Calculating Tension in a Nonmassless Rope with Unequal Vertical Forces

In summary, when calculating the tension at the midpoint of a vertical rope with two unequal vertical forces acting on either end, you can find the net acceleration of the rope and choose either half of the rope to calculate the tension. The tension acts inside the rope and can be found by using the equation Fnet = ma. In the example, the tension is equal to 20 N.
  • #1
agam goel
1
0
When 2 unequal vertical forces act on the 2 ends of a vertical rope, how do I calculate the tension at the midpoint?
First I calculated the net acceleration of the rope, then I choose any 1 half of the rope for fbd of it and then where and how does the tension act?
 
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  • #2
The tension of the rope acts inside the rope. If you cut the rope, you will find the tension, acting outwards in either of the cut ends, as seen in the picture. Then, once you know that you can calculate the tension using anyone half of the ropes. In the example, let's say the rope has mass 1 kg. Then, the weight of the role is 1 (10) = 10 N, acting at the center of mass of the rope, that is halfway up or down, i.e. in the middle, not shown on the diagram. Then, for acceleration a, the equation is, Fnet = ma. ∴ 30-10-10(weight of the rope) = 1 (a). This gives a = 10ms-2. Now, taking the upper half, which has half the mass, and again applying the equation, we have 30-T-5 (weight of the upper half now acting downwards at the center of the half) = 0.5 (10). Thus, T = 20 N. You will arrive at the same answer, if you work on the bottom half of the rope. Hope it helped. :smile:
 

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What is tension in a nonmassless rope?

Tension refers to the force that is exerted on a rope when it is pulled taut. In a nonmassless rope, this force is caused by the weight of the rope itself and any other objects attached to it.

How is tension calculated in a nonmassless rope?

To calculate tension in a nonmassless rope, you can use the formula T=mg, where T is the tension, m is the mass of the object pulling on the rope, and g is the acceleration due to gravity. This assumes that the rope is in equilibrium, meaning that the forces acting on it are balanced.

What factors affect tension in a nonmassless rope?

The tension in a nonmassless rope is affected by several factors, including the mass of the objects attached to it, the angle at which the rope is pulled, and the strength and elasticity of the rope itself.

Why is tension important in a nonmassless rope?

Tension is important in a nonmassless rope because it determines the maximum weight that the rope can support without breaking. It is also crucial for ensuring the stability and safety of any objects or structures that are being held in place by the rope.

How can tension in a nonmassless rope be controlled?

Tension in a nonmassless rope can be controlled by adjusting the force at which the rope is pulled or by using additional support systems, such as pulleys or anchors. It is important to carefully consider and calculate the tension in a rope to prevent it from exceeding its maximum capacity.

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