Question

If the loop the car is currently on has a radius of 26.0 m , find the minimum height h so that the car will not fall off the track at the top of the circular part of the loop.

Answer 1

The minimum height h is 65m so that the car will not fall off the track at the top of the circular part of the loop.

What is mechanical energy?

Potential energy plus kinetic energy are combined to form mechanical energy. According to the principle of mechanical energy conservation, mechanical energy is constant in an isolated system when only conservative forces are acting on it. Potential energy increases when an object moves in the opposite direction of a conservative net force. Kinetic energy also changes as an object's speed, not velocity, changes. However, nonconservative forces, such as frictional forces, will always be present in real systems; however, if these forces are of minimal magnitude, mechanical energy changes little, making the idea of its conservation a reasonable approximation.

For completing the vertical circle the minimum speed at the bottom must be $\sqrt{5gR}$

so conserving mechanical energy

$mgh=\frac{1}{2} m (v_{bottom})^{2}$

$gh=\frac{1}{2} 5gR$

⇒ h= $\frac{5}{2} \times 26$

h = 65m

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