Soln: Acceleration of System & Tension in Ropes

[kj99]

Homework Statement

Find the Acceleration of the system and the tensions in the three ropes.

*If you can't see the picture there's a triangle (ABC), a train of four objects and three pulleys (one exactly at each corner). Side AC (hypotenuse) at the bottom, side AB to the left and side AC to the right.
Angle A=37
Angle B=53
Angle C=90
There is only kinetic friction between A and B of 0.125.

mass A= 10kg (hangs straight off the pulley at Angle A)
mass B= 5kg (on AB)
mass C= 10kg (on BC)
mass D= 20kg (hanging off the pulley at Angle C)

Up is positive

Homework Equations

The Attempt at a Solution

I got an acceleration of 28.96m/s/s but I'm fairly sure it's wrong lol. I used these equations using scalar values:

m1: Fnet= T1 - Fg
10a= T1 - (10)(10)
T1= 10a+ 100

m2: Fnet= T2 -T1 - Fres - Fg//
5a= T2 - T1 - (0.125)(50cos37) - 50sin37
T2= T1 + 5a + 35.08

m3: Fnet= T3 + Fg// - T2
10a= T3 + 100sin53 - T2
T3= T2 + 10a -79.86

m4: Fnet= Fg - T3
20a= 200 - T3
T3= 200-20a

After finding these four equations I just started at the last equation and kept substituting from there.

 

[TSny]

Your equations look correct. But as you noted, your final answer for the acceleration can't be correct. ( It's greater than free fall acceleration.) I guess you will need to check your algebra. It's easy to slip up on a sign or something.

 

[kj99]

Your equations look correct. But as you noted, your final answer for the acceleration can't be correct. ( It's greater than free fall acceleration.) I guess you will need to check your algebra. It's easy to slip up on a sign or something.

Is this how you would approach and solve this question?

 

[TSny]

Is this how you would approach and solve this question?

Yes. But what would happen if you added all the red equations below:

m1: Fnet= T1 - Fg
10a= T1 - (10)(10)
T1= 10a+ 100

m2: Fnet= T2 -T1 - Fres - Fg//
5a= T2 - T1 - (0.125)(50cos37) - 50sin37
T2= T1 + 5a + 35.08

m3: Fnet= T3 + Fg// - T2
10a= T3 + 100sin53 - T2
T3= T2 + 10a -79.86

m4: Fnet= Fg - T3
20a= 200 - T3
T3= 200-20a

 

[kj99]

Yes. But what would happen if you added all the red equations below:

Yeah I tried it again and I got 7.66m/s/s. I probably messed up in my substitutions somewhere along the way.

 

[TSny]

Yeah I tried it again and I got 7.66m/s/s. I probably messed up in my substitutions somewhere along the way.

Darn. That's not what I get. Of course I could be making an error in solving the equations. (But I did check my work.)

 

[kj99]

Darn. That's not what I get. Of course I could be making an error in solving the equations. (But I did check my work.)

Lol idk, I'll try the question with vectors instead of vectors maybe.

 

[TSny]

I still like my suggestion in post #4.