UNIVERSITY OF MASSACHUSETTS DARTMOUTH COLLEGE OF ENGINEERING EGR 101 INTRODUCTION TO ENGINEERING I
This assignment is due Thursday, June 13, 2013. Use engineering paper. Show all of your steps. Present your work neatly and clearly. Box your final answers.
Problem 1
a. Convert 102500000 Hz to MHz, where the prefix M stands for Mega. b. Convert 0.240 ms to m s. c. Convert 0.00355 C to mC . d. Convert 375mF to mF . e. Convert 5 x 1010 Hz to THz, where the prefix T is Tera. f. Convert 8.5 x 102 W to kW, where the prefix k stands for kilo.
Problem 2
The power of a motor is rated at 170 hp (horsepower) at a rotational speed of 5500 rpm (revolutions per minute).
a. What is the rated power in kW? (1 hp = 746 W) b. What is the rated speed in rad/s?
Problem 3
There is a magnetic force F associated with a moving charge q at speed v, whose magnitude is given by
F= qvB sin(q )
Derive the units of B using SI primary units if the equation is dimensionally homogeneous. The primary units in SI are kg for mass, s for time, m for length and C for charge.
Problem 4
Consider the relationship F= kr AV 2 , where F is force, r is density, A is area and V is speed, and k is a constant. Derive the units of k using SI primary units if the equation is dimensionally homogeneous. The primary units in SI are kg for mass, s for time, m for length and C for charge.
Problem 5
Waves from antennas are known as electromagnetic waves. The wave can be described as a sinusoidal electric field E in V/m (Volts/meter). If E is described by the function
E= Eo cos( kx -w t) where x is a spatial coordinate in m and t is time in s; k and w are known as the wave number and angular frequency, respectively.
What are the units of Eo ? What is the unit of the argument of the cosine function kx-w t ? What are the units of the wave number k? What are the units of the angular frequencyw ?
Problem 6
Are the following equations dimensionally homogeneous?
Ft= M2 gx .
Mx F = . t 2
MV F = . t 2
M F= V . t where F is force in N, M is mass in kg, V is speed in m/s, x is distance in m, t is time in s, and g is the acceleration due to gravity in m/s2.