# Acceleration and Tension in Multiple Pulleys

• Lanox
In summary, the problem involves two blocks, m1 and m2, on a horizontal frictionless surface connected by a rope passing through a set of massless and frictionless pulleys. The tension in each rope and the acceleration of each block need to be determined. Using the equation Sum(F) = ma, the tension in the rope connected to m1 is found to be m1a. For m2, the equation m2g - 2T = m2a is used, where T is the tension in the rope connected to m2. However, it is assumed that both masses have the same acceleration, which may not be the case. The length of the rope is also assumed to be constant, which may not be
Lanox

## Homework Statement

Block "m1" sits on a horizontal frictionless surface. Block "m2" is hanging below the pulleys as shown. All of the pulleys are massless and frictionless. Given [m1, m2]. Determine:

a. The tension in each rope.
b. The acceleration of each block.

Sum(F) = ma

## The Attempt at a Solution

block m1:
F = m1a
Tension = m1a

block m2:
m2g - T - T = m2a
m2g - 2T = m2a
2T = m2g - m2a

*insert tension found through working block m1

2(m1a) = m2g - m2a
2m1a + m2a = m2g
a(2m1 + m2) = m2g
a = m2g/(2m1 + m2)

a. T = m1a
b. Acceleration = m2g/(2m1 + m2)

I've been been looking around the internet and asking my peers about this problem and we all seem to have varying answers. Could someone verify as to whether or not I'm doing this properly?

Thanks

You have assumed both masses have the same acceleration. Do they?

Orodruin said:
You have assumed both masses have the same acceleration. Do they?

Hm, might it be that block m1 has a greater acceleration due to the rope pulling directly on it? If so how would the acceleration differ?

Lanox said:
Hm, might it be that block m1 has a greater acceleration due to the rope pulling directly on it? If so how would the acceleration differ?
If mass 1 moves 1 cm, how far does mass 2 move? Hint: The rope is likely assumed to have a fixed length.

Orodruin said:
If mass 1 moves 1 cm, how far does mass 2 move? Hint: The rope is likely assumed to have a fixed length.
I believe that mass 2 would also move one centimeter, or would the existence of the rope connected to the hook create a different outcome?

I suggest you write the length of the rope as a function of the positions of the masses.

Lanox said:
I believe that mass 2 would also move one centimeter, or would the existence of the rope connected to the hook create a different outcome?

I recommend a pulley. Connect one to a string and use it to lift something. If you don't have a pulley make one out of a key ring. Just loop the string (or a shoe lace) through the ring and use it to lift the keys, just as you would to lift m2.

Supposing mass m2 moves down by 1 cm. How much longer became both vertical pieces of the rope?
The length of the whole rope is constant. How much shorter becomes the horizontal piece?

## What is acceleration in multiple pulleys?

Acceleration in multiple pulleys refers to the rate of change in the velocity of a system when multiple pulleys are involved. It is affected by the number of pulleys, their mass, and the tension in the ropes connecting them.

## How is acceleration calculated in multiple pulleys?

The acceleration in a system of multiple pulleys can be calculated using the formula a = Fnet/m, where Fnet is the net force acting on the system and m is the mass of the system. The net force can be determined by subtracting the tension in the ropes pulling upward from the tension in the ropes pulling downward.

## What is tension in multiple pulleys?

Tension in multiple pulleys refers to the force exerted by the ropes connecting the pulleys. It is equal throughout the entire length of the rope and is affected by the mass of the object being lifted, the number of pulleys, and the angle of the ropes.

## How is tension calculated in multiple pulleys?

The tension in a system of multiple pulleys can be calculated using the formula T = Fnet/n, where T is the tension in the rope, Fnet is the net force acting on the system, and n is the number of ropes pulling in the same direction. The net force can be determined by adding up all the forces acting on the system.

## What is the relationship between acceleration and tension in multiple pulleys?

The relationship between acceleration and tension in multiple pulleys is inverse. This means that as the number of pulleys and the tension in the ropes increases, the acceleration decreases. This is because more force is needed to overcome the increased tension in the ropes.

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