Motion Along Curved Paths Video Lessons

Example

Problem: A roller-coaster car shown in the figure is pulled up to point 1 where it is released from rest. (a) Assuming no friction, calculate the speed at point 2.(b) Assuming no friction, calculate the speed at point 3.(c) Assuming no friction, calculate the speed at point 4.

FREE Expert Solution

In this problem, we are given the heights (in the image) and asked to calculate the velocity. The height and velocity are indicators of the energy possed by an object. Thus, this is a conservation of energy problem.

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.

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Problem Details

A roller-coaster car shown in the figure is pulled up to point 1 where it is released from rest.

(a) Assuming no friction, calculate the speed at point 2.

(b) Assuming no friction, calculate the speed at point 3.

(c) Assuming no friction, calculate the speed at point 4.