Newton's Laws of Motion

Question

A 23.0 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? (Enter a number.)

 __N

    

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? (Enter a number.)

__ N

    

Compare each force with her weight. (For each answer, enter a number.)

(force from (a))/(weight) =__

(force from (b))/(weight) =__

Answer 1

Hey John,

1. Centripetal force can be calculated with F_c = mv²/R
2. m and R are given in both problems
3. v is given, too, but you need the tangential speed of the rotating object at the point where the child is, rather than the revolutions per minutes
4. First, we need the speed in radians/sec, so I'll use 2 conversion factors (one for revolutions to radians, and the other for minutes to seconds. I'll use part a.
5. ω = 45.0 rev/min * (2*pi radians / 1 rev) * (1 min / 60 sec)
6. This gives us ω = 1.5*pi rad/sec
7. Now we need to go from rotational speed to linear speed where the child is.
8. v = ω*R
9. Just plug in to find v in m/s
10. Go back to your centripetal force equation and plug in the 3 numbers.
11. Part B is the same as a with different numbers
12. Part C should be straightforward. Just remember that the mass is 23.0 kg, so the child's weight is F_g = mg = 23.0 *g