Question

Suppose you and a friend, each a mass of 60 kg, go to the park and get on a 4.0-m-diameter merry-go-round. You stand on the outside edge of the merry-go-round, while your friend pushes you so that you rotate once every 6.0 seconds. What is the magnitude of the (apparent) outward force that you feel?

a. 7 N
b. 63 N
c. 130 N
d. 260 N

Answer 1

The magnitude of the apparent outward force that the person feels on the merry-go-round is approximately 260 N, which corresponds to option (d). This is calculated using the formula for centripetal force.

Step-by-step explanation:

The question pertains to the concept of centripetal force which is a force that keeps an object moving in a circular path and is directed towards the center of the circle. To calculate the apparent outward force, also known as the centrifugal force effect, we will use the formula:

Fc = m × v2 / r, where:

v is the linear velocity of the object, and

r is the radius of the circular path.

First, we calculate the linear velocity (v):

v = circumference / time = (π × diameter) / period = (π × 4.0 m) / 6.0 s ≈ 2.094 m/s

Then, we calculate the centripetal force:

Fc = (60 kg) × (2.094 m/s)2 / (4.0 m / 2) ≈ 60 kg × 4.394 m/s2 ≈ 263.64 N

The apparent outward force that the person feels is approximately 260 N, which corresponds to option (d).

Answer 2

c. 130 N

Step-by-step explanation:

F = ma.................. Equation 1

Where F = force, m = mass of one person, a = outward acceleration.

But,

a = v²/r........................... Equation 2

Where v = velocity, r = radius.

and

v = 2πr/T........................ Equation 3.

Where T = Period,

Given: T = 6.0 s and π = 3.14, r = 4/2 = 2 m

Substitute into equation 3

v = 2(3.14)(2)/6

v = 2.09 m/s

Substituting the value of v into equation 2

a = (2.09)²/2

a = 4.368/2

a = 2.184 m/s²

Also given: m = 60 kg, and a = 2.184 m/s²

Substitute into equation 1

F = 60(2.184)

F = 131.04

F ≈ 130 N.

The right option is c. 130 N