I'm I on the right track? Tension question

[Kingyou123]

Homework Statement

Three masses as shown below are resting on a horizontal, frictionless surface. The blocks are connected by massless, frictionless ropes. A force F of 60 N acts on the system as shown. Find the tensions in each of the other two ropes. m1= 10kg, m2 = 20 kg and m3 = 30 kg.

Homework Equations

ΣF=ma

The Attempt at a Solution

ΣF=ma
60N=(10kg+20kg+30kg)a
1=a
Tension of the rope between m1 and m2
Ft=(10kg+20kg)1m/s
Ft=30N
The second part confuses me, wouldn't it be the weight of (m1+m2) since m3 is pulling both? Or is the first part completely irrelevant?

 

[JBA]

Your first equation is fine, but your second is in error. Ask yourself: How much tension is removed from the 60N load as you proceed away from that load point.

 

[haruspex]

Tension of the rope between m1 and m2
Ft=(10kg+20kg)1m/s

Can you explain in detail why the tension would be that? Did you draw a free body diagram for m1?

 

[JBA]

The total tension on the rope to m1 is 60N = (m1 + m2 + m3)a, so what would the tension on the rope be if m1 were removed.

 

[Kingyou123]

Can you explain in detail why the tension would be that? Did you draw a free body diagram for m1?

Would it be Ft=m(a×g)?

 

[Kingyou123]

The total tension on the rope to m1 is 60N = (m1 + m2 + m3)a, so what would the tension on the rope be if m1 were removed.

Oh okay thank you, that's what I originally thought it was :)

 

[haruspex]

Would it be Ft=m(a×g)?

Eh? Why would you multiply two accelerations together? If you meant +, it still makes no sense.
Your FBD is ok, but what do you deduce from it regarding horizontal forces and accelerations?

 

[sophiecentaur]

Looks ok to me.
The 60N F is acting on all the masses - gives you the acceleration. All three masses are accelerating at a.
The second piece of string T2 is accelerating masses two and one - gives you the force / tension in that string.
The last string T1 is just accelerating the m1.

Your first equation is fine, but your second is in error.

I don't see your reasoning here. It looks OK to me. Oh I see - he has mixed up the numbering of the masses (here "Tension of the rope between m1 and m2" when he means m2 and m3 - but still gets the right answer.
It just shows how much better it is to use the notation (T1, T2, T3) given in any question - to avoid that sort of confusion

 

[Kingyou123]

Looks ok to me.
The 60N F is acting on all the masses - gives you the acceleration. All three masses are accelerating at a.
The second piece of string T2 is accelerating masses two and one - gives you the force / tension in that string.
The last string T1 is just accelerating the m1.

I don't see your reasoning here. It looks OK to me. Oh I see - he has mixed up the numbering of the masses (here "Tension of the rope between m1 and m2" when he means m2 and m3 - but still gets the right answer.
It just shows how much better it is to use the notation (T1, T2, T3) given in any question - to avoid that sort of confusion

I'm sort of confused now.. so T1=(10kg+20kg)1m/s which gives me 30N and the second part would be T2=(20kg+30kg)1m/s, right or this is formula completely messed up?

 

[JBA]

No, I said that your first equation is correct all of the tension forces are horizontal and additive. Gravity has no effect since the surface under the blocks is frictionless. When I said what would be the tension with the m1 mremoved I meant: If you move m1 to the left side of the equation, then what is the result. At the same time a/gc is the correct term because m1/gc, m2/gc, m3/gc are the masses of each block.

 

[JBA]

F total = 10 + 20 + 30 so what is left if you subtract m1=10 and then subtract m1 +m2 = 30 + 20

Sorry I made a typo see this edit

 

[haruspex]

Looks ok to me.

if you read exactly what is in the OP, it would appear that Kingyou has involved the masses of both m1 and 2 in finding the tension in the rope between them. This is regardless of how the tensions are numbered.

 

[JBA]

No if I subtract both m1 and m2 then that leaves the tension between m2 and m3.

Lets look at from a different perspective. If you are holding a rope with m1 + m2 + m3 hanging down and you grab the rope below m1 and remove it how much weight will you be holding? and then do the same thing with m2 then how much weight will you be holding.

 

[Kingyou123]

No if I subtract both m1 and m2 then that leaves the tension between m2 and m3.

Lets look at from a different perspective. If you are holding a rope with m1 + m2 + m3 hanging down and you grab the rope below m1 and remove it how much weight will you be holding? and then do the same thing with m2 then how much weight will you be holding.

so the tension between m1 and m2 is just t1=(10kg)1m/s? and then the tension between t2=(10kg+20kg)1m/s?

 

[JBA]

No the tension between m1 and m2 = m2 + m3.
To get the correct solutions use your first equation and start subtracting the masses starting at m1 not m3.

 

[Kingyou123]

No the tension between m1 and m2 = m2 + m3.
To get the correct solutions use your first equation and start subtracting the masses starting at m1 not m3.

Thank you, so the first part would be t1=(20kg+30kg)1m/s 50 N and then t2=(30kg)1m/2

 

[JBA]

Yes, good job, even if it took us a bit of time to get there. But you need to eliminate the "1 m/s" (that is the unit for velocity).

t1=(20kg+30kg)= 50 Kg and then t2 = 30 Kg

 

[insightful]

so the tension T₁ between m1 and m2 is just t1=(10kg)1m/s²? and then the tension T₂ between m2 and m3 =(10kg+20kg)1m/s²?

This is correct if you change as shown in red.

 

[JBA]

Alright, at this point I realize that I have been adding to the confusion all along by missing the fact that T1 is between m2 & m3 and T2 is between m1 and m2. rather than the reverse.
I apologize for this oversight when viewing the figure.

Kingyou123, I wish you would have named me directly when referring to the error. I saw your note but didn't realize it was my error you were referring to.

 

[Kingyou123]

Alright, at this point I realize that I have been adding to the confusion all along by missing the fact that T1 is between m2 & m3 and T2 is between m1 and m2. rather than the reverse.
I apologize for this oversight when viewing the figure.

Kingyou123, I wish you would have named me directly when referring to the error. I saw your note but didn't realize it was my error you were referring to.

It's okay, I figured it out thank you for the help

 

[haruspex]

so the tension between m1 and m2 is just t1=(10kg)1m/s? and then the tension between t2=(10kg+20kg)1m/s?

Yes. I don't understand where the thread went after this. Seems like someone has the numbering backwards from that shown in the OP.

 

[sophiecentaur]

No the tension between m1 and m2 = m2 + m3.
To get the correct solutions use your first equation and start subtracting the masses starting at m1 not m3.

That's not right. The only relevant thing is that t1 is accelerating m1. You know a so you know T1 from f=ma.
(And your equation mixes the units; tension can't be a mass.)

Problems like this are always best approached by choosing the right order to do your sums. In this case, you just have to work from F to T2 and T1 and at each step you have all you need from the last one.
PS Never put numbers into formulae until the very last minute. You lose the pattern and spotting errors is much harder. A random 10, 20 or 30 in an expression makes it very hard to work out what's going on. If you don't like Algebra then bite the bullet and come to terms with it. It will save many errors in the future.