13. The two objects described in the table at right are each dropped into a deep

Question

13. The two objects described in the table at right are each dropped into a deep lake of fresh water. The density of the water is 1 g/cm throughoutGreen obiect 6008 800 cm the lake (ie., ignore temperature effects) Mass Volume Yellow object 600 g 400 cm a) Explain whether each object will sink or float in the lake. b) Find the buoyant force exerted on each of the objects if each is completely submerged. c) Find the acceleration of each of the objects if they are set down on the surface of the lake and then released. If the acceleration is zero, state that explicitly d) A crown is made out of the same material as the yellow object. When the crown is placed gently into a full bucket of water, 360 cm3 of water spills out. What is the mass of the crown

Explanation / Answer

a)We know that,

density = mass/volume

density(green) = 600/800 = 0.75 g/cm^3

density(yellow) = 600/400 = 1.5 g/cm^2

The GREEN OBJECT WILL FLOAT WHILE THE YELLOW WILL SINK, since green is less dense than water and yellow is more dense.

b)Buoyant force is given by:

Fb = rho V g

F(green) = 750 x 0.0008 x 9.81 = 5.89 N

F(yellow) = 1500 x 0.0004 x 9.81 = 5.89 N

Hence, F(yellow) = 5.89 N ; F(green) = 5.89 N

c) F = ma => a = F/m

a(green) = 5.89/0.6 = 9.81 m/s^2

a(yellow) = 5.89/0.6 = 9.81 m/s^2

d)m = density x volume

m = 1000 x 0.00036 = 0.36 kg

Hence, m = 0.36 kg

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