How High Must a Marble Track Be to Complete a Loop-the-Loop?

  • Thread starter Thread starter dmahmoudi
  • Start date Start date
  • Tags Tags
    Marble Physics
Click For Summary

Homework Help Overview

The problem involves determining the minimum height a marble must be released from in order to successfully complete a loop-the-loop of radius R without falling off. The context includes considerations of energy conservation and forces acting on the marble during its motion.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the use of energy principles, including both rotational and translational kinetic energy, to analyze the marble's motion. Questions arise regarding how to incorporate the loop-the-loop's geometry and the forces acting on the marble, particularly at the top of the loop.

Discussion Status

Some participants have provided insights into the forces involved, such as the normal force and gravitational force, and how they relate to centripetal acceleration. There is an exploration of the conditions under which the marble will maintain contact with the track, particularly focusing on the velocity required at the top of the loop.

Contextual Notes

Participants note the importance of finding the height that allows the marble to achieve the necessary velocity at the top of the loop, emphasizing that insufficient velocity would result in the marble losing contact with the track.

dmahmoudi
Messages
3
Reaction score
0
A marble rolls down a track and around a loop-the-loop of radius R. The marble has mass m and radius r. What minimum height h must the track have for the marble to make it around the loop-the-loop without falling off?

I'm stumped - I'm assuming I need to use energy for this problem, but how do I factor in the loop-the-loop. Maybe with rotational kinetic energy?
 
Physics news on Phys.org
dmahmoudi said:
A marble rolls down a track and around a loop-the-loop of radius R. The marble has mass m and radius r. What minimum height h must the track have for the marble to make it around the loop-the-loop without falling off?

I'm stumped - I'm assuming I need to use energy for this problem, but how do I factor in the loop-the-loop. Maybe with rotational kinetic energy?

There are two forces on the marble - the normal force applied by the track and the force of gravity. At the top of the track both forces point down towards the centre of the track. By Newton's second, the sum of these forces cause a centripetal acceleration. Use energy to find v and thus the centripetal acceleration at the top of the loop. Use Newton's second to find the normal force at the top. Find the height at which the normal force is zero. If released above this height, the marble goes loop-the-loop. If released below this height, the marble goes plop.

Regards,
George
 
dmahmoudi said:
A marble rolls down a track and around a loop-the-loop of radius R. The marble has mass m and radius r. What minimum height h must the track have for the marble to make it around the loop-the-loop without falling off?

I'm stumped - I'm assuming I need to use energy for this problem, but how do I factor in the loop-the-loop. Maybe with rotational kinetic energy?

You will need both rotational and translational kinetic energy to find the velocity of the marble as a function of its height relative to the starting height. You will then need to find the starting height that will give the marble the velocity at the top of the loop such that gravity will be just sufficient to provide the centripetal force needed for the circular path of the marble (i.e., there will be no normal force from the track at the top of the loop). Any lower velocity at the top would result in the marble being separated from the track by the gravitational force (separation would occur before the marble reached the top of the loop).
 
Awesome, so I see. Thanks for the help guys!
 

Similar threads

  • · Replies 12 ·
Replies
12
Views
13K
  • · Replies 13 ·
Replies
13
Views
3K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 9 ·
Replies
9
Views
16K
  • · Replies 10 ·
Replies
10
Views
7K
Replies
4
Views
4K
Replies
3
Views
6K
  • · Replies 1 ·
Replies
1
Views
2K
Replies
14
Views
5K
Replies
5
Views
2K