Loop-de-loop: why does the track have to start higher than the highest point of the loop?

Question

When you roll (or slide) something through a loop-de-loop, why do you have to start the track higher than the top of the loop?

I'm not talking about something that propels itself, like a toy race car with a motor.

Imagine a track with zero friction. You have a track that leads down into a loop-de-loop. The loop reaches a height of 1 meter. The part of the track that leads down has to start HIGHER than 1 meter, even considering zero friction. I remember this fact from physics, but I don't understand why.

Can anybody explain this to me? It doesn't matter whether the object slides (like a small block) or rolls, as long as you assume zero friction.

Answer 1

On an ideal, frictionless track, if you started at exactly the height of the highest point on the loop, when you get to the loop, you will decelerate and come to a stop at the top.

Conservation of energy requires that the sum of the cart's potential and kinetic energy be constant.

If you begin at rest 1 meter in the air, you have zero kinetic energy, and 1 meter's worth of potential energy. As you accelerate down the hill, you lose potential energy and gain an identical amount of kinetic energy. However, when you approach the top of the loop, your potential energy climbs to 1 meter's worth. Right at the top, when you have 1 meter's worth of potential energy, you MUST (by conservation of energy) have exactly zero kinetic energy. Zero kinetic energy means you have zero velocity. The cart comes to rest at the top of the loop.

Answer 2

The ball has two types of energy. One is translational energy, from the pull of gravity towards the center of earth. The other is rotational energy, from the reaction force of the loop-de-loop on the ball.
The formula for translational energy is E = (1/2)*m*v*v
The formula for rotatational energy is E = (1/2) * I * w*w

where I = moment of inertia and
w = omega = angular velocity.

The previous answers are all wrong because they neglect the rotational energy. It is this rotational energy that keeps the ball from coming up to height h in the loop-de-loop.

LOL, when I was a student, I didn't believe this until I went down to the Physics lab and set up the experiment. I thought the ball would go all the way to the top, but it didn't. It went around to about the ten o'clock position then derailed and fell down to the table. I still remember my amazement when this happened, even years later!

Answer 3

easy, the higher you go the more potential (gravitational) energy you gain, when going around a loop-de-loop, you need that energy to go all the way around. And thanx to the 2nd law of thermodynamics (BIG words- basically that energy can't come from thin air) you have to have more potential energy starting off to clear the loop-de-loop. In a perfect world, thiese can be level, but due to friction and other factors, you must be higher than the loop-de-loop to overcome these factors. A little complicated, but it's just kinda a general concept in my head.

Answer 4

Potential energy becomes kinetic energy. Using this fact, the track must start higher than the loop-de-loop because there must be enough gravitational potential energy to be converted to kinetic energy to complete the loop.

Answer 5

An object in motion will move in a straight line at the same speed unless a force acts on it to change its direction or speed. As an example, suppose I kick a soccer ball so that it is going to roll past you very quickly. As it passes you, if you tap it slightly at a right angle to its path, it will turn a little bit in the way you tap it. Similarly, a third person could stand by that path, tap it a little and cause it to turn a little more. If we got enough people, we could all keep tapping it so as to make it go in a circle. As long as each person kept tapping it towards the middle, it would continue going in a circle. But if one person let it go, it would just keep going in a straight line. For a roller coaster, the track is acting like all those soccer players lined up in a circle. It is constantly forcing the cart to go in a circle, even though it would go in a straight line if the track were not there. The force that the track applies to the cart is called the "normal" force because normal means perpendicular, and the force should be perpendicular to the path in order to keep the cart turning as it goes around the circle. Now you may wonder what role does gravity play? It is important in how the track is designed. If you get the cart going very fast, and then angled it upward on a ramp, it would rise to a certain height, but finally the constant pull of gravity would slow it down, and it would start to fall back down the ramp. The top of the loop is designed to be much lower than the height the cart would fly up in the air if there were no track.. So the track is actually having to push against the cart to make it turn in a tighter loop than it would naturally fly if there weren't a track. For most roller coasters, you will be towed up a large hill at the beginning, and then you start coasting. The top of the loop is lower than the height of the first large hill, and this is done to make sure that the cart has enough speed at the bottom of the loop to get through the loop. Hope this helps!

Answer 6

the height of the object gives it the energy needed to later go up to the top of the loop. if you start at lower or equal you would not have enough energy to get to the top of the loop. it is one of those laws. your object can not "get" more energy than it started with. potential converted to kinetic etc.

Answer 7

Well, wouldn't gravity factor in? Wouldn't the drop allow it to pick up the unnecessary propulsion to make the loop?

Answer 8

probably it needs to gain the momentum from the higher height to complete the loop...

Answer 9

Gravity. It automaitcally makes you lose your energy like this.
Thats all their is to it. But on top of that, zero friction is impossible.

Answer 10

confusing problem. check out onto google or bing. that will can assist!