Swing Energy: Solve for Max Speed of 20kg Child

In summary, the conversation discusses a problem involving a 20 kg child on a swing with 3.0-m-long chains, trying to determine the maximum speed when swinging out to a 45 degree angle. The conversation mentions using conservation of energy and trigonometry to solve the problem, but there is some confusion about the initial kinetic energy and potential energy of the child. The final solution is to use the equation 1/2mv^2 = mgh to calculate the maximum velocity.
  • #1
JoshMP
38
0

Homework Statement



A 20 kg child is on a swing that hangs from 3.0-m-long chains. What is her maximum speed if she swings out to a 45 degree angle?

Homework Equations



KE= 1/2mv^2
Ug= -mgy

The Attempt at a Solution



I tried to use conservation of energy to solve this problem. Ki + Ugi= Kf + Ugf
Ki=0 (v=0), so Ugi= Kf +Ugf. Then I solved for vf and got 7.67 m/s, which is incorrect. What am I doing wrong? Thanks.
 
Physics news on Phys.org
  • #2
The initial KE isn't 0J...if it was, the child wouldn't be able to achieve a new height with the swing.
 
  • #3
Well i would assume that her velocity is at its maximum when her potential energy is 0, which is at the bottom of the swing. We can figure out her potential energy by using the Conservation of energy and some trig:

She hangs 3m from the top of the swing set, therefore we'll set our y-coord 0 point at the spot where the swing is hanging straight up and down.
Now by using:
3-(3*Cos45) - (finding the adjacent side of the right triangle and subtracting it from 3m to get the height she has risen when she is at 45degrees)
we get the height above the 0 point that the girl is.

using 1/2mv2 = mgh - (The left side of the equation has 0 for potential energy and the right side has 0 for kinetic energy)
you should be able to figure out what her maximum velocity is.

~John
 

Related to Swing Energy: Solve for Max Speed of 20kg Child

1. What is swing energy?

Swing energy is the amount of kinetic energy that a swinging object possesses due to its motion. In this case, it refers to the kinetic energy of a child on a swing.

2. How is swing energy calculated?

Swing energy can be calculated using the formula: E = 1/2 * m * v^2, where E is the energy in joules, m is the mass of the swinging object in kilograms, and v is the velocity of the object in meters per second.

3. What is the maximum speed of a 20kg child on a swing?

The maximum speed of a 20kg child on a swing can be calculated by solving the swing energy formula for v. This would result in v = √(2E/m), where E is the maximum energy input that the child can give to the swing. This energy can vary depending on the height at which the child is released and the length of the swing.

4. What factors affect the maximum speed of a child on a swing?

The maximum speed of a child on a swing can be affected by several factors, including the height at which the child is released, the length of the swing, and the initial energy input by the child. Other factors such as air resistance and friction can also play a role in determining the maximum speed.

5. What is the significance of solving for the maximum speed of a child on a swing?

Solving for the maximum speed of a child on a swing can help us understand the relationship between energy and motion. It can also provide insights into the factors that affect the speed of a swinging object. Additionally, this information can be used to ensure the safety of children on swings by determining the appropriate height and length for a swing set.

Similar threads

  • Introductory Physics Homework Help
Replies
5
Views
2K
  • Introductory Physics Homework Help
Replies
5
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
3K
  • Introductory Physics Homework Help
Replies
1
Views
1K
  • Introductory Physics Homework Help
Replies
12
Views
2K
  • Introductory Physics Homework Help
Replies
1
Views
3K
  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
901
  • Introductory Physics Homework Help
Replies
1
Views
1K
Back
Top