The Calculation of Dog's Mass in Circular Motion

Understanding Circular Motion and Centripetal Force

Circular motion occurs when an object moves in a circular path around a center point. In this scenario, the dog is sitting on a merry-go-round 1.22 meters away from the center. The merry-go-round is rotating at an angular speed of 1.07 rad/s. In circular motion, an object experiences a centripetal force that keeps it moving in a circular path. The magnitude of this centripetal force can be calculated using the formula F = mv²/r, where F is the force, m is the mass of the object, v is the velocity, and r is the radius of the circular path.

Calculating the Dog's Mass

Given that the centripetal force maintaining the dog's circular motion is 32.3 N, we can calculate the mass of the dog using the following steps: Step 1: Substitute the formula for velocity in circular motion (v = ωr) into the centripetal force formula: F = m(ωr)²/r F = mω²r Step 2: Rearrange the formula to solve for the mass (m): m = F/ω²r Step 3: Now, plug in the values: F = 32.3 N, r = 1.22 m, ω = 1.07 rad/s Step 4: Calculate the mass of the dog: m = 32.3 / (1.22 * 1.07) m = 24.74 kg Therefore, the mass of the dog is approximately 24.74 kg. This calculation shows that the dog's circular motion is maintained by a force of 32.3 N due to its mass.

What is the formula for centripetal force in circular motion?

The formula for centripetal force in circular motion is F = mv²/r, where F is the force, m is the mass of the object, v is the velocity, and r is the radius of the circular path.

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