Question

Sinking Object. A stone has a mass of 1.0kg and density 5000kg/m³ is dropped in water. It crossed the surface of the water with an initial velocity of V₀= -0.55m/s ĵ.

a) Calculate the acceleration of the stone

b) Calculate the position of the stone after 1.0 seconds. Use an upward y-axis with its origin at the surface of the water

c) The stone settles on the bottom of the container. What is Fɴ?

Answer 1

g = acceleration of gravity, about 9.81 m/s^2
Vstone = mass stone/density stone
= 1 kg/ 5000 kg/m^3 = 0.2 *10^-3 = 2 * 10^-4 m^3
weight stone =1 g
Density of water = 1000 kg/m^3
Force of buoyancy up on stone = weight of water displaced
= 1,000 * g * Vstone = 10^3 * g * 2 * 10^-4 = 0.2 g

net force down = weight - buoyancy
= 1 g - .2 g = 0.8 g
F = m a
a = F/m = 0.8 g / 1
a = .8 g downward (which we could have guessed from the beginning because the rock is five times the mass of water it displaces)

(b) x = -(1/2)(.8 g) t^2

(c) force up on rock from bottom = weight - buoyancy
= .8 m g