Suppose you and a friend, each of mass 65 , go to the park and get on a 4.5 -diameter merry-go-round. You stand on the outside edge of the merry-go-round, while your friend pushes so that it rotates once every 5.0 seconds.


What is the magnitude of the outward force that you feel?

To determine the magnitude of the outward force that you feel, we can use the concept of centripetal force. The centripetal force is the force that keeps an object moving in a circular path, and it always acts towards the center of the circle.

The formula for centripetal force is:

F = m * a

Where:
F is the centripetal force
m is the mass of the object
a is the centripetal acceleration

In this case, your mass is given as 65 kg, and the diameter of the merry-go-round is 4.5 meters. The radius, r, of the merry-go-round can be calculated by dividing the diameter by 2:

r = 4.5 m / 2 = 2.25 m

Next, let's calculate the speed, v, at which you are moving on the merry-go-round. The speed can be determined by dividing the circumference of the circle by the time it takes to complete one rotation:

v = 2πr / t

Where:
π is a mathematical constant approximately equal to 3.14159
t is the time taken for one rotation, given as 5.0 seconds

Plugging in the values:

v = (2 * 3.14159 * 2.25 m) / 5.0 s

v ≈ 2.828 m/s

Now, let's calculate the centripetal acceleration using the formula:

a = v^2 / r

Plugging in the values:

a = (2.828 m/s)^2 / 2.25 m

a ≈ 3.56 m/s^2

Finally, let's calculate the centripetal force experienced by you using the formula:

F = m * a

Plugging in the values:

F = 65 kg * 3.56 m/s^2

F ≈ 231.4 N

So, the magnitude of the outward force that you feel is approximately 231.4 Newtons.

To find the magnitude of the outward force that you feel, we need to consider the rotational motion and the centripetal force acting on you.

First, let's calculate the angular velocity (ω) of the merry-go-round. The angular velocity is given by the formula ω = 2π / T, where T is the time it takes for one complete rotation.

So, ω = 2π / 5.0 s = 1.26 rad/s.

Next, we need to calculate the tangential velocity (v) at the outer edge of the merry-go-round. The tangential velocity is given by the formula v = r * ω, where r is the radius of the merry-go-round.

Given that the diameter of the merry-go-round is 4.5 m, the radius is half of that, so r = 2.25 m.

Therefore, v = 2.25 m * 1.26 rad/s = 2.835 m/s.

Now, we can calculate the centripetal force (Fc) acting on you. The centripetal force is given by the formula Fc = m * a, where m is your mass and a is the centripetal acceleration.

The centripetal acceleration is given by the formula a = v^2 / r.

Therefore, a = (2.835 m/s)^2 / 2.25 m = 3.58 m/s^2.

Finally, we can calculate the centripetal force Fc = m * a.

Given that your mass is 65 kg, the centripetal force is Fc = 65 kg * 3.58 m/s^2 = 232.7 N.

Therefore, the magnitude of the outward force that you feel is approximately 232.7 N.