1)An alloy of copper zinc has a mass of 4.9kg.when suspended in water.0.98kg of water was displaced by it.calculate the mass of zinc in the alloy if 2.5 and 19.6 are the specific gravity of the zinc and copper respectively
2) A steel ball of diameter 0.2mm, falls with a terminal velocity of 0.0029m/s through oil in a relatively large jar.Calculate the viscosity of oil, assuming the densities of the oil and the ball ar to be 7200 and 420kg/m^3 respectively .if the radius is doubled,calculate the new terminal velocity.[take g=9.8m/s^2]
.98 kg of water is .98 *10^-3 m^3 of volume
mass of zinc = z
mass of copper = (4.9-z)
volume of zinc = z * 2.5*10^-3 m^3
volume of copper = (4.9-z)* 19.6*10^-3 m^3
so
z*2.5*10^-3+(4.9-z)*19.6*10^-3 =.98*10^-3
1) To calculate the mass of zinc in the alloy, we need to use the concept of specific gravity. Specific gravity is the ratio of the density of a substance to the density of a reference substance. In this case, we have the specific gravity values for zinc (2.5) and copper (19.6).
First, we need to calculate the volume of the alloy. We can use the formula:
Volume = Mass / Density
The density of water is approximately 1000 kg/m^3. Since 0.98 kg of water was displaced by the alloy, the volume of the alloy can be calculated as:
Volume of Alloy = Mass of Water Displaced / Density of Water
= 0.98 kg / 1000 kg/m^3
= 0.00098 m^3
Next, let's calculate the mass of the alloy using its density. The density of the alloy can be calculated using specific gravity:
Density of Alloy = Specific Gravity of Copper * Density of Copper
= 19.6 * 1000 kg/m^3
= 19600 kg/m^3
Mass of Alloy = Density of Alloy * Volume of Alloy
= 19600 kg/m^3 * 0.00098 m^3
= 19.208 kg
Now, we can calculate the mass of zinc in the alloy. Since the alloy is a combination of copper and zinc, the mass of copper can be calculated first:
Mass of Copper = Mass of Alloy - Mass of Zinc
= 19.208 kg - Mass of Zinc
Given that the mass of the alloy is 4.9 kg, we have:
4.9 kg = 19.208 kg - Mass of Zinc
Mass of Zinc = 19.208 kg - 4.9 kg
= 14.308 kg
Therefore, the mass of zinc in the alloy is 14.308 kg.
2) To calculate the viscosity of oil, we can use the equation for terminal velocity:
Terminal Velocity = (2 * (density of steel ball - density of oil) * g * radius^2) / (9 * viscosity)
Rearranging the equation, we can solve for viscosity:
Viscosity = (2 * (density of steel ball - density of oil) * g * radius^2) / (9 * terminal velocity)
Let's substitute the given values:
Density of steel ball = 420 kg/m^3
Density of oil = 7200 kg/m^3
Radius = 0.2 mm = 0.2 x 10^-3 m
Terminal velocity = 0.0029 m/s
g = 9.8 m/s^2
Viscosity = (2 * (420 kg/m^3 - 7200 kg/m^3) * 9.8 m/s^2 * (0.2 x 10^-3 m)^2) / (9 * 0.0029 m/s)
After calculating this expression, the viscosity of the oil can be determined.
To calculate the new terminal velocity when the radius is doubled, we can use the same equation and substitute the new radius value:
New Terminal Velocity = (2 * (density of steel ball - density of oil) * g * (2 * radius)^2) / (9 * viscosity)
Using the known values, we can calculate the new terminal velocity.