Question

You pull a solid iron ball with a density of 7.86 g/cm3 and a radius of 1.20 cm upward through a fluid at a constant speed of 7.00 cm/s. The fluid exerts a drag force that is directly proportional to speed, and the proportionality constant is 0.950 kg/s. What is the magnitude of the force (in N) you exert on the ball? (You may ignore the buoyant force.)

Answer 1

Answer:

  F = 0.625 N

Explanation:

given,

radius of iron ball = 1.20 cm

density of iron ball = 7.86 g/cm³

speed of iron ball = 7 cm/s

drag force proportionality constant = 0.980 kg/s

force exerted on the ball = ?

mass of the ball

m = ρ V

    = $\rho \times \dfrac{4}{3}\pi r^3$

net force acting on the ball

F = mg + k v

  = $\rho \times \dfrac{4}{3}\pi r^3\times g + k v$

  = $7.86\times 10^{3} \times \dfrac{4}{3}\pi 0.012^3\times 9.81 + 0.950\times 0.07$

  F = 0.625 N

so, force require to pull the ball upward is equal to 0.625 N