A dog sits 1.22 m from the center of a merrygo-round with an angular speed of 1.07 rad/s. If the magnitude of the force that maintains the dog's circular motion is 32.3 N, what is the dog's mass?

24.74 kg

Explanation:

The formula of centripetal force is given as

F = mv²/r ... Equation 1

Where F = Force, m = mass of the dog, v = velocity of the dog, r = radius of the circle

Also,

v = ωr ... Equation 2

ω = angular velocity

Substitute equation 2 into equation 1

F = m (ωr) ²/r

F = mω²r ... Equation 3

Make m the subject of the equation,

m = F/ω²r ... Equation 4

Given: F = 32.3 N, r = 1.22 m, ω = 1.07 rad/s

Substitute into equation 4

m = 32.3 / (1.22*1.07)

m = 24.74 kg.

Thus the mass of the dog = 24.74 kg