A man is swinging his child, Wii weighs 28.5 kilograms, in horizontal circle which has a radius of 0.75 meters and it takes the child 1.75 seconds to make one revolution. a) What is the magnitude and direction of the force the man exerts on his child? b) What is the magnitude and direction if the force adopted by the child on the man?

a. force=centripetal force=m*w^2*r

= 28.5*(2PI/1.75)^2*.75 Newtons

b. Wording makes no sense, but the force on the man is the equilibrant to the force the man exerts: equal in magnitude, opposite direction

To solve this problem, we can use the principles of circular motion. Let's break down the two parts of the question:

a) Magnitude and direction of the force exerted by the man on his child:
We know that in circular motion, there is a centripetal force acting towards the center of the circle. This force is provided by the tension in the string through which the child is swinging.

The centripetal force can be calculated using the formula:

F = m * (v^2 / r)

where:
F is the centripetal force,
m is the mass of the child (28.5 kg),
v is the linear velocity (circumference / time),
and r is the radius of the circular path (0.75 m).

First, we need to calculate the linear velocity. Since the child takes 1.75 seconds to complete one revolution (T), we can find the velocity as:

v = 2πr / T

Substituting the values:

v = (2 * 3.14 * 0.75 m) / 1.75 s

Now we can substitute the calculated velocity and given radius into the formula to find the centripetal force:

F = 28.5 kg * ((2π * 0.75 m) / 1.75 s)^2 / 0.75 m

Calculating this will give you the magnitude of the force. The direction of the force is towards the center of the circle, or radially inward.

b) Magnitude and direction of the force adopted by the child on the man:
According to Newton's third law of motion, for every action, there is an equal and opposite reaction. Therefore, the force adopted by the child on the man is equal in magnitude but opposite in direction to the force exerted by the man on the child. So the magnitude will be the same as calculated in part a, but the direction will be radially outward (away from the center of the circle).

By following these steps, you should be able to calculate both the magnitude and direction of the forces in the given scenario.