Final answer:
The child's speed at the lowest point is 5.2 m/s and the force exerted by the seat on the child at the lowest point is 235N.
Step-by-step explanation:
To find the child's speed at the lowest point, we can use the conservation of mechanical energy. At the lowest point, the swing has its maximum gravitational potential energy and zero kinetic energy. Therefore, the total mechanical energy is equal to the potential energy:
mgh = 1/2mv^2
Plugging in the values, we get:
35.0kg * 9.8m/s^2 * 2.98m = 1/2 * 35.0kg * v^2
Solving for v, we find the child's speed at the lowest point to be 5.2 m/s.
To find the force exerted by the seat on the child at the lowest point, we can use Newton's second law. At the lowest point, the net force on the child is the tension in the chains minus the weight of the child:
F_net = T - mg
Plugging in the values, we get:
F_net = 436N - 35.0kg * 9.8m/s^2
Solving for F_net, we find the force exerted by the seat on the child at the lowest point to be 235N.