# Tension and Friction [Tension in a horizontal direction] Help.

My question is if I actually did the said problem correctly and if there is perhaps an easier way of coming across an answer. Thanks!

## Homework Statement

There are two blocks present (A and B) A is connected to B via a rope and the applied force is affecting B (to the right).

Find the force of tension in the string if the coefficient of friction is u=0.13
mA = 40 kg
mB = 25 kg
Fapplied = 150 N
u = 0.13

See below.

## The Attempt at a Solution

Tapplied – Tblock – μmBg = mBa

Tblock – μmAg = mAa
Tapplied – μmBg – μmAg = a
mA + mB
Tblock – μmAg = mAa

Tblock – μmAg = mA(Tapplied – μmBg – μmAg)
mA + mB
Tblock = mA(Tapplied – μmBg – μmAg) + mAg
mA + mB
Tblock = 40(150 – (0.13)(25)(-9.8) – (0.13)(40)(-9.8)) + (40)(-9.8)
40 + 25
Tblock = 40(150 + 31.85 + 50.96) + (-392)
65
Tblock = 40(232.81) + (-392)
65
Tblock = 40(3.58) + (-392)
Tblock = 143.3 + (-392)
Tblock = -248.73

tiny-tim
Homework Helper
Welcome to PF!

Hi Caerus! Welcome to PF! (try using the X2 tag just above the Reply box )
Tapplied – Tblock – μmBg = mBa

Tblock – μmAg = mAa
Tapplied – μmBg – μmAg = a
mA + mB

It would be a lot easier to write the third one Tapplied = (a + µg)(mA + mB). (oh, and you missed out a µ in the middle of your calculations, which is why your 392 is so large )

Woah, that did help thanks.

Question: My answer, for the tension of the rope with friction, was identical to the tension of the rope without friction. Does that mean that friction has no direct effect on the tension of the rope. I assume so.

tiny-tim
Homework Helper
Let's write a + µg = b, to save space.

The the first two equations are Tblock = Tapplied - bmB

and Tblock = bmA

then eliminating b (which eliminates µ also, of course) gives Tblock = … ? I appreciate the help tiny-tim! I solved my problem and everything has become much clearer to me. My final question however, and I hope you can assist me, are there any other cases in which the force of tension is zero except for when the force applied is zero? I think it has to do with the coefficient of friction.

tiny-tim
Homework Helper
?? how can the tension be zero if the back block is moving?

I suppose I should have phrased the question a little better...

If I'm not mistaken, say my force applied was 0 N. Which would obviously mean the tension between the two blocks would be zero but would there be any other possibility for the tension to equal 0 even when there is an applied force?

tiny-tim
Homework Helper
If the applied force is small enough (but non-zero), then it's possible for the blocks not to move, and for the tension to be zero … what would be the maximum applied force for that? Hmm, let's see. I know that 1 N would bring it awfully close but as for anything else. I cannot think of one. I do however think that if the coefficient of friction was a large enough number to cancel out the applied force, then the force of tension would equal zero. Right?

tiny-tim
You can't change the coefficient of friction, but you can change the applied force … how small would be applied force have to be? 