# Is tension equal to the force a person applies horizontally to an inanimate object? [closed]

Suppose a person is pulling on a rock, such as below:

Should the tension in the string be exactly equal to the force the person applies when the whole system, (person, rope and the rock) are accelerating towards the persons direction? Because according to newton's second law, F being the applied force of the men:
F-T=ma
the force can't be equal to the tension applied, and if this is the case, can someone give me an intuition on how is this possible? Why isn't the full force I am applying to the string being converted into the tension in the string? Consider the rope to be massless, Thank you.

## closed as unclear what you're asking by Aaron Stevens, GiorgioP, Jon Custer, Buzz, ZeroTheHeroJul 20 at 0:59

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• How can the person be accelerating towards the person? Can you clarify on what is actually going on? Also you need to specify what you mean by force of the man. Humans have many muscles that can produce forces. In this scenario the arms pull on the rope and the legs push on the ground. Which force or forces are you specifically referring to? – Aaron Stevens Jul 13 at 5:02
• @AaronStevens ok, so the system is completely horizontal. Usually in word problems it is not really specified whether the force is from the hands or the legs, rather it is just the force from a source(although distributing the force between legs and arms may actually clear up my misconception). So if, suppose, the person applies a force of 10N onto the rope, my question is, will this force of 10N converted into a tension of 10N? If yes, should this mean that the person becomes static since the net force on the person becomes 0? (T=-F) If not, where does the rest of the applied force go? – Hammad Jul 13 at 16:57

It would require an additional force to move the person, but if we consider only the force the person exerts on an inelastic, massless rope, then all force will apply to moving the rock. If the rock is in a frictionless environment, it will begin to accelerate immediately. If friction is involved, it will accelerate when force is greater than friction. If the rope is elastic, then some force will go into tension of the rope. If force is constant then once the rope tension equals force applied then all force will go to accelerating the rock.

• So that additional force comes from his leg where as the force in his hand in in equilibrium with the tension in the string? – Hammad Jul 13 at 17:23
• whatever is moving the man does not affect the tension of the rope, it is the man's action on the rope and the reaction of the rock. Unless you want to pull the man with something else and then consider the tension force on the man between it and the rope – Adrian Howard Jul 13 at 17:43

You are, for some reason, assuming that the force applied by the man is acting on the man. That is your issue.

If the ground is frictionless then if the man pulls on the rope with a force $$F$$ to the left, then by N3L the rope pulls on the man with a force $$F$$ to the right. In this case there is only one horizontal force acting on the man. Therefore, for the man $$F=ma$$

If there is friction, then the analysis of the forces does not change, but now you have an additional friction force $$f$$ acting to the left on the man such that $$F-f=ma$$.

In either case the applied force magnitude is equal to the tension magnitude, but the applied force by the man is not acting on the man. Don't just plug all forces in the problem into N2L and expect a valid answer. You need to only include the forces acting on the object in question.

• I see now. The force applied by the men does not act on man, rather the object the rope is pulling on. The only force acting on the man tension, against the man. So if the men is stationary, then the tension acting on the man is balanced by some other force (most probably friction) and if the man is accelerating towards the direction he is pushing in (left) then there is a net force acting on the man, most probably from his legs. The force applied by the men onto the rope has nothing to do with the men's motion, right? – Hammad Jul 14 at 16:02
• @Hammad The force applied by the men onto the rope has nothing to do with the men's motion, right? I wouldn't say it has nothing to do with it. You just don't say that the force her exerts on the rope acts on himself. You can say that the force he exerts on the rope then causes the rope to exert a force on him. So I would say his force still has something to do with his motion. Just be careful about how you understand it. – Aaron Stevens Jul 14 at 16:22