# How much will be the tension in the string if it is stretched by equal and opposite forces of 10 N each from each end?

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Paul N. Share
Feb 9, 2016

10 N

#### Explanation:

While many people would like to simply add the forces from each end to get a total force, this is fundamentally incorrect.

This is an application of Newton's Third Law: "For every action there is an equal and opposite reaction." The only way someone on one end of the string can exert a force of 10 N on the other end of the string is of the other end of the string exerts a 10 N force in the opposite direction.

Suppose I hang a 1 kg mass from a spring scale. This pulls with a force of approximately 10 N. Next, remove the weight and attach the spring scale to a wall. Pull on the scale until it reads 1 kg. That's the same 10 N force that the weight (and gravity) exerted downward when it was hanging. Lastly, consider what would happen if you attached a second spring scale to the wall and the end of the string to that spring scale. When you pull one hard enough to make it read 1 kg, the spring scale on the opposite end will also show 1 kg. They are indicating equal forces in opposite directions.

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zainoo Share
Feb 5, 2016

#### Answer:

The answer is 10N ...

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The string is balanced i.e it is not in motion which means that the net force is 0. If we consider the first force the action and second force the reaction (newton's 3rd law) so the second force will be equal to tension (10N) to make the net force (T-F) 0. If the tension will be 20N then net force (T-F) will be 10N and the body will not be in rest (equilibrium)

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Mar 14, 2016

Following Newton's third law (... equal and opposite forces...), the string stretches until it reaches its tightest point.

You might imagine this to be like a tug-of-war game with both sides dead even.

Since we are focusing on horizontal forces, and since exactly two horizontal forces are pulling in opposite vector directions to the same extent, these cancel each other out, as seen here:

$\sum {F}_{x} = T - {F}_{x} = m {a}_{x} = 0$

As stated in the question, it would mean that $T = {F}_{x}$ (so $T - {F}_{x} = 0$). Thus, if ${F}_{x} = \text{10 N}$, $T = \textcolor{b l u e}{\text{10 N}}$.

(Additionally, even if $m$ is small, ${a}_{x}$ must therefore be ${\text{0 m/s}}^{2}$.)

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Feb 18, 2018

10 Newtons

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Take any point along the string, it must be pulled equally in both directions. Now take the very edges that are pulled with 10N. They too must be balanced, therefore the string has tension of 10N. (Newton's 3rd Law)

...A common misconception is to add 10N to 10N to get 20N, but there is no justification for this error.

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Aliha Share
Apr 4, 2016

10N

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The tension will be 10N because if the string is hung and being streched by force of 5N the opposite force acting in different direction will be exerting same force offcourse the opposite force will be tension which is caused in string due to its weight or gravity acting on it and according to Newton's 3rd Law To every action there is an equal but opposite reaction the tension will be equal to force acting on body
The tension will nit be 20 or 0 because force is vector quantity and it cannot be added or subtracted like scalar quantities because it also has direction that cannot be cancelled .

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