Loop-the-loop

Definition

A loop-the-loop is a circular path that an object follows, often seen in roller coasters or toy tracks. It involves the conversion of kinetic energy to potential energy and vice versa as the object travels through the loop.

5 Must Know Facts For Your Next Test

1. The minimum speed at the top of the loop is determined by setting the gravitational force equal to the centripetal force required to keep the object on its path.
2. The normal force at the top of the loop can be zero if speed conditions are met, meaning gravity alone keeps it on track.
3. The height needed to complete a loop-the-loop without falling off is proportional to 2.5 times the radius of the loop.
4. Energy conservation principles apply: potential energy at the highest point equals kinetic energy at lower points minus losses due to friction.
5. Friction and air resistance cause real-world loops to require more initial energy than ideal calculations suggest.

Review Questions

• What is required for an object to just barely stay on track at the top of a loop-the-loop?
• How does potential and kinetic energy interchange as an object travels through a loop-the-loop?
• What role does friction play in determining whether an object completes a loop-the-loop?

Related terms

Centripetal Force:

The inward force required for an object to follow a circular path.

Kinetic Energy:

The energy possessed by an object due to its motion, given by $\frac{1}{2}mv^2$.

Potential Energy:

The stored energy of an object due to its position or state, often related to height in gravitational fields.