Answer :
Final answer:
To determine the dog's mass on the merry-go-round, the formula for centripetal force is used, substituting the given values for force, radius, and angular speed. After performing the calculation, the dog's mass is found to be approximately 10.8 kilograms.
Explanation:
The question asks to find the dog's mass, given its distance from the center of a merry-go-round, the angular speed of the merry-go-round, and the force maintaining the dog's circular motion. To solve this, we use the formula for centripetal force: F = m × r × ω^2, where F is the force, m is the mass of the dog, r is the radius of the circular path, and ω is the angular speed. Rearranging this formula to solve for m, we get m = F / (r × ω^2).
By plugging in the given values: F = 48.3 N, r = 1.86 m, and ω = 1.55 rad/s, we can calculate the mass of the dog. The calculation is as follows:
m = 48.3 N / (1.86 m × (1.55 rad/s)^2)m = 48.3 N / (1.86 m × 2.4025 rad^2/s^2)m = 48.3 N / 4.47065 N/kgm ≈ 10.8 kg
Therefore, the dog's mass is approximately 10.8 kilograms.
