A child of mass m sits in a swing supported by two chains, each of length R. The tension in each chain at the lowest point is T. Find the force of the seat on the child at the

lowest point

How do you know that?

To find the force of the seat on the child at the lowest point, we need to consider the forces acting on the child. At the lowest point, there are two forces acting on the child: the force of gravity and the tension in the chains.

1. Force of gravity (weight):
The force of gravity acting on the child can be calculated using the formula: F = m * g, where m is the mass of the child and g is the acceleration due to gravity (approximately 9.8 m/s² on Earth).

2. Tension in the chains:
At the lowest point of the swing, the tension in the chains is in the upward direction, counteracting the force of gravity to keep the child in motion. The tension in each chain is T.

Now, let's calculate the force of the seat on the child (N).

At the lowest point, the force of gravity and the tension in the chains are in the same direction. So, the force of the seat on the child can be found by subtracting the tension in the chains from the force of gravity:

N = F - T - T = F - 2T

Therefore, the force of the seat on the child at the lowest point is equal to the force of gravity minus twice the tension in each chain.

It's important to note that the force of the seat on the child will vary with the position of the swing, and this calculation is specific to the lowest point of the swing.