Statics of Particle homework help

[mumu94]

Homework Statement

In the following diagram (see attachment), w=80N and the net force is 0.

The Attempt at a Solution

I basically made two free body diagrams and applied Net Force = 0 for each axis, obtaining 4 equations with 4 variables (T1,T2,T3,T4). I got T1=56N T2=98N T3=115N T4=189N

However, my answers are apparently completely different from the "correct ones", which are: T1=37N, T2=88N, T3=77N, T4=139N.

I would like to know whether my answers are correct or not.

Help is appreciated! Thanks!

 

[Nugatory]

I would like to know whether my answers are correct or not.

Either I've fat-fingered something with my calculator, or your answer for T2 (98N) is correct. I haven't checked any of the others, but they're all connected together so there isn't much point after you've found one wrong.

BTW, your method of solving the problem, although correct and the most general approach, is not the easiest. For this particular diagram, it's easier to start at the bottom and work up:
- What does T2 have to be to cancel out the vertical force from the weight?
- now that we know T2, what does T1 have to be to not have any horizontal aceleration?
- And work your way up to T3 and T4.

 

[mumu94]

Either I've fat-fingered something with my calculator, or your answer for T2 (98N) is correct. I haven't checked any of the others, but they're all connected together so there isn't much point after you've found one wrong.

BTW, your method of solving the problem, although correct and the most general approach, is not the easiest. For this particular diagram, it's easier to start at the bottom and work up:
- What does T2 have to be to cancel out the vertical force from the weight?
- now that we know T2, what does T1 have to be to not have any horizontal aceleration?
- And work your way up to T3 and T4.

Thanks! I have another question concerning the same topic, about this problem:

(see attachment)

"If the kinetic friction coefficient between m2 and the table is 0.56, W1 = 1.5N and W2= 2.5N. What is M3 so that the system will move at a constant velocity?"

How can I know the direction of the friction force in this case, or would it have two solutions, one so that the system moves to the right, and one so that it moves to the left?

 

[Nugatory]

How can I know the direction of the friction force in this case, or would it have two solutions, one so that the system moves to the right, and one so that it moves to the left?

Try solving it both ways, once left moving and once right moving. See what answers you get.