Final answer:
The child's speed at the lowest point of the swing is 4.14 m/s, and the force exerted by the seat on the child at the lowest point is 239 N (upward).
Step-by-step explanation:
To find the child's speed at the lowest point, we can use the conservation of mechanical energy. At the highest point, all of the child's energy is potential energy, and at the lowest point, all of the child's energy is kinetic energy. Therefore, the child's speed at the lowest point can be calculated using the formula:
KE = 1/2 * m * v^2
where KE is the kinetic energy, m is the mass of the child, and v is the speed. Rearranging the formula to solve for v, we get:
v = sqrt(2 * KE / m)
Plugging in the values, we have:
v = sqrt(2 * 346 N * 2.94 m / 41.0 kg) = 4.14 m/s
So, the child's speed at the lowest point is 4.14 m/s.
b) To find the force exerted by the seat on the child at the lowest point, we can use Newton's second law, which states that the force is equal to the mass times the acceleration. In this case, the acceleration is the centripetal acceleration, which can be calculated using the formula:
ac = v^2 / r
where ac is the centripetal acceleration, v is the speed, and r is the radius (in this case, the length of the chains). Plugging in the values, we have:
ac = (4.14 m/s)^2 / 2.94 m = 5.84 m/s^2
Now, we can calculate the force using the formula:
F = m * ac
Plugging in the values, we have:
F = 41.0 kg * 5.84 m/s^2 = 239 N (upward)