### Physics Problem on Centripetal Force**(a)** A 19.0 kg child is riding a playground merry-go-round that is rotating at 35.0 revolutions per minute (rev/min). What centripetal force (in Newtons, N) must she exert to stay on if she is 2.50 meters (m) from its center? (Enter a number.)\[ \text{Centripetal Force} = \_\_\_\_ \, \text{N} \]**(b)** What centripetal force (in Newtons, 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.)\[ \text{Centripetal Force} = \_\_\_\_ \, \text{N} \]**(c)** Compare each force with her weight. (For each answer, enter a number.)\[ \left( \frac{\text{force from (a)}}{\text{weight}} \right) = \_\_\_\_ \]\[ \left( \frac{\text{force from (b)}}{\text{weight}} \right) = \_\_\_\_ \]---#### Explanation:There are no graphs or diagrams associated with this problem. The calculations involve using the formula for centripetal force and comparing the calculated forces with the gravitational weight of the child. For reference:- **Centripetal Force Formula**: \[ F_c = m \cdot r \cdot \omega^2 \] where \( F_c \) is the centripetal force, \( m \) is the mass, \( r \) is the radius, and \( \omega \) is the angular velocity in radians per second.- **Weight Formula**: \[ W = m \cdot g \] where \( W \) is the weight and \( g \approx 9.81 \, \text{m/s}^2 \) is the acceleration due to gravity.

This problem can be solved using centripetal force concept

(a) A 19.0 kg child is riding a playground merry-go-round that is rotating at 35.0 rev/min. What centripetal force (in N) must she exert to stay on if she is 2.50 m from its center? (Enter a number.) 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? (Enter a number.) N (c) Compare each force with her weight. (For each answer, enter a number.) (force from (a))/(weight) = (force from (b))/(weight) =

(a) A 19.0 kg child is riding a playground merry-go-round that is rotating at 35.0 rev/min. What centripetal force (in N) must she exert to stay on if she is 2.50 m from its center? (Enter a number.) 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? (Enter a number.) N (c) Compare each force with her weight. (For each answer, enter a number.) (force from (a))/(weight) = (force from (b))/(weight) =

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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(a) A 19.0 kg child is riding a playground merry-go-round that is rotating at 50.0 rev/min. What centripetal force (in N) must she exert to stay on if she is 2.50 m from its center? (Enter a number.)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 5.00 m from its center? (Enter a number.)N (c) Compare each force with her weight. (For each answer, enter a number.) (force from (a))/(weight) = (force from (b))/(weight)=
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