The kinetic energy of a uniformly rolling ball is 20 J, its velocity = 20 m / s, the mass of the ball?

univerkov | May 8, 2021 | education

Initial data: Eк (kinetic energy of a rolling ball) = 20 J; V (ball speed) = 20 m / s.

The mass of the ball is determined from the formula for calculating the kinetic energy (the sum of the kinetic energies of the rotational and translational motions of the ball): Ek = Ekp + Ekvr.

Ekp = m * V ^ 2/2 = 0.5m * V ^ 2; Eqvr = I * w ^ 2/2 = 2/5 * m * R ^ 2 * (V / R) ^ 2/2 = 0.2 * m * V ^ 2.

Ek = 0.5m * V ^ 2 + 0.2 * m * V ^ 2 = 0.7 * m * V ^ 2.

m = Ek / (0.7 * V ^ 2).

Calculation: m = 20 / (0.7 * 20 ^ 2) = 40/400 = 0.071 kg or 71 g.

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