Minimum Height for Loop in Frictionless Incline Track

Click For Summary

Homework Help Overview

The problem involves determining the minimum height from which a mass must be released on a frictionless incline to successfully navigate a loop at the bottom of the track. The discussion centers around the application of energy conservation principles in the context of mechanics.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the formula related to energy conservation and question the implications of the velocity at the top of the loop. There is uncertainty about the conditions under which the block maintains contact with the track and the interpretation of the minimum height derived from the equation.

Discussion Status

The conversation is ongoing, with participants exploring the validity of the formula and its assumptions. Some have pointed out potential inaccuracies in the interpretation of the velocity at the top of the loop, while others are clarifying the relationship between kinetic and potential energy in this context.

Contextual Notes

There is a reference to an answer key from a past exam that may contain inaccuracies regarding the velocity at the top of the loop, which is being critically examined by participants. The discussion also highlights the need for a minimum kinetic energy value to solve for the minimum height.

mrshappy0
Messages
97
Reaction score
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.
 
Physics news on Phys.org
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.)
 
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.
 
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.
 
Okay, well more importantly is that equation an example of the Mechanical Energy= Kinetic Energy+ potential energy?
 
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.)
 

Similar threads

Minimum h for Car to Remain on Track Around Loop
  • · Replies 6 ·
Replies
6
Views
2K
Understanding the Minimum Speed to Keep Carriage on Tracks in a Loop
  • · Replies 5 ·
Replies
5
Views
2K
Starting height of marble rolling around a loop the loop
  • · Replies 12 ·
Replies
12
Views
13K
Loop the Loop Problem Solution | N > 0, Energy Conservation Method
  • · Replies 8 ·
Replies
8
Views
4K
How high does the frictionless ramp have to be for the ball....
  • · Replies 5 ·
Replies
5
Views
2K
Conservation of energy problem: Ball rolling down inclined plane and then through a loop-the-loop
  • · Replies 10 ·
Replies
10
Views
3K
Why does the speed change at the bottom of the loop-the-loop?
  • · Replies 5 ·
Replies
5
Views
2K
Why Can't Conservation of Energy Be Used to Solve the Loop Problem in Physics?
  • · Replies 3 ·
Replies
3
Views
2K
Conservation of Energy on a frictionless incline
  • · Replies 2 ·
Replies
2
Views
4K
Magnitude of force of a disk on a circular track
  • · Replies 6 ·
Replies
6
Views
3K