# Tension problem: 2 ropes, 3 blocks

• JoshBuntu
In summary: I don't understand how mass C, which is hanging from block B, would contribute to the second tension. I'm sorry if this is confusing.:In summary, the tension in the cord connecting B and C is 3.8 m/s^2. Block A moves 0.250 seconds in the first 0.250 seconds, but doesn't reach the pulley.
JoshBuntu

## Homework Statement

The diagram is here http://img375.imageshack.us/img375/5930/tensionproblem.png

What is the tension in the cord connecting B and C? How far does A move in the first 0.250 seconds of movement assuming it does not reach the pulley?

F=ma

## The Attempt at a Solution

Tension1=(Mass of A)(acceleration)
(Mass of B)(gravity) - Tension1=(Mass of B)(acceleration)
I assumed that the tension in each equation was equal and so set the equations equal, solving for (acceleration):
(acceleration) = [(mass of B)(gravity)]/[(mass of A)(mass of B)] = 3.8 m/s^2

And honestly I just don't know what the hell I'm doing. I've been at this for over 3 hours. I tried to teach this tension thing to myself. What's also really confusing me is that cord between B and C! I don't understand any of the concepts and I don't have anyone to help me, and I also don't know whether or not I'm on the right track. Please help ):

#### Attachments

• tension problem.png
2.2 KB · Views: 819
Last edited by a moderator:
JoshBuntu said:
And honestly I just don't know what the hell I'm doing.
I've been at this for over 3 hours. I tried to teach this tension thing to myself. What's also really confusing me is that cord between B and C! I don't understand any of the concepts and I don't have anyone to help me, and I also don't know whether or not I'm on the right track. Please help ):
Its all about drawing good free body diagrams of each block, identifying the forces acting on each block, including tension and weight forces, and then applying Newton's laws. Hint: Tension forces always pull away from the body on which they act. The tension in a cord wrapped around an ideal pulley is the same on both sides of that pulley. They are not necessarily the same when connected to each side of a block (2 different cords). The magnitude of the accelerations of all blocks are the same. Are you familiar at all with free body diagrams?

JoshBuntu said:
Tension1=(Mass of A)(acceleration)
(Mass of B)(gravity) - Tension1=(Mass of B)(acceleration)

Your first equation is correct, but the tension of the second rope between B an C is missing from the second equation. The tension of the second rope is different from the tension in the first rope. And you have a third equation for mass C.

When you have all three equations, you can add them together and all tensions will cancel and you get the acceleration. From the acceleration, you can calculate the tensions.

ehild

You should look at the system in three parts, blocks A-C. What forces act on each?

You'll have two tension forces because there are two different ropes. For your equation for block B, you need to add the second tension force. You need a third equation for block C.

Edit: way too late...

Mass A, normal force acting up and weight acting down which cancel each other, and Tension1 acting to the right

Mass B, Weight acting down and Tension1 acting up, weight greater than Tension1(?)

Mass C, Weight acting down and Tension1 acting up, weight greater than Tension2(?)

ehild: What do you mean? Should I treat blocks B and C as one mass (adding their masses and treating as a single block)? Also, would like, gluing blocks B and C together be different than having them attached by a rope?

On B, you also have the second tensile force acting downwards. Mass C has tension 2 acting upwards. (T1 =\= T2!)

Once you have your three equations, you can solve them like any system of equations to find the acceleration, and then the tensions.

:O Ok I will try that right now! Don't leave me!

Ok so tell me if I'm right!

The second tension (Tension2) between B and C is (Tension2)=(mass of C)(acceleration)

and (Tension1)=(mass of A)(acceleration)

so I think the correct form of the second equation that I previously got wrong is:
(mass of B)(gravity)+(Tension2) - (Tension1) = (mass of B + mass of C)(acceleration)

and substituting for Tension2:
(mass of B)(gravity)+[(mass of C)(gravity)-(mass of C)(acceleration)] - (Tension1) = (mass of B + mass of C)(acceleration)

?

For the second tension, you need to take the weight of the block into account.

THERE is where I have a problem! block C is hanging on the rope, so it's creating a tension. So like, block B is kind of acting like a ceiling that block C is hanging from by a rope - how does block B constitute a tension to the second tension? Isn't block B just falling while block C is pulling the rope down? ):

All of the ropes are in tension, so if we "cut" the ropes, there will be a tension force pulling on each block. Note that the blocks are all moving with the same speed.

JoshBuntu said:
O

ehild: What do you mean? Should I treat blocks B and C as one mass (adding their masses and treating as a single block)? Also, would like, gluing blocks B and C together be different than having them attached by a rope?

You can imagine that B and C are glued together, but then your second equation must include the sum of masses of B and C.

If you read the text of the problem it asks the tension in the rope connecting B and C, So it is better to include it and handle the three masses separately.

If you draw a proper free body diagram, you will see the forces acting on B are:
MBg +T2-T1=MBa

and those for C are the weight of C (down) and T2 (up)

ehild

Woah, woah, I think I got this. Is the final formula for Tension2:

Tension2 = [(mass of A)(mass of C)(gravity)]/[(mass of C) + (mass of B) + (mass of A)]

with the answer for tension 2 being 36.8 Newtons?

And thank you ehild! Now I get it, I think. Tension2 is pulling down on block B along with the weight of block B. These 2 forces together are greater than Tension1. okokokok. Before I wasn't really getting what tension 2 was actually doing it. It's pulling down on block B and pulling up on block C with equal magnitudes, right??

JoshBuntu said:
Woah, woah, I think I got this. Is the final formula for Tension2:

Tension2 = [(mass of A)(mass of C)(gravity)]/[(mass of C) + (mass of B) + (mass of A)]

with the answer for tension 2 being 36.8 Newtons?

You have a typo, there must be a "+" between mass of A and mass of B in the numerator. The 36.8 N for tension 2 is OK.

And yes, a massless rope has the same tension along all this length, pulling the bodies at both ends with forces of equal magnitude and opposite direction along the rope.

ehild

Yay! (: But WAIT? "there must be a "+" between mass of A and mass of B in the numerator" There is no mass of B in the numerator... was I supposed to have one there? Because I solved the equation just as I typed it here with only multiplication in the numerator and got 36.8 Newtons...

You are right, it is the right formula, right result, I was not quite awake when I replied

ehild

## 1. What is a tension problem with 2 ropes and 3 blocks?

A tension problem with 2 ropes and 3 blocks involves determining the tension force acting on each rope in a system of 3 blocks connected by 2 ropes. This type of problem is commonly seen in physics and engineering.

## 2. How do you solve a tension problem with 2 ropes and 3 blocks?

To solve a tension problem with 2 ropes and 3 blocks, you need to first draw a free body diagram of the system and label all the forces acting on each block. Then, use Newton's laws of motion to set up and solve equations for the tension forces in each rope.

## 3. What factors affect the tension in a rope?

The tension in a rope is affected by several factors, including the weight of the objects attached to the rope, the angle at which the rope is pulled, and the properties of the rope itself, such as its elasticity and thickness.

## 4. Can the tension in a rope ever be greater than the weight of an object?

Yes, the tension in a rope can be greater than the weight of an object. This can happen when the object is accelerating or when the rope is being pulled at an angle, which increases the effective weight of the object.

## 5. What are some real-life applications of tension problems with 2 ropes and 3 blocks?

Tension problems with 2 ropes and 3 blocks have various real-life applications, such as determining the tension in cables holding up a suspension bridge, calculating the force required to lift a heavy object with a pulley system, or understanding the mechanics of a rock-climbing harness.

• Introductory Physics Homework Help
Replies
1
Views
1K
• Introductory Physics Homework Help
Replies
18
Views
2K
• Introductory Physics Homework Help
Replies
38
Views
2K
• Introductory Physics Homework Help
Replies
12
Views
220
• Introductory Physics Homework Help
Replies
27
Views
2K
• Introductory Physics Homework Help
Replies
18
Views
378
• Introductory Physics Homework Help
Replies
2
Views
910
• Introductory Physics Homework Help
Replies
13
Views
1K
• Introductory Physics Homework Help
Replies
18
Views
254
• Introductory Physics Homework Help
Replies
19
Views
1K