# Homework Help: Net Force and Tension

1. Feb 21, 2013

### student34

1. The problem statement, all variables and given/known data

A girl pulls her 4.00kg sled connected to a weightless rope. She pulls the rope on the sled and it goes faster and faster on a frictionless ice surface. The sled has an acceleration of
2.50m/s^2. What is the tension on the rope? What is the net force?

2. Relevant equations

F = ma

3. The attempt at a solution

F(net) = 4.00kg*2.50m/s^2 = 10.0N

T = 4.00kg*2.50m/s^2 = 10.0N

If my answers are correct, where is the reaction force to F(net) for Newton's 3rd law? I understand that the reaction force to the tension is the what the rope is attached to, but then what is the reaction force to F(net)?

2. Feb 21, 2013

### ehild

The rope pulls the sledge forward by 10 N force and the sledge pulls the rope by 10 N backwards. The reaction force is exerted by the sledge on the rope. You need the net force exerted on the sledge.
What other forces act on the sledge?

ehild

3. Feb 21, 2013

### student34

Besides the tension, I can't think of any other.

4. Feb 21, 2013

### ehild

It is gravity and the normal force from the ground, but they cancel.

ehild

5. Feb 21, 2013

### student34

My issue is that T = 10.0N ,and its reaction force equals 10.0N. Then what force is accelerating the sled?

6. Feb 22, 2013

### ehild

The force exerted on the sled accelerates it.

The reaction force is exerted by the sled and acts on the rope.

ehild

7. Feb 22, 2013

### Simon Bridge

The sled presses on the ground with force equal to it's weight ... the reaction force to the weight acts at the center of the Earth and points up to the sled. The sled and the earth do not accelerate towards each other though, because the ground is in the way. Reaction forces do not cancel out the applied force.
The ground provides a force pointing up at the sled balancing the weight and this same force is communicated down to the center-of-mass of the Earth (arising from the material composition of the Earth and how it interacts - the details are not important for this model).

Horizontally, it looks like the girl pulls on the rope and the sled also pulls on the rope - with the same force, in the opposite direction - so we wonder how the rope can accelerate.

I think that's the jist of the conceptual problem here.

8. Feb 22, 2013

### student34

Am I correct by saying that T = 10N and the reaction force to T equals -10N?

If I am correct, then what esle is exerting the force to accelerate the sled since T and the reaction force cancel out?

9. Feb 22, 2013

### ehild

The rope is weightless so massless. Exactly zero force is needed to accelerate it.
Had it mass, the tension would not be constant along the rope.

ehild

10. Feb 22, 2013

### student34

Yes, that's my issue. What is the net force?

11. Feb 22, 2013

### ehild

The force and the reaction force act on different objects.

The sled is accelerated by the force of tension exerted by the rope.

The rope "feels" the force exerted by the girl and the force by the sled which is the negative of the force it exerts on the sledge. The rope is massless, ma=0, so the forces of the sledge and of the girl cancel.

The rope exerts force on the girl: the reaction of he girl's force.

ehild.

12. Feb 22, 2013

### ehild

"Net force" on what?

ehild

13. Feb 22, 2013

### student34

Let me ask this differently. There are forces in this situation that are cancelled out by their reaction force. What is the force that isn't cancelled out by its reaction force causing the sled to accelerate?

14. Feb 22, 2013

### ehild

Only forces acting on the same body add up. You can not add forces acting on different objects.
Action and reaction are always together. If B acts on A with force F, A acts on B with -F. And both A and B will accelerate, as maaa=F and mbab=-F.

Give the net force on the sledge.

ehild

15. Feb 22, 2013

### student34

Ohhhh, I think it finally sunk in. So the sled is the reaction force to T. And since we used up the sled's reaction force on T, there is nothing left but to have a net force on the sled. Is that accurate?

16. Feb 22, 2013

### ehild

"What is the net force" is a wrong question. You have to specify the system you want the net force exerted on. The net force on the whole system Earth + girl+ rope+sled is zero. But the net force acting on the sled and only on the sled is equal to 10 N.

ehild

17. Feb 22, 2013

### student34

The net force on the system is zero even though it is accelerating? I thought that the net force is mass multiplied by acceleration.

18. Feb 22, 2013

### Simon Bridge

The reaction to gravity (see example above) should provide a clue - the reaction force does not cancel the action force because they act on different bodies. The forces kinda pass each other.

If I pull on the rope, the sled experiences my action force. I experience a reaction force from the sled. Proceed by isolating the bodies ... the sled experiences an unbalanced force which, as far as the sled is concerned, comes from the rope. That's it. The sled accelerates.

The question was about the sled, not me. That's important.
If I act to maintain a constant force on the sled, then I will have to move too. You want to see what happens to me, you have to look at all the forces on me. There is the reaction tension in the rope, and some other force that is accelerating me - probably due to my feet pushing on the ground as I walk.

So - the "system" (being me+sled) gets to accelerate because there is an unbalanced force on me, and I'm attached to the sled.

Also see: http://tap.iop.org/mechanics/newton/212/file_46379.pdf
https://www.amazon.com/Thinking-Physics-Is-Gedanken/dp/B003X9VLGC

Last edited by a moderator: May 6, 2017
19. Feb 22, 2013

### ehild

Acceleration is specified only for the sledge. The net force on it is ma=10 N.
ehild

20. Feb 22, 2013

### MrWarlock616

T and its reaction do cancel, but that's only noticeable when you only consider the rope.

21. Feb 22, 2013

### student34

Ah, I am pretty sure that I got it now. Like you said earlier, the reaction to the sled's acceleration would be the Earth. So the Earth would accelerate some extremely small amount one way, and the girl and the sled accelerate the other way . In which case there's no net force, and one can argue that there is always an inertial frame of reference that has no net force going all the way back to the Big Bang.

22. Feb 22, 2013

### ehild

Well. The internal forces cancel. Without external force, the acceleration of the centre of mass of a system is zero. If the system is the whole Universe, its centre of mass does not accelerate as there is nothing else "external" for the Universe.

ehild