In this part of the experiment you will measure the mass and diameter of several

Question

                    In this part of the experiment you will measure the mass and diameter of several clay                 

                    spheres to find the density of the clay.                 

                    1)  For a spherical object, what is the equation to find mass in terms                 

                    of density of the material, its diameter and any necessary constants? How should                 

                    the data of mass and diameter be plotted to obtain a linear graph, other than loglog graph? Make a sketch of the graph with both axes labeled. How does the                 

                    density of the sphere relate the slope of the graph? Write an equation for the                 

                    density with the slope as a variable.                 

Explanation / Answer

Density is defined as the ratio of the mass of an object to its volume:
density = p
mass = m
volume = v

p = m/v

for a spherical object:
volume = (4/3)(pi)(r^3)
volume = (4/3)(pi)(d^3)/8
volume = (1/6)(pi)(d^3)

1)
p = m/v
m = p(v)
m = p(1/6)(pi)(d^3)

2)
since:
m = p(1/6)(pi)(d^3)

mass should be plotted on the y - axis
cube root of d should be plotted on the x - axis
by doing so, you get a linear function with a slope defined as:
slope = p(1/6)(pi)

3)
the density would be equal to:
p = 6*slope/pi

4)
data is needed to solve this portion

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