# Why is the tension force equal to friction force

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1. Mar 24, 2017

### mooguy

1. The problem statement, all variables and given/known data
The 1.0 kg block in the figure is tied to the wall with a rope. It sits on top of the 2.0 kg block. The lower block is pulled to the right with a tension force of 20 N. The coefficient of kinetic friction at both the lower and upper surfaces of the 2.0 kg block is μk = 0.300.

What is the tension in the rope holding the 1.0 kg block to the wall?

2. Relevant equations
f=ma
F(friction force) = μ*m*g

3. The attempt at a solution

Here is the full diagram

I drew out a force body diagram that looks like this for just the first block(I think this is right)

Although I'm still confused as to why is it that the tension force and the friction force are the same. I thought tension and friction are completely different forces and how do I know when to associate forces to tension

Last edited: Mar 24, 2017
2. Mar 24, 2017

### Diegor

Where is the figure that is mentioned in the statement? Anyway the normal force mg is not correctly calculated. You should check the direction of the forces think in your block where is it pulled from?

3. Mar 24, 2017

### Staff: Mentor

What direction is the friction force acting on the 1 kg block? (a) in the same direction that the 2 kg block is moving (b) in the opposite direction that the 2 kg block is moving?

4. Mar 24, 2017

### mooguy

Friction should be acting in the opposite direction that the 2kg block is moving.

5. Mar 24, 2017

### mooguy

The diagram I drew was just of the 1kg block. the force of gravity pulling down on the 1kg block should just be 1*9.8. the 1kg block should be pulled from the left, since that rope from tied to it and the friction force should be the only thing pulling it back while the 2kg block is being pulled forward.

6. Mar 24, 2017

### Staff: Mentor

Wrong

7. Mar 24, 2017

### Diegor

Ok in your diagram I see 1N as normal force is that the result from 1kg x9,8 m/s2? If both forces tension and friction are in the same direction would it be possible for the block to stay in equilibrium?

8. Mar 24, 2017

### vela

Staff Emeritus
If the only vertical force is gravity, shouldn't the block fall?

9. Mar 24, 2017

### mooguy

Ohh I see the mistake. Aahh ok. No it would not be possible for the block to stay in stay in equilibrium if tension and friction are in the same direction. That's where I think I went wrong. I was confusing the directions of friction. So if we say that motion to the left is negative and motion to the right is positive, then T=-F(Friction) for the 1KG block?

10. Mar 24, 2017

### Staff: Mentor

There really isn't any motion in either direction for the 1kg block. But you now do have the correct directions for the forces.

Last edited: Mar 25, 2017