Questions about Chapter 1: Measurement.

Question 1:

A pipe delivers 600 gallons of water per minute.  How long does it take to fill a swimming pool having a rectangular base of 10 m x 10 m and a depth of 2 m ?  Give your answer in minutes. [ 1 Gallon = 3.79 liters ; 1 liter = 1000 cm3  ]

ANS:    88 minutes.

Question 2:

Force is a physical quantity with dimensions equal to the dimension of mass multiplied by the dimension of acceleration.  Suppose the force acting on an object is given by

F = K ma vb xc   ,

where m, v and x have the dimensions of mass, velocity and distance, respectively. K is a dimensionless constant.  Use dimensional analysis to find the numerical values of the constants a, b and c.

ANS:    a  =  1   ;      b   =  2      ;    c   =   -1.

Question 3:

Assume the density of nitrogen gas, r , in a container that measures 1.0mx2.0mx4.0m  is 1/800 that of water, and r ( water ) = 1.0 g/cm3.  Find the number of nitrogen molecules in the container, given that the molecular weight of nitrogen M = 28 g and Avogadro’s number is NA = 6.02x1023 molecules/mole.

ANS:     2.15x1026 molecules.

Question 4:

The acceleration “ a ” of a particle is given by the following equation

a = B v2 + ( s C ) / t2

where v is the velocity, t is the time and s is the displacement.  Determine the dimensions of B and C.

ANS:   unit of B is 1/m and C is dimensionless.