# Solving Tension in Strings: Accelerating Force & Resultant Force

• PhysicStud01

## Homework Equations

Accelerating force = F
Resultant force = ma

## The Attempt at a Solution

D is the correct option.
Tension in string = T
REsultant force = F - T = ma
T = F - ma

or if there is no friction, is the accelerating force the resultant itself?

How do I proceed from here. Is the mass not constant?

This is one of those questions where you have to know when to quit. It asks for the string segment with the greatest tension. Do you have any doubts regarding the segment you identified?

This is one of those questions where you have to know when to quit. It asks for the string segment with the greatest tension. Do you have any doubts regarding the segment you identified?
actually, I don't know how to arrive at the answer. I know the equations I gave should apply here but how do I choose which one of the strings to choose?

I can't give up. THere should be some principles which apply so that i can arrive at the answer.
When I look at it, it seems that all the tension are the same. the same force causes them to move at the same speed, right?

it seems that all the tension are the same.
The rightmost block has a mass, does it not? It is being accelerated at a constant rate "a." The next block connected to it is also accelerating at the same rate. Label the blocks L to R as 1, 2, 3, 4, ... , N, however many there are. They have masses, "m1, m2, ... , mN. The "net" force on each block is then "amN. What you have to identify are where the net forces for each block are applied, and the string tensions necessary to apply them to achieve the acceleration. Give it a try.

The rightmost block has a mass, does it not? It is being accelerated at a constant rate "a." The next block connected to it is also accelerating at the same rate. Label the blocks L to R as 1, 2, 3, 4, ... , N, however many there are. They have masses, "m1, m2, ... , mN. The "net" force on each block is then "amN. What you have to identify are where the net forces for each block are applied, and the string tensions necessary to apply them to achieve the acceleration. Give it a try.
On block 5 (right most), resultant force = m_5 a to the right. tension is to the left.
m_5 a = F - T_Z
T_Z = F - m_5 a

T_Z also act on block 4.
Similarly, for block 4, m_4 a = F - (T_Y) - (T_Z)
(T_Y) + (T_Z) = F - m_4 a

is this correct. I'm confused with this. How do know that T_Z is greater?

How many blocks does string segment Z have to accelerate? How many does Y accelerate? And X? And W?

How many blocks does string segment Z have to accelerate? How many does Y accelerate? And X? And W?
Z has to accelerate 4 blocks. Y need to accelerate 3. X = 2. W = 1. how does this tell me which one is bigger?

but for block 4, tension Z and Y acts to the left, right. while the force acts to the left. so block 5 and block 4 are not really the same when it comes to the number of forces acting on them.

+ the tensions are to the left. they are not actually causing acceleration. it's more like a resistive force, right?

What's the force each string segment has to exert? You can assume the blocks have non-zero masses, and it's already been stated that they are all accelerating at the same rate.

What's the force each string segment has to exert? You can assume the blocks have non-zero masses, and it's already been stated that they are all accelerating at the same rate.
string z exerts a force such that the resultant acceleration of the 4 block on its left is a
string Y exerts force such that aacceleration of 3 block on its left is a

T = F - ma

For Z,
T = F - 4a

For Y, T = F - 3a

don't the string become larger as we move from right string to left?

larger as we move from right string to left?
I assume you meant "force in the string." What makes you think the force is large in the leftmost string? It's accelerating only one block.

I assume you meant "force in the string." What makes you think the force is large in the leftmost string? It's accelerating only one block.
because the at the leftmost, the tension is such that the resultant acceleration on only 1 block is a.
F - T = 1a
T = F - 1a

while at the rightmost, the tension is such that the resultant acceleration on 4 blocks is a.
F - T = 4a
T = F - 4a

for the leftmost, T is greater, from these calculations. Right?

What force do you have to apply to the left most block to accelerate it at rate a? That is the only tension in string segment W.

What force do you have to apply to the left most block to accelerate it at rate a? That is the only tension in string segment W.
the force causing the acceleration is the 'accelerating force' as displayed in the figure. that's the F i used in the equations

the 'accelerating force' as displayed in the figure
This force accelerates all five blocks. If all five have the same mass, how much force is required to accelerate one?

This force accelerates all five blocks. If all five have the same mass, how much force is required to accelerate one?
F / 5. But don't the values of the tensions affect this. so, it's not exactly F/5., but a value that will cause the acceleration to be the same everywhere. so i think that the force varies for each block? am i right?

Each block experiences the same acceleration. That means each block, since we've declared them to have identical masses, experiences the same net force. The net force on each block is the sum of the forces acting on the block. The leftmost block has only one force acting on it, the tension in string segment W, and that is equal to the net force on the leftmost block. The next block to the right has two forces acting on it, the tension in W, and the tension in X. The tension in W pulls the leftmost (block 1) to the right, and at the same time is pulling left, or dragging , or holding back against block 2. To get a net force on block 2, the tension in X must be twice that of the tension in W. Can you take it from here for the third, fourth, and fifth blocks and remaining string segments?

Each block experiences the same acceleration. That means each block, since we've declared them to have identical masses, experiences the same net force. The net force on each block is the sum of the forces acting on the block. The leftmost block has only one force acting on it, the tension in string segment W, and that is equal to the net force on the leftmost block. The next block to the right has two forces acting on it, the tension in W, and the tension in X. The tension in W pulls the leftmost (block 1) to the right, and at the same time is pulling left, or dragging , or holding back against block 2. To get a net force on block 2, the tension in X must be twice that of the tension in W. Can you take it from here for the third, fourth, and fifth blocks and remaining string segments?
so, basically, any specific string pulls one block to the right and another block to the left. SO, in 1 string, the direction of the force (tension) is both to the right and left??

(tension) is both to the right and left??
Pick up a piece of string in your right hand. Pull it to the right from one end without touching the other end. Does it tighten at all? Now take hold of the other end with your left hand and pull.

Pick up a piece of string in your right hand. Pull it to the right from one end without touching the other end. Does it tighten at all? Now take hold of the other end with your left hand and pull.
thanks a lot. I think i got it