Solving Tension Problem: Help for Boxes B & C in Figure 5-50

[snoggerT]

In Figure 5-50, three ballot boxes are connected by cords, one of which wraps over a pulley having negligible friction on its axle and negligible mass. The masses are mA = 28.0 kg, mB = 40.0 kg, mC = 22.0 kg.

Box A is on the table and B/C are hanging from the table from the pulley system. So B/C would be on the vertical

(a) When the assembly is released from rest, what is the tension in the cord that connects boxes B and C?
F=ma
I'm not really sure where to start for finding the tension between the 2 boxes. Any hints to get me started would be nice, thanks.

 

[PhanthomJay]

In Figure 5-50, three ballot boxes are connected by cords, one of which wraps over a pulley having negligible friction on its axle and negligible mass. The masses are mA = 28.0 kg, mB = 40.0 kg, mC = 22.0 kg.

Box A is on the table and B/C are hanging from the table from the pulley system. So B/C would be on the vertical

(a) When the assembly is released from rest, what is the tension in the cord that connects boxes B and C?



F=ma



I'm not really sure where to start for finding the tension between the 2 boxes. Any hints to get me started would be nice, thanks.

Draw free body diagrams of each block. Apply Newton 2 for each block. What can you say about the acceleration of each block?

 

[snoggerT]

Draw free body diagrams of each block. Apply Newton 2 for each block. What can you say about the acceleration of each block?

I'm pretty sure I drew my free body diagrams right, but that leaves me with mg, T and a. of which I only know mg, so I don't really know how to figure out my tension or acceleration. I know that Acceleration is the same for all the blocks.

 

[PhanthomJay]

I'm pretty sure I drew my free body diagrams right, but that leaves me with mg, T and a. of which I only know mg, so I don't really know how to figure out my tension or acceleration. I know that Acceleration is the same for all the blocks.

You have 3 fbd's, and 3 unknowns, the tension in the cable between block A and B, the tension in the cable between block B and C, and the acceleration. Solve for these values using 3 equations with 3 unknowns.

 

[snoggerT]

You have 3 fbd's, and 3 unknowns, the tension in the cable between block A and B, the tension in the cable between block B and C, and the acceleration. Solve for these values using 3 equations with 3 unknowns.

I don't know. I'm absolutely lost right now with these tension problems. I guess I'm going to go back and re-read the chapter to see if I can get a better understanding of it. the problem is that there is about 1/3 of a page on tension in the book. thanks for the help though.

 

[PhanthomJay]

I don't know. I'm absolutely lost right now with these tension problems. I guess I'm going to go back and re-read the chapter to see if I can get a better understanding of it. the problem is that there is about 1/3 of a page on tension in the book. thanks for the help though.

What did you come up with in your FBD's? Here's the bottom block C FBD: $$M_c(g) -T_c = M_c(a)$$

 

[snoggerT]

What did you come up with in your FBD's? Here's the bottom block C FBD: $$M_c(g) -T_c = M_c(a)$$

- I had that for the block C, but I have 2 unknowns in that equation (a and T). The only other thing I could think of would be to figure out the equation for block B and then relate the 2 equations together. I'm just not sure how to set the equation up for block B since it's mass is larger than Block C.

 

[PhanthomJay]

- I had that for the block C, but I have 2 unknowns in that equation (a and T). The only other thing I could think of would be to figure out the equation for block B and then relate the 2 equations together. I'm just not sure how to set the equation up for block B since it's mass is larger than Block C.

Draw the FBD for block B and see what you get. You have 2 tension forces plus the block B weight, all acting on Block B. Tension forces always pull away from the object. Then draw the FBD of Block A. You will now have 3 equations with 3 unknowns, and the problem is solvable.