Raindrops, each having a radius of 1 mm and a mass of 4 mg , are falling at a speed of 30 m/s onto the head of a bald person. Upon splashing on the head, the drops come to rest. Assuming equivalently that the drops travel a distance equal to their radii on the head during the impact, determine the force exerted by an individual drop on the head.

Step-by-step solution

Given, mass of a raindrop, m = 4 mg = 4 10⁻⁶ kg Initial speed of the raindrop, u = 30 m/s Final speed of the raindrop, v = 0 m/s Distance traveled during impact, s = r = 1 mm = 10⁻³ m Using the work-energy theorem, the work done by the stopping force equals the change in kinetic energy of the raindrop: F s = 1 2 m u^2 F 10⁻³ = 1 2 4 10⁻⁶ (30)^2 F 10⁻³ = 2 10⁻⁶ 900 F 10⁻³ = 1.8 10⁻³ F = 1.8 N By Newton's third law, the force exerted by the drop on the head is equal in magnitude to the stopping force, which is 1.8 N