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

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In summary: 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.In summary, the tension in the cord connecting boxes B and C is F=ma. Block B has a weight Wb and is subjected to a tension T. Block A has a mass mA and is subjected to a tension T. Block B has a weight Wb and is subjected to a tension T. Block A has a mass mA and is subjected to an acceleration a.
  • #1
snoggerT
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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.
 
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  • #2
snoggerT said:
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?
 
  • #3
PhanthomJay said:
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.
 
  • #4
snoggerT said:
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.
 
  • #5
PhanthomJay said:
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.
 
  • #6
snoggerT said:
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: [tex]M_c(g) -T_c = M_c(a)[/tex]
 
  • #7
PhanthomJay said:
What did you come up with in your FBD's? Here's the bottom block C FBD: [tex]M_c(g) -T_c = M_c(a)[/tex]

- 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.
 
  • #8
snoggerT said:
- 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.
 

1. How can I solve the tension problem in boxes B & C in Figure 5-50?

To solve the tension problem in boxes B & C, you will need to first identify the forces acting on the boxes. Then, use Newton's second law of motion and apply it to each box separately. This will allow you to determine the net force on each box and calculate the tension in the strings. Finally, you can use the equations for tension and equilibrium to solve for the unknown variables.

2. What is the importance of solving tension problems in physics?

Solving tension problems is important in physics because it allows us to understand and analyze the forces acting on objects in various situations. It also helps us to determine the stability and equilibrium of systems, which is crucial in many real-world applications such as building structures and designing machines.

3. What are the common mistakes made when solving tension problems?

One common mistake is not considering all the forces acting on the objects in the system. It is important to identify all the external and internal forces, including tension, weight, and friction. Another mistake is not properly applying Newton's second law of motion or using incorrect values for the forces. It is crucial to carefully label and use the correct variables in the equations.

4. Are there any tips for solving tension problems more efficiently?

Yes, there are a few tips that can help you solve tension problems more efficiently. First, draw a free-body diagram for each object in the system to visualize the forces acting on it. Then, label all the known and unknown variables and use the correct equations to solve for the unknowns. It can also be helpful to break down the problem into smaller, more manageable steps.

5. Can I use the same approach to solve tension problems with different configurations?

Yes, the approach for solving tension problems is the same regardless of the configuration or number of boxes involved. However, the equations and variables used may vary depending on the specific scenario. It is important to carefully analyze the forces and use the appropriate equations for each individual case.

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