You have a beach ball which has a radius of 19 cm and a mass of 0.5 kg. You have

Question

You have a beach ball which has a radius of 19 cm and a mass of 0.5 kg. You have a lead ball which has the same radius but has a mass of 100 kg. A) You immerse the beach ball under the water. What is the buoyancy force felt by the beach ball? B) To keep the beach ball stationary under the water what is the force you need to apply? (UP is positive) C) You immerse the lead ball under the water, what is the buoyancy force felt by the lead ball? D) To keep the lead ball stationary under the water what is the force you need to apply? (UP is positive)

Explanation / Answer

Buoyacy force = V*rho*g

V = 4/3*pi*(r)^3

(A) Buoyacy force on beach ball = 4/3*pi*(r)^3 * 1 * 9.8

Fb = 4/3 * 3.14 * (22 x 10^-2)^3 * 9.8

Fb = .43 N

(B) Gravity on beach ball = mg = .2 x 9.8 = 1.96 N

Fb = .43 N

net force = 1.96 - .43 = 1.53 N (on upward side to keep the ball stationary)

(C) Fb on lead ball = V*rho*g = 4/3*pi*(r)^3 * 1 * 9.8

Fb = 4/3 * 3.14 * (22 x 10^-2)^3 * 1 * 9.8

Fb = .43 N (same as beach ball)

(D) gravity on lead ball = mg = 120 * 9.8 = 1176 N

Fb = .43 N

Net force to keep the ball stationary = 1176 - .43 = 1175.57 N (on upward side)

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