Final answer:
The speed of the merry-go-round is approximately 3.33 m/s, which does not match any of the options provided. The net force experienced by the child, or the centripetal force, is approximately 196 N, again not matching any of the provided options. The direction of the centripetal force is radially inward, not upward or downward as the options suggest.
Step-by-step explanation:
To determine the speed of the merry-go-round, we need to convert the rotational velocity from revolutions per minute (rev/min) to meters per second (m/s). The radius is given as 1.25 m, and the rotational speed as 40 rev/min. Converting to meters per second:
- Speed (v) = (40 rev/min) x (1 min/60 s) x (2π x 1.25 m/1 rev) = (40/60) x (2π x 1.25) = 3.33 m/s
Therefore, the correct speed is not listed among the options provided.
The net force experienced by the child, which is the centripetal force, can be found using the formula F = (mv^2)/r. The mass of the child (m) is 22.0 kg, the speed (v) we found is 3.33 m/s, and the radius (r) is 1.25 m. Substituting the values:
- Net force (F) = (22.0 kg x (3.33 m/s)^2) / 1.25 m = (22.0 x 11.09) / 1.25 = 244.98 / 1.25 = approximately 196 N
The direction of the centripetal force is towards the center of the circle, which means the correct direction is not upward or downward but rather radially inward towards the center of the merry-go-round.