F=md/2t**2

comparing the two the acceleration at b is twice a

2006-10-15 16:04:41 · answer #1 · answered by Anonymous · 0 0

The acceleration is constant throughout the entire system. This is only because you have a pulley in which there is no force of friction reducing the acceleration at that point in the system.

2006-10-15 22:57:31 · answer #2 · answered by TM 3 · 0 0

massless puley.
one end fixed.
so, movement of the pulley and object in upward direction is same.
acceleration=the rate of change of velocity.
which is same in the both the cases.

2006-10-16 01:19:17 · answer #3 · answered by Anonymous · 0 0

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