Pressure and fluids The two objects described are each dropped into a deep lake
ID: 1466765 • Letter: P
Question
Pressure and fluids
The two objects described are each dropped into a deep lake of fresh water. The density of the water is 1g/cm^3 throughout the lake (i.e ignore temperature effects) Explain whether each object will sink or float in the lake. Find the buoyant force exerted on each of the objects. 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. 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 cm^3 of water spills out. What is the mass of the crown?Explanation / Answer
The ability of an object to float is described as its buoyancy. The buoyancy of an object is its tendency to float on or rise in a liquid. An object that floats in water is said to be positively buoyant. An object that sinks is negatively buoyant. To determine an object's buoyancy, both its mass and volume* must be taken into consideration. The relationship between object's volume and mass is called its density*. Density is defined as the mass of an object per unit volume. Mathematically, this relationship is described using the following equation
density = mass / volume
The standard metric unit for density is grams per cubic centimeter (g/cm3
whether or not an object will float or sink depends on its own density and the density of the liquid it is placed in. In the case of water, an object with a density less than 1 g/cm3 will float. The closer its density is to 1 g/cm3, the more of it will sit below the water level
a) density of green object, dg = 600g/800 cm3 = 0.75 g/cm3
density of yellow object, dy = 600g /400 cm3 = 1.5 g/cm3
here for green object dg< dw . hence it will sink
for yellow object dy > dw hence it will float
b) The buoyant force (Fb) holding the object up. This can be measured as the force of gravity acting on a mass of water equal to the amount of water the object displaces when fully immersed.
for green object ,Fbg = 800 cm3 of water =800 g of water = 0.8 kg x 9.8 ms-2 = 7.84 kg m s-2 = 7.84 N
for yellow object, Fby = 400 cm3 of water =400 g of water = 0.4 kg x 9.8 ms-2 =3.92 kg m s-2 = 3.92 N
d) density of crown = 360 cm3 of water =360 g of water