Question

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

Answer 1

To find the speed of the child at the bottom of the swing, we use conservation of energy. The potential energy at the top is converted to kinetic energy at the bottom, which allows us to solve for the speed.

Step-by-step explanation:

To calculate the speed of a 20kg child at the bottom of the swing arc, we can use the principles of conservation of energy. The swing converts potential energy at the highest point to kinetic energy at the lowest point. At the 45 degree angle, we will find the vertical height the swing has fallen to get the potential energy and then we'll calculate the kinetic energy at the bottom of the arc which will give us the speed.

First, we calculate the height h the child has fallen from the rest position using trigonometry: h = L - L * cos(<45 degrees>), where L is the length of the chain, 3.0 m. Now, the potential energy at the highest point is equal to the kinetic energy at the lowest point: m * g * h = 1/2 * m * v^2. Solving for v gives us the speed of the child at the bottom of the arc.