Question

A 6.5-cm-diameter ball has a terminal speed of 26 m/s. What is the ball’s mass? Use ρ = 1.2 kg/m3 for the density of air at room temperature.

Answer 1

The equation for drag is:

D = Cρv²A/2

Where C is the coefficient of drag, ρ is the density of air, A is the cross-sectional area of the ball.

Value of c is 0.207

The forces acting on the falling tennis ball is the upward force of drag (D) and the downward force of the ball’s weight (mg). Since it is at terminal velocity, there is zero acceleration. From Newton’s 2nd law:

∑F = 0 = D - mg
mg = D
m = D / g

The density of air is about 1.2kg/m³, and A is:

A = 2πr
= π(0.0325m)²
= 0.00664m²

The mass of the ball then is:

m = D / g
= Cρv²A/2 / g
= 0.207(1.2kg/m³)(26m/s)²( 0.00664m²)/2 / 9.8m/s²
= 0.057kg (57 grams) ....Answer.

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