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 can use the concept of Newton's second law of motion, which states that force is equal to mass multiplied by acceleration (F = m*a).
In this case, the acceleration of the child can be determined by considering the motion of the swing at the lowest point. At the lowest point, the child is experiencing the gravitational force and the tension in the chains.
First, let's calculate the gravitational force acting on the child using the formula Fg = m*g, where m is the mass of the child and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Fg = (37.5 kg) * (9.8 m/s^2)
Fg = 367.5 N
Next, we need to consider the tension in the chains. At the lowest point of the swing, the tension in the chains is acting horizontally and upward to support the weight of the child. This tension also contributes to the force exerted by the seat on the child.
Since there are two chains, each with a tension of 433 N, the total upward force from the tension in the chains is:
2 * 433 N = 866 N
Now, let's determine the net force acting on the child at the lowest point. The net force is the sum of the gravitational force and the upward force from the tension in the chains:
Net Force = Fg + upward force from tension
Net Force = 367.5 N + 866 N
Net Force = 1233.5 N
Finally, we can equate the net force to the mass of the child multiplied by the acceleration at the lowest point:
Net Force = m*a
1233.5 N = (37.5 kg) * a
To find the acceleration, divide both sides of the equation by 37.5 kg:
a = 1233.5 N / 37.5 kg
a ≈ 32.896 m/s^2
Now that we have the acceleration, we can find the force exerted by the seat on the child at the lowest point by using Newton's second law:
Force exerted by the seat = mass of the child * acceleration
Force exerted by the seat = (37.5 kg) * 32.896 m/s^2
Force exerted by the seat ≈ 1229.4 N
Therefore, the force exerted by the seat on the child at the lowest point is approximately 1229.4 N.