# 2 blocks connected by massless string VS. pulley system

• Ocata
In summary, the tension in the massless cable connected to the internal portions of the blocks A and B would be 10kg(9.8+178.18N) and 10kg(9.8+178.2N), respectively.
Ocata
(Note: The title would better describe the subject if written like this:

"2 blocks on a horizontal frictionless surface connected by a massless string vs. pulley system")Hello, I have a problem regarding pulling two blocks of different masses connected by a string horizontally with opposing forces and evaluating the tension. Then, I would like to find out if this problem is set in such a way that it is analogous to two blocks on a pulley.

1. Homework Statement
If you pull to the left with a force such that if Block A were an isolated mass, it would accelerate 9.8m/s^2 ..and you pull to the right of Block B with such a force that if Block B were an isolated mass, it would accelerate 9.8m/s^2.

Note: Let mass of block 1 be A and mass of block 2 be B. So m1 = A and m2 = B.

Question 1: In what direction would the system accelerate?

Question 2: What is the net force of the system?

Question 3: What is the acceleration of the system?

Question 4: What would be the tension in the massless cable connected to:
1. the internal portion of A (T1 on to m1)
2. the internal portion of B (T1 on to m2)

Question 5:
If you were to take the internal cable of this system and drape it over a pull, with Block A hanging down on the left side of the pulley and Block B hanging down on the right side of the pulley, would your values for tension change?

F=ma

## The Attempt at a Solution

[/B]
Then the block B would require more force:

FA = [A(a) = 10kg(9.8m/s^2) = 98N] < FB = [B(a) = 100kg(9.8m/s^2) = 980N]

So the net force on the system would be Fnet = FA + FB = B(a) - A(a) = 980N - 98N = 882N

The acceleration would be F/(A+B) = 882N/110kg = 8.0181m/s^2

For Tensions,

First establish net force of each block:

Fnet_A = A(a) = 10kg(8.018m/s^2) = 80.18N
Fnet_B = B(a) = 100kg(8.018m/s^2) = 801.81N,

Then Tension in strings are:

Tension of left most string on Block A

FA = 10kg(9.8m/s^2) = 98N = T1/A

Tension of internal string on Block A

FA = T2/A - T1/A ==> T2/A = F1 + T1/A = A(a2) + A(a1) = A(a2+a1) = 10kg(9.8+8.018) = 178.18N

Tension of internal string on Block B

FB = T3/B - T2/B ==> T2/B = T3/B - F2 = B(a1) - B(a2) = B(a1 - a2) = 100kg(9.8 - 8.018) = 178.2N

Tension of right most string on Block B

FB = 100kg(9.8m/s^2) = 980N = T3/B

Question 5

I think that if you were to drape the internal string over a pulley, the tensions in the string would remain exactly the same because gravity, at 9.8m/s^2, would be pulling on each box just as the blocks are being pulled from opposite directions horizontally.

Thank you

#### Attachments

• Tension no Friction.JPG
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That all looks good to me.

Ocata
Great! Thank you. So it would be true that if you put the string on a pulley with the same masses, the system of blocks would accelerate downward at 8.018m/s^2 on the side of the pulley with the bigger block?

Ocata said:
Great! Thank you. So it would be true that if you put the string on a pulley with the same masses, the system of blocks would accelerate downward at 8.018m/s^2 on the side of the pulley with the bigger block?
Yes.

Ocata
haruspex said:
Yes.

Thank you

## 1. How does a pulley system work?

A pulley system is a simple machine that uses a wheel with a groove to change the direction of a force. It is made up of a rope or cable wrapped around the wheel and connected to a load, allowing the load to be lifted or moved with less effort.

## 2. What is the purpose of a massless string in a pulley system?

A massless string is used in a pulley system to transfer the force from one end of the string to the other without adding any weight or resistance to the system. This allows for a more efficient transfer of force, making it easier to lift or move heavy loads.

## 3. How does the number of pulleys affect the mechanical advantage of the system?

The mechanical advantage of a pulley system is directly related to the number of pulleys used. The more pulleys in the system, the greater the mechanical advantage, which means less force is needed to lift or move a load.

## 4. What is the difference between a fixed pulley and a movable pulley?

A fixed pulley is attached to a structure and only changes the direction of the force, while a movable pulley is attached to the load and also provides a mechanical advantage by reducing the amount of force needed to lift the load.

## 5. How does the mass of the load affect the tension in the string?

The mass of the load does not affect the tension in the string in a pulley system. The tension in the string is determined by the force applied to the string and the number of pulleys in the system. As long as the string does not stretch or break, the tension will remain constant regardless of the load's mass.

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