Question

Suppose you and a friend, each of mass 55 kg , go to the park and get on a 4.5-m-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 7.0 seconds. Part APart complete What is the magnitude of the (apparent) outward force that you feel?

a. 12 N
b. 50 N
c. 100 N
d. 200 N

Answer 1

99.57 N

Step-by-step explanation:

mass, m = 55 kg

diameter = 4.5 m

radius, r = 4.5 / 2 = 2.25 m

time period, T = 7 second

Angular velocity, ω = 2π/T = 2π/7 = 0.897 rad/s

Apparent froce is the centripetal force.

F = m x r x ω²

F = 55 x 2.25 x 0.897 x 0.897

F = 99.57 N

Thu, the apparent force is 99.57 N .

Answer 2

c. 100 N

Step-by-step explanation:

`m` = mass of each = 55 kg

`T` = Time period of rotation = 7.0 sec

Angular frequency is given as

`w = (2\pi )/(T) \\w = (2(3.14) )/(7)\\w = 0.897 rads^(-1)`

`d` = Diameter of the merry-go-round = 4.5 m

Radius of the merry-go-round is given as

`r = (d)/(2) = (4.5)/(2) = 2.25 m`

Magnitude of outward force is same as the centripetal force and is given as

`F = m r w^(2) = (55) (2.25) (0.897)^(2) \\F = 100 N`