Tension in rope when the system is accelerating

In summary, the problem involves two masses hanging from a platform, with one mass connected to the platform by a rope and the other mass connected to the first mass by a second rope. The platform has a mass of 200kg, the first mass is 70kg, and the second mass is 90kg. The system is accelerating upwards at a rate of 2 m/s^2 and the ropes are assumed to be massless. To find the tension in the top rope, the sum of the forces acting on the two masses must be equal to the mass times the acceleration. This can be solved using Newton's 2nd law or by considering the system in an accelerating frame of reference. It is suggested to use g =
  • #1
KKazaniecki
12
0
hey, I'm currently going through a mechanics course on edx.org . And part of last's week homework was this problem. well okay I don't know how to add images so I'm going to try my best to describe it.

There is a platform has a mass of 200kg. From that platform a rope hangs( with tension TA with a mass of 70kg at the end of it ( say a human ). Then from that mass ( human ) another rope holds another mass 90kg. it says it in the problem that g = 10 m/s^2 and the acceleration of the whole thing is 2 m/s^2 .Also the ropes are ideal ropes so have no mass.

What is the tension Ta ( of the first rope ) ?


here's the question copied " Man A (70kg) and Man B (90kg) are hanging motionless from a platform (200kg) at rest. What is the tension, TA, in the top rope if the platform accelerates upward at a constant rate of 2 m/s2? Assume the ropes are massless and use g = 10 m/s2. "


hope I made it clear . So after I submitted my answer ( forgot what it was now ) It showed me the correct answer which is 1920 N. I could just accept it and move on. But I'll rather learn the physics behind it. And it's a problem I'm struggling with so I'll help me develop my understanding of physics.
Okay so I have no idea on how to approach it. I tried so many ways but I never get the answer they get. So if you could , please explain the solution for me :)
 

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  • #2
Assume g=12m/s^2 and just compute the weight.
 
  • #3
A.T. said:
Assume g=12m/s^2 and just compute the weight.

thanks , that works .Could you explain why ? isn't acceleration due to gravity downwards , and the system acceleration upwards . So why do they add up together?
 
  • #4
Add the masses of the two men together and find the net force acting on them using Newton's 2nd law. That net force is a resultant of the weight of the men downwards and the rope's tension upwards.
 
  • #5
KKazaniecki said:
thanks , that works .Could you explain why ? isn't acceleration due to gravity downwards , and the system acceleration upwards . So why do they add up together?
If the reference frame accelerates upwards, the objects tend to accelerate downwards. This is just like artificial gravity from acceleration added to the normal gravity. In General Relativity they are in fact the same thing.

The formal ways to solve it are these:

- Intertial frame:Find the tensions that together with gravity produce the required net forces for the acceleration of 2m/s^2 of each mass.

- Non-Inertial frame: In the Accelerating rest frame of the masses the net forces must be zero, but there is an inertial force -ma acting on every mass m.

- Intertial frame (quasi static): In this trivial case, its the same as the non-Inertial frame. But if you encounter a problem where interacting bodies accelerate differently, then you cannot construct a common rest frame for them. In this case you replace each individual acceleration a with a force -ma for every object, and assume that all net forces must be zero. This allows you to figure out the interaction forces at one time instant, but not the movement over time (hence "quasi static").
 
  • #6
Why don't you just apply Newton's 2nd law?

Draw a free body diagram of each man or (even easier) both men together. What forces act? (Hint: The tension in the rope above man A is one of those forces.) Apply ∑F = ma.
 
  • #7
A.T. makes things difficult for newcomers. He isn't wrong, just that it's unnecessarily difficult to follow and very easy to make mistakes. So stick to the simplest possible frame of reference and g = 9.8 (or 10 in this case).

To corroborate my argument: even the makers of the exercise fall into such a trap: They clearly state the two guys are hanging motionless. It is very difficult to explain how a motionless person can be motionless if the platform he hangs from accelerates with 2 m/s2! Motionless is pretty meaningless in this way ! (Intentionally provocative to trigger the people from the world's best universities -- even "best" is relative :smile:).
 
  • #8
BvU said:
Motionless is pretty meaningless in this way ! (Intentionally provocative to trigger the people from the world's best universities -- even "best" is relative :smile:).
Motionless obviously just means that they hang passively, without climbing up or down the rope. Since the platform is initially at rest they are motionless. Then the platform accelerates upwards.
 
  • #9
yeah... using g=12m/s^2 is easier and simpler. But to someone not familiar with the ideas of general relativity, it might be best to just use g=10m/s^2 and solve such that there is an upward acceleration of 2m/s^2.
 
  • #10
Let's err on the safe side and not expect KK to be familiar with GR ideas :smile:
 
  • #11
thanks guys for your help, I understand it now :)
 

1. How does tension in a rope change when the system is accelerating?

When a system is accelerating, the tension in a rope will also change. The tension will increase in the direction of the acceleration, and decrease in the opposite direction. This is because the rope experiences a force in the direction of the acceleration, causing it to stretch and increase in tension.

2. What factors affect the tension in a rope when the system is accelerating?

The tension in a rope when the system is accelerating is affected by several factors. These include the mass and acceleration of the system, the length and elasticity of the rope, and any external forces acting on the system. Additionally, the angle at which the rope is attached to the system can also affect the tension.

3. How can the tension in a rope be calculated during acceleration?

The tension in a rope during acceleration can be calculated using Newton's second law, which states that force is equal to mass times acceleration (F=ma). By determining the mass and acceleration of the system, the tension in the rope can be calculated using this equation.

4. Does the tension in a rope affect the acceleration of the system?

Yes, the tension in a rope can affect the acceleration of the system. If the tension is greater than the force required to accelerate the system, the system will accelerate at a faster rate. However, if the tension is less than the required force, the acceleration of the system will be slower or may not occur at all.

5. Can the tension in a rope exceed the weight of the system during acceleration?

Yes, the tension in a rope can exceed the weight of the system during acceleration. This is because the tension is caused by the force applied to the rope, which can be greater than the force of gravity acting on the system. However, the tension in the rope cannot exceed the force applied to the system, as it is limited by the maximum force the rope can withstand before breaking.

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