Four different tensions on a cord with four different disks attached.

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In summary, the figure shows four disks suspended by cords, with the top cord pulling with a force of 98N and the shorter cords having tensions of T1=56.6 N, T2=50.8 N, and T3=8.1 N. To calculate the mass of each disk, the tensions on both sides of the disk must be factored in, taking into account that the disks are in equilibrium.
  • #1
bearhug
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The figure shows an arrangement in which four disks are suspended by cords. The longer, top cord loops over a pulley and pulls with a force of magnitude 98N on the wall to which it is attached. The tensions in the shorter cords are T1=56.6 N, T2=50.8 N, and T3=8.1 N. What is the mass of disk A,B,C,D?

Unfortunately I can't put the figure on here so hopefully the question is descriptive enough. What's throwing me off on this question is that there are four different tensions. Everything is vertical and I'm wondering if in order to calculate the mass of each disk do the tensions on both sides of the disk need to factored in? For example disk A is at the top and has a cord above with a tension of 98N and has a cord attached below with tension of 56.6N that attaches to disk B. This is what's confusing me, any help is appreciated.
 
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  • #2
bearhug said:
Everything is vertical and I'm wondering if in order to calculate the mass of each disk do the tensions on both sides of the disk need to factored in? For example disk A is at the top and has a cord above with a tension of 98N and has a cord attached below with tension of 56.6N that attaches to disk B.
You need to take advantage of the fact that the disks are in equilibrium, which means that the net force is zero on each. If two ropes pull on a disk, you must include both tensions in calculating the net force.
 
  • #3


I would approach this question by first considering the basic principles of physics and how they apply to this scenario. The first thing to note is that the total force acting on each disk is equal to the sum of the tensions on all the cords attached to it. In this case, we have four different tensions (T1, T2, T3, and 98N) acting on each disk.

Using Newton's second law, F=ma, we can set up four equations, one for each disk, to solve for the mass of each disk. The equations would look something like this:

Disk A: T1 + T2 + T3 + 98N = ma
Disk B: T2 + T3 + 98N = mb
Disk C: T3 + 98N = mc
Disk D: 98N = md

Since we have four equations and four unknowns (the mass of each disk), we can solve for each mass separately. By substituting the given values for T1, T2, and T3, we can solve for the mass of each disk.

Disk A: (56.6N) + (50.8N) + (8.1N) + (98N) = ma
Disk B: (50.8N) + (8.1N) + (98N) = mb
Disk C: (8.1N) + (98N) = mc
Disk D: (98N) = md

Solving for each mass, we get:
ma = 213.5 kg
mb = 156.9 kg
mc = 106.1 kg
md = 98 kg

So, the mass of each disk is approximately 213.5 kg, 156.9 kg, 106.1 kg, and 98 kg, respectively. It is important to note that these values are approximate, as we are assuming that the cords and pulley are massless and there is no friction present in the system.

In conclusion, by using basic principles of physics and setting up equations for each disk, we can determine the mass of each disk in this scenario. It is important to consider all the forces acting on each object in order to accurately solve for the mass.
 

1. What is the purpose of the experiment with four different tensions on a cord and four different disks attached?

The purpose of this experiment is to study the relationship between the tension applied to a cord and the resulting motion of four attached disks.

2. How are the four different tensions applied to the cord?

The four different tensions are applied by attaching weights of varying masses to each of the four disks, which are connected to the cord.

3. What factors might affect the results of this experiment?

The results of this experiment may be affected by factors such as the material and weight of the disks, the length and elasticity of the cord, and external influences such as air resistance or friction.

4. What types of data should be collected during this experiment?

Data that should be collected during this experiment include the masses of the disks, the corresponding tensions on the cord, and the resulting displacement or motion of the disks.

5. How can the results of this experiment be interpreted and applied in real-world situations?

The results of this experiment can be interpreted to understand the relationship between tension and motion in systems with multiple masses, which can be applied in various real-world situations such as analyzing the movement of objects suspended by cords or understanding the behavior of pulley systems.

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