Question 1 (a) A 15.0 kg child is riding a playground merry-go-round that is rot

Question

Question 1

(a) A 15.0 kg child is riding a playground merry-go-round that is rotating at 45.0 rev/min. What centripetal force (in N) must she exert to stay on if she is 1.50 m from its center?

____ N

(b) What centripetal force (in N) does she need to stay on an amusement park merry-go-round that rotates at 3.00 rev/min if she is 7.00 m from its center?

___N

(c)

Compare each force with her weight.

=___

___   

Question 2    You and your family take a road trip on a long holiday weekend. In a certain section of the trip where the road is particularly uneven, the car goes over a bump that is curved downward with a radius of 22.5 m. See diagram below. The mass of the car and its passengers is 1250 kg.

(a) When the car is at the highest point of the bump its speed is 7.05 m/s. Determine the magnitude and direction of the force exerted by the road on the car at this highest point.

(b) If the speed at the highest point is above a certain maximum value the car will lose contact with the road. Calculate this maximum speed.
__m/s   

PLEASE DONT GIVE ANY INNCORECT ANSWERS THANKS FOR YOUR HELP !

Explanation / Answer

Fc = m * v^2 ÷ r

Circumference = 2 * * 1.5 = 3 *
Let’s determine the distance the child moves during 45 rotations.
d = 45 * 3 * = 135 *
To determine the velocity in m/s, divide this distance by 60.
v = 2.25 *
Fc = 15 * (2.25 * )^2 ÷ 1.5 = 499.65 N

b) Circumference = 2 * * 7 = 14 *
Let’s determine the distance the child moves during 3 rotations.
d = 3 * 14 * = 42 *
To determine the velocity in m/s, divide this distance by 60.
v = 0.7 *
Fc = 15 * (0.7 * )^2 ÷ 7 = 10.36 N

c) 499.65 / 15*9.81 = 3.369

10.36 / 15*9.81 = 0.07

2) mg - Fn = mv^2/r

Fn = mg - mv^2/r

= 1250*9.81 - 1250*(7.05)^2 / (22.5)

= 9501.25 N ............. upward


Fn=0 => mv^2/r=mg

v = sqrt(gr)

= sqrt(9.81*22.5m)
= 14.86 m/s

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