Homework Assignment #2

Due October 8, 2003

Textbook, pages 40-42

Problems numbers 1,3,5,10, and 13

 

1.                 The aerodynamic drag D of an object moving at a speed of V is given by the equation:

D = C_dpAV²/2

 

          Where p is the air density (mass per unit volume) and A is the projected area of the object.  Determine the dimensions of  C_d in both gravitational and absolute systems.

 

 

3.     The deflection d (which has the fundamental dimension of length) of a cantilever beam of length L is given by the mechanics of materials equation:

d = PL³/3EI

                Where P is the force on the end of the beam and E is the modulus of elasticity, which has the same dimensions as pressure. Determine the dimensions of I, which is the moment of inertia.

 

5.     A dynamics energy balance states that:

 ½mv² + ½Iw² +mgh = constant

          Given that M is mass, v is velocity, w is angular velocity, and h is a distance, determine the dimensions of the remaining variables in the gravitational system.

 

10.             Convert the following quantities into the SI units N, m, and s

a.      555.4 in³

b.     45.0 lb/ft²

c.     1.33 ft/sec²

d.     450 ft-lb-sec²

 

13.             Perform the indicated conversions:

a.                  725 J/m² to lb/ft

b.                 5.25 KWh to ft-lb

c.                 62.4 lbm/ft³ to kg/m³

d.                 17.5 kha to mi²

18.     A pile of sand on level ground is approximately cone-shaped.  If the pile is 25 feet high and 65 feet in diameter, determine the mass of the sand in metric tons.  Assume the specific weight of the sand is 105 lb/ft³.