A 37.5-kg child swings in a swing supported by two chains, each 3.05 m long. The tension in each chain at the lowest point is 433 N. the force of the seat on the child is 498.5 N.
b)Find the force exerted by the seat on the child at the lowest point. (Ignore the mass of the seat.)
To find the force exerted by the seat on the child at the lowest point, we need to consider the different forces acting on the child.
At the lowest point of the swing, there are two forces acting on the child: the tension in the chains and the force of the seat on the child.
The tension in the chains can be calculated using Newton's second law, which states that force equals mass multiplied by acceleration (F = m * a). In this case, the acceleration is the centripetal acceleration of the swing, given by the formula a = v^2 / r, where v is the velocity and r is the radius.
Since the swing is located at the lowest point, the velocity will be at its maximum. The maximum velocity, v, can be calculated by the formula v = √(g * r), where g is the acceleration due to gravity (approximately 9.8 m/s^2).
Substituting the given values, we have v = √(9.8 m/s^2 * 3.05 m) ≈ 5.62 m/s.
Now, let's calculate the tension in the chains. Using Newton's second law, F = m * a, for the child's mass, m = 37.5 kg, and centripetal acceleration, a = v^2 / r, we have F = 37.5 kg * (5.62 m/s)^2 / 3.05 m ≈ 114.39 N.
We also know that the force of the seat on the child at the lowest point is given as 498.5 N.
Finally, to find the force exerted by the seat on the child, we need to consider the net force acting on the child at the lowest point. Since the child is in equilibrium, the net force is zero.
Net force = Tension in chains - Force of seat = 0
So, Tension in chains = Force of seat.
Therefore, the force exerted by the seat on the child at the lowest point is 498.5 N.
They already have told you the answer:
" the force of the seat on the child is 498.5 N"
That is also the force of the child on the seat.