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

[tnutty]

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.

 

[tiny-tim]

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!

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.

 

[nlightner]

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!