Question

2. Hail forms high in the atmosphere and can be accelerated to a high speed before it reaches the ground. Estimate the terminal speed of a spherical hailstone that has a diameter of 1.5 cm. Hint: The mass of a piece of hail that has a volume of 1 cm3 is about 1 g

3. The coefficient of kinetic friction between a refrigerator (mass 118 kg) and the floor is 0.16, and the coefficient of static friction is 0.96. After struggling to move the refrigerator, you finally apply enough force to get it moving. What is the minimum force required to keep it moving with a constant velocity?

Answer 1

Terminal velocity means that the weight is equal to the drag force.
m*g = ½ρv²CA
stone volume V = (1/6)πd³ = (1/6)π(1.5cm)³ = 1.767 cm³
so mass m = ρ*V = 1g/cm³ * 1.767cm³ = 1.767 g = 0.001767 kg

ρ = density of fluid; 1.27 kg/m³ for air

C = 0.47 for a sphere

A = πd²/4 = π(1.5cm)²/4 = 1.76 cm² = 1.76*10^-4 m²
so
0.001767kg * 9.8m/s² = ½ * 1.27kg/m³ * v² * 0.47 * 1.76*10^-4m²
v² = 329.6 m²/s²
v = 18.15 m/s

3)

minimum force required while moving = kinetic friction
= 0.16* 118*9.8
=185.02 N