Solving the Swing Tension: A 25kg Child's Story

In summary, a 25 kg child is swinging on a 3.5 m swing with a speed of 3.3 m/s at the bottom of the swing. The tension on the swing's chain to hold the child can be solved using Newton's second law by considering the child's motion in a circle and the forces acting on them.
  • #1
tnutty
326
1

Homework Statement


A 25 kg child is swinging on a 3.5 m swing. At the bottom of the swing
the speed of the child is moving at 3.3 m/s. What is the tension on the
swing’s chain to hold the child?


Homework Equations





The Attempt at a Solution


Can you help me i am confused about this.
 
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  • #2
tnutty said:
A 25 kg child is swinging on a 3.5 m swing. At the bottom of the swing
the speed of the child is moving at 3.3 m/s. What is the tension on the
swing’s chain to hold the child?

Can you help me i am confused about this.

Hi tnutty! :smile:

The child is moving in a circle.

The forces on the child are the tension in the chain and the force of gravity.

Use good ol' Newton's second law to relate these forces to the child's acceleration. :smile:
 
  • #3

I can offer some guidance on how to approach this problem. First, we need to understand the physical principles involved in a swinging motion. When a child is swinging, there are two main forces acting on them: gravity, which pulls them towards the ground, and the tension in the swing's chain, which pulls them towards the pivot point of the swing.

To solve for the tension in the chain, we can use Newton's Second Law, which states that the net force on an object is equal to its mass multiplied by its acceleration (F=ma). In this case, we know the mass of the child (25 kg) and their speed at the bottom of the swing (3.3 m/s). We also know that at the bottom of the swing, the net force acting on the child is equal to the tension in the chain minus their weight (mg), since they are not accelerating in the horizontal direction.

So, we can set up the equation F=ma, where F is the net force, m is the mass of the child, and a is their acceleration. The acceleration, in this case, is the centripetal acceleration, which is given by a=v^2/r, where v is the speed and r is the radius of the swing (in this case, half of the length of the swing, or 1.75 m). We can plug in the values we know and solve for the tension in the chain:

F = ma
F = (25 kg)(3.3 m/s)^2 / 1.75 m
F = 122.14 N

Therefore, the tension in the chain to hold the child is approximately 122 N. This value may vary slightly depending on the accuracy of the given measurements and any assumptions made about the motion of the swing, but it should provide a good estimate.

I hope this helps to clarify the problem for you. Remember to always identify the relevant physical principles and equations, and plug in the given values to solve for the unknown variable. Good luck with your homework!
 

Related to Solving the Swing Tension: A 25kg Child's Story

1. How do you define "Swing Tension"?

"Swing Tension" refers to the amount of force or resistance experienced by a swing when it is in motion. It is affected by factors such as the weight of the person on the swing, the length of the swing's ropes or chains, and the angle at which the swing is pulled back.

2. Why is it important to solve the swing tension for a 25kg child?

Solving the swing tension for a 25kg child is important because it can affect their safety and comfort while using the swing. If the tension is too high, it could cause the child to feel uncomfortable or even fall off the swing. If the tension is too low, the child may not be able to swing properly and may have a less enjoyable experience.

3. What factors contribute to swing tension?

Several factors contribute to swing tension, including the weight of the person on the swing, the length of the swing's ropes or chains, and the angle at which the swing is pulled back. Other factors such as wind resistance and friction can also play a role in swing tension.

4. How can you adjust swing tension for a 25kg child?

The best way to adjust swing tension for a 25kg child is to adjust the length of the swing's ropes or chains. Shortening the ropes or chains will increase the tension, while lengthening them will decrease the tension. It is important to also consider the child's weight and the angle at which the swing is pulled back when making adjustments.

5. Are there any safety precautions to consider when solving swing tension for a 25kg child?

Yes, there are some safety precautions to consider when solving swing tension for a 25kg child. It is important to make sure the child is securely strapped into the swing and that the swing is properly installed and maintained. It is also recommended to have an adult supervise and assist with adjusting the swing tension to ensure the child's safety.

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