Newton's law problem on homogeneous flexible rope

In summary, the problem involves a homogeneous flexible rope resting on a wedge with angles α and β with respect to the horizontal. The wedge is moved with an acceleration of a to keep the rope stationary, and the tension in the rope is assumed to be in the horizontal direction. The solution involves using Newton's laws and the concept of pseudo forces to find the acceleration a by eliminating the tension. However, it is easier to find an acceleration where the angles differ from the gravitational acceleration + acceleration vector by the same amount.
  • #1
Titan97
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Homework Statement


A homogeneous flexible rope rests on a wedge whose sides make angles α and β with horizontal. The centre of rope lies on C. With what acceleration should the wedge be moved for the rope to stay stationary with respect to wedge? (all surfaces are smooth).

Homework Equations


##F_{ext}=Ma##

The Attempt at a Solution


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My first doubt is the direction of tension. I think its horizontal.
If α>β, then the wedge should be accelerated in left direction. Let that acceleration be ##a##.
Using Newton's laws and concept of pseudo forces,
##Tcos\alpha+\frac{m}{2}acos\alpha=\frac{m}{2}gsin\alpha##
Similarly,
##Tcos\beta-\frac{m}{2}acos\beta=\frac{m}{2}gsin\beta##
I can easily find ##a## now by eliminating ##T##. But is my method correct?
 
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  • #2
Tension will always be in the direction of the rope, which makes your method a bit difficult. You cannot assume the tension to change direction at the edge without the edge providing a non negligible force. If you want to do it with tension, the tension shoulf be the same on both sides and in the direction of the rope. However, the easier way is to search for an acceleration where the angles differ from the gravitational acceleration + acceleration vector by the same amount.
 
  • #3
I did not understand that. I will try solving using tension.
 

FAQ: Newton's law problem on homogeneous flexible rope

1. What is Newton's law problem on homogeneous flexible rope?

Newton's law problem on homogeneous flexible rope refers to a physics problem that involves analyzing the motion of a rope that is undergoing tension and acceleration due to an external force. This problem is based on Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration.

2. What are the key components of this problem?

The key components of Newton's law problem on homogeneous flexible rope include the mass of the rope, the external force acting on the rope, the tension in the rope, and the acceleration of the rope. These components are used to calculate the net force and solve for the motion of the rope.

3. How is this problem solved?

This problem is solved by applying Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration. By setting up and solving equations that incorporate the key components of the problem, the motion of the rope can be determined.

4. What are some real-world applications of this problem?

This problem has many real-world applications, such as analyzing the motion of a rope being pulled by a person or a machine, understanding the behavior of a rope in a pulley system, and calculating the forces acting on a rope during rock climbing or other activities that involve ropes.

5. What are some tips for solving this problem?

Some tips for solving Newton's law problem on homogeneous flexible rope include clearly defining and labeling all components of the problem, setting up equations that incorporate Newton's second law of motion, and using proper units and equations to ensure accurate calculations. It is also important to check your work and consider any external factors that may affect the motion of the rope.

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