# Solve Pendulum Problem: Max Speed of Child in Motion

• gangrene
In summary, the conversation discusses solving a physics problem involving a child on a swing. The student tried using energy conservation and setting the maximum kinetic energy equal to the maximum potential energy, but was unsure of the change in height needed for the calculation. Another person provides clarification by explaining that there are two height values to account for, one when the pendulum is in equilibrium and one when it is at its maximum angle. They also provide an image to further illustrate the concept.
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

-----------------------------

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?

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.

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

Tony Zalles said:
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.

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

#### Attachments

• Untitled-1.jpg
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## 1. What is a pendulum problem?

A pendulum problem involves calculating the motion of a pendulum, which is a weight suspended from a fixed point that swings back and forth due to gravity.

## 2. How do you solve a pendulum problem?

To solve a pendulum problem, you can use the equation T = 2π√(L/g), where T is the period (time for one swing), L is the length of the pendulum, and g is the acceleration due to gravity. You can also use conservation of energy or Newton's laws of motion.

## 3. What is the maximum speed of a child in motion on a pendulum?

The maximum speed of a child on a pendulum will depend on the length of the pendulum, the angle at which it is released, and the acceleration due to gravity. It can be calculated using the equation v = √(2gL(1-cosθ)), where v is the maximum speed, g is the acceleration due to gravity, L is the length of the pendulum, and θ is the angle at which it is released.

## 4. How does the mass of the child affect the maximum speed on a pendulum?

The mass of the child does not affect the maximum speed on a pendulum. The maximum speed is determined by the length of the pendulum, the angle at which it is released, and the acceleration due to gravity. The mass of the child only affects the period of the pendulum.

## 5. What are some real-life applications of solving pendulum problems?

Solving pendulum problems has real-life applications in fields such as engineering, physics, and mathematics. It can be used to design and analyze pendulum clocks, amusement park rides, and earthquake-resistant structures. It can also be used to study the motion of celestial bodies, such as pendulum clocks used in old astronomical observatories.

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