Dimensional Analysis Homework 1

Dimensional Analysis Homework 1
due Nov. 13 (3 sig figs for all where appropriate)
1. Newton’s law of gravitation says that F=Gm1m2/r2, where F is the
force between two masses, m1 and m2, that are a distance r apart. What
are the dimensions [MaLbTc] of G, where [M] is the dimension of mass,
[L] the dimension of length, and [T] the dimension of time?
2a. Convert 5,280 feet to furlongs (1 furlong = 201.16800 meters).
2b. Convert 1 year to fortnights (1 fortnight = 14 days).
2c. What is a Joule in terms of horsepower-hour? (1 horsepower =
745.699872 watts)
[] Angle
3. In a certain given system the energy, E, is dependent only on mass (m),
distance (d), and gravitational acceleration (g),
E = const. mxdygz
From dimensional analysis (show work), determine x, y, and z.
4. Consider the table above, and the quantities mass density, pressure, and
energy. Do these quantities (pressure, energy, and mass density) have
independent dimension? (Stated another way, can you combine, with
some power for each quantity, two of the quantities to generate the units of
the third quantity? – If yes, then all three quantities do not have
independent dimension.)
5. Do the same question as #4 above, only now for the quantitites
force, pressure, and energy.