# Pendulum question

1. May 3, 2005

### gangrene

this question has been bugging me for the last few days and my incompetent professor refuses to help me through email.

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Question 10 (1 point)

A child of mass 15.22 kG sitting on a swing whole length is 2.97
meters is pulled up an angle 42.9 degrees and released. The maximum
speed of the child during the subsequent motion (in Meters/sec) is?

Student response 3.98
Correct answer 1.26E0 (1.26 * 10^0 )

Score 0 / 1

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I tried solving this problem by energy conservation and setting max kinetic energy = max potential energy. I figure when the child swings back to equilibrium angle 0, the speed would be greatest with max kinetic energy and with 0 potential energy. The height I used for max potential energy was 2.97-2.97cos42.9 (L-Lcos42.9).

am I doing something wrong?

2. May 3, 2005

### Staff: Mentor

3. May 11, 2005

### Tony Zalles

Hi,

I actually remember coming across this problem a while back,
if I remember correctly, Itired to solve this but got stuck in trying to apply conservation of energy to the system because I was not able to figure out the [change in height] from initial position to the bottom where velocity would have been at its max.

If anyone was able to figure this out, it would be nice if they could explain how.

Thanks,

-Tony Zalles.

4. May 11, 2005

### gangrene

ok there's two height values to account for. the first value is when the pendulum is in equilibrium making an angle 0 degrees while the other value is when the pendulum is at it's max angle.

for the height when the pendulum is in equilibrium, the height is simply the length of the pendulum L since it's perfectly vertical and there is no x compenent.

for the height when the pendulum is at its max angle, the height is Lcos(max angle). when the pendulum is at its max angle, its vertical height is its y component.

the difference in height between the two is L-Lcos(max angle).
or simplified to L(1-cos(maxangle))

hope that helps

5. May 11, 2005

### quasar987

gangrene said all there is to say but here it is in image.

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