Motion Along Curved Paths Video Lessons

Example

# Problem: A 350 kg roller coaster starts from rest at point exttip{A}{A} and slides down the frictionless loop-the-loop shown in the accompanying figure.A. How fast is this roller coaster moving at point B exttip{B}{B}?B. How hard does it press against the track at point Bexttip{B}{B}?

###### FREE Expert Solution

We'll use the law of conservation of energy:

$\overline{){{\mathbf{K}}}_{{\mathbf{i}}}{\mathbf{+}}{{\mathbf{U}}}_{{\mathbf{i}}}{\mathbf{+}}{{\mathbf{W}}}_{{\mathbf{nc}}}{\mathbf{=}}{{\mathbf{K}}}_{{\mathbf{f}}}{\mathbf{+}}{{\mathbf{U}}}_{{\mathbf{f}}}}$, where Wnc is the work done by non-conservative forces such as friction.

Potential energy:

$\overline{){\mathbf{U}}{\mathbf{=}}{\mathbf{m}}{\mathbf{g}}{\mathbf{h}}}$

Kinetic energy:

$\overline{){\mathbf{K}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{{\mathbf{mv}}}^{{\mathbf{2}}}}$

A.

In this problem, we don't have no-conservative forces, and hence Wnc = 0.

95% (289 ratings)
###### Problem Details

A 350 kg roller coaster starts from rest at point and slides down the frictionless loop-the-loop shown in the accompanying figure.

A. How fast is this roller coaster moving at point B ?

B. How hard does it press against the track at point B?