More Conservation of Energy Problems Video Lessons

Example

# Problem: 1. Use conservation of Energy to determine the final speed of an object that free-falls a height y.2. Show the time derivative of the final speed equation becomes ay = g3. Show that the integral of the final speed equation can be written as y = 1/2 gt2

###### FREE Expert Solution

1.

Conservation of energy:

$\overline{){{\mathbf{K}}}_{{\mathbf{0}}}{\mathbf{+}}{{\mathbf{U}}}_{{\mathbf{0}}}{\mathbf{+}}{{\mathbf{W}}}_{{\mathbf{nc}}}{\mathbf{=}}{{\mathbf{K}}}_{{\mathbf{f}}}{\mathbf{+}}{{\mathbf{U}}}_{{\mathbf{f}}}}$, where Wnc is the work done by non-conservative forces such as friction.

There is no non-conservative force in this problem.

Therefore, Wnc = 0

So, we have:

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###### Problem Details

1. Use conservation of Energy to determine the final speed of an object that free-falls a height y.

2. Show the time derivative of the final speed equation becomes ay = g

3. Show that the integral of the final speed equation can be written as y = 1/2 gt2