Minimum Height for Loop in Frictionless Incline Track

In summary: Sure. But if you actually wanted to solve for the minimum height, you'd need to input a minimum value for the kinetic energy term. (You'd solve for that term by applying Newton's 2nd law at the top of the loop.)
  • #1
mrshappy0
99
0

Homework Statement


A mass is placed at the top of a frictionless incline track. The bottom of the track goes into a loop. At what minimum height does the block with mass m have to be released above the ground in order to reach point b (the top of the loop).


Homework Equations




mg(hmin)=mvb2/2 +mg2R.

The Attempt at a Solution



The above formula shows that the minimum height has to be 2R because vb=0. I understand that Ugravity= mgh. But I don't understand why mv^2/2 was added on the right side. I am sitting here study my textbook and can't make sense of it.
 
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  • #2
mrshappy0 said:
The above formula shows that the minimum height has to be 2R because vb=0.
How fast must the block be moving at the top of the loop in order to maintain contact? (vb = 0 won't work.)
 
  • #3
That is from the answer key of a past exam. Maybe I stated it incorrectly. It seems right. If the block is just barely reaching that point that means that it is also stopping there which would make the velocity zero.
 
  • #4
mrshappy0 said:
That is from the answer key of a past exam. Maybe I stated it incorrectly. It seems right. If the block is just barely reaching that point that means that it is also stopping there which would make the velocity zero.
There's a minimum speed required at the top (greater than zero) otherwise the block will leave the track before ever reaching the top.

There's nothing wrong with that formula: it's just energy conservation. But if the answer key says that vb = 0, that's incorrect.
 
  • #5
Okay, well more importantly is that equation an example of the Mechanical Energy= Kinetic Energy+ potential energy?
 
  • #6
mrshappy0 said:
Okay, well more importantly is that equation an example of the Mechanical Energy= Kinetic Energy+ potential energy?
Sure. But if you actually wanted to solve for the minimum height, you'd need to input a minimum value for the kinetic energy term. (You'd solve for that term by applying Newton's 2nd law at the top of the loop.)
 

FAQ: Minimum Height for Loop in Frictionless Incline Track

What is a conservative force?

A conservative force is a type of force in physics that is path independent, meaning that the work done by the force on an object depends only on the initial and final positions of the object, not the path taken. This is in contrast to non-conservative forces, which depend on the path taken and can result in energy being lost or gained.

What are some examples of conservative forces?

Examples of conservative forces include gravity, electrostatic force, and elastic force. These forces all follow the principle of conservation of energy, where the total energy of a system remains constant even as the object moves or changes position.

How is work related to conservative forces?

Work is the energy transferred to or from an object by a force. In the case of conservative forces, work done by the force is independent of the path taken and only depends on the initial and final positions of the object. This means that the total work done by a conservative force is equal to the change in potential energy of the object.

What is the significance of conservative forces in physics?

Conservative forces play a crucial role in many physical phenomena, such as motion, energy, and stability. They are fundamental to concepts such as potential energy and the conservation of energy, and are used in many practical applications, such as in engineering and the design of structures.

How do you solve a conservative force problem?

To solve a conservative force problem, you typically need to determine the initial and final positions of the object, as well as the force acting on the object. From there, you can use equations such as the work-energy theorem and the principle of conservation of energy to calculate the work done by the force and the change in potential energy of the object. These calculations can then be used to determine the final position or velocity of the object.

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