Classical mass rope mass problem

In summary, the conversation discusses a system with two masses connected by a rope, one on an incline and the other hanging off a cliff. The speaker's initial reasoning was that the tension force on the mass on the incline would be equal to the weight of the hanging mass, resulting in incorrect results for acceleration and tension. The conversation then points out the flaw in this reasoning, explaining that the tension force is not equal to the weight of the hanging mass.
  • #1
kasperrepsak
31
0
hey,

This question is about a system where one mass is on an incline and another hanging of it. They are connected with a rope.. Its a classical mass rope mass problem. My reasoning was that since the mass hanging of the cliff is pulling on the rope with a force of mg, the rope will be pulling the mass on the cliff with that same force.. so T (Tension force) on the mass on the cliff = weight of mass hanging of the cliff.
Using this reasoning i ended up with bad results for acceleration and tension force for the system. In books other approaches to these problems are used.. but i would like to know where my reasoning is wrong? Does it have to do with part of the force being neutralised by the edge of the cliff? (or in some problems a massless/frictionless pulley). Ofc we totally disregard friction and mass of rope in these problems.

thanks
 
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  • #2
Welcome to Physics Forums.
kasperrepsak said:
hey,

This question is about a system where one mass is on an incline and another hanging of it. They are connected with a rope.. Its a classical mass rope mass problem. My reasoning was that since the mass hanging of the cliff is pulling on the rope with a force of mg, the rope will be pulling the mass on the cliff with that same force.. so T (Tension force) on the mass on the cliff = weight of mass hanging of the cliff.
Using this reasoning i ended up with bad results for acceleration and tension force for the system. In books other approaches to these problems are used.. but i would like to know where my reasoning is wrong? Does it have to do with part of the force being neutralised by the edge of the cliff? (or in some problems a massless/frictionless pulley). Ofc we totally disregard friction and mass of rope in these problems.

thanks
Let's assume that the mass-rope system is initially at rest. If the rope exerts a force mg on the mass and gravity exerts a force mg in the opposite direction, will the mass ever move?
 
  • #3
Hootenanny said:
Welcome to Physics Forums.

Let's assume that the mass-rope system is initially at rest. If the rope exerts a force mg on the mass and gravity exerts a force mg in the opposite direction, will the mass ever move?

which mass r ye talking about?
 
  • #4
kasperrepsak said:
which mass r ye talking about?
The mass hanging off the cliff.
 
  • #5
Hootenanny said:
The mass hanging off the cliff.

ofc it wont.. obviously there is something wrong here in my reasoning.. but could you tell me where my reasoning is wrong as opposed to showing me what weird consequences that would have?
 
  • #6
kasperrepsak said:
ofc it wont.. obviously there is something wrong here in my reasoning.. but could you tell me where my reasoning is wrong as opposed to showing me what weird consequences that would have?
That is precisely where your reasoning is wrong. You have assumed that the tension in the rope is equal to mg, which it isn't.
 
  • #7
aha ok, thank you :)
 

1. What is the Classical mass rope mass problem?

The Classical mass rope mass problem is a physics problem that involves determining the acceleration of a system comprised of a mass connected to a rope or string, which is attached to a fixed point, and another mass hanging off the end of the rope. This problem is often used to illustrate concepts of Newton's laws of motion and energy conservation.

2. How do you solve the Classical mass rope mass problem?

To solve the Classical mass rope mass problem, you first need to draw a free body diagram of the system, identifying all the forces acting on each mass. Then, you can use Newton's second law (F=ma) to determine the acceleration of the system. Finally, apply principles of energy conservation to find the final velocities of the masses.

3. What are the assumptions made in the Classical mass rope mass problem?

The Classical mass rope mass problem assumes that the rope or string is massless and can only support tension forces. It also assumes that there is no friction or air resistance acting on the masses. Additionally, the problem assumes that the rope is inextensible, meaning it does not stretch or compress.

4. Can the Classical mass rope mass problem be solved using calculus?

Yes, the Classical mass rope mass problem can be solved using calculus. In fact, it is often used as an introductory example in calculus-based physics courses to demonstrate the application of derivatives and integrals in solving real-world problems.

5. What are some real-life applications of the Classical mass rope mass problem?

The Classical mass rope mass problem has many real-life applications, such as determining the acceleration of objects attached to ropes or cables, such as elevators or ski lifts. It is also used in analyzing the motion of pendulums and other systems with swinging masses, as well as in pulley systems and other mechanical devices.

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