1. The mass, m, of a sphere depends on the density, \(\rho\), of the material and the diameter, d. By
measuring the mass and diameter of several spheres of the same material, the density of the material
can be calculated.
\(m = \frac{\rho \pi d^3}{6}\)
Raw data:
m, d
Graphing data:
y-axis: m , x-axis: d$^2$
Uncertainty for graphing data:
$\delta_y = \frac{\delta m}{m}$ , $\delta_x = 2 \frac{\delta d}{d}$
You may use the blank area below for scratch work:
Desired quantity: \(\rho\)
Find the desired quantity from the slope of the graph:
slope = $\frac{\rho \pi}{6}$
Find the uncertainty of the desired quantity:
2. The intensity I of a point source of light depends on the distance, r, from the light source. By
measuring the intensity at various distances, the power output, P, of the light source can be found.
\(I = \frac{P}{4\pi r^2}\)
Raw data:
Desired quantity:
Graphing data:
Find the desired quantity from the slope of the graph:
y-axis: , x-axis:
Uncertainty for graphing data:
Find the uncertainty of the desired quantity:
$\delta_y = $ , $\delta_x = $
