# UNIVERSITY OF MASSACHUSETTS DARTMOUTH COLLEGE OF ENGINEERING

```UNIVERSITY OF MASSACHUSETTS DARTMOUTH
COLLEGE OF ENGINEERING
EGR 101 INTRODUCTION TO ENGINEERING I
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This assignment is due Thursday, February 14, 2013.
Use engineering paper.
Show all of your steps.
Present your work neatly and clearly.
Problem 1
a.
b.
c.
d.
e.
f.
Convert 102500000 Hz to MHz, where the prefix M stands for Mega.
Convert 0.240 ms to  s.
Convert 0.00355 C to  C .
Convert 375 F to mF .
Convert 5 x 1010 Hz to THz, where the prefix T is Tera.
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  
 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  k  AV 2 , where F is force,  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  t 
where x is a spatial coordinate in m and t is time in s; k and  are known as the wave
number and angular frequency, respectively.
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What are the units of Eo ?
What is the unit of the argument of the cosine function kx  t ?
What are the units of the wave number k?
What are the units of the angular frequency  ?
Problem 6
Are the following equations dimensionally homogeneous?
 Ft  M 2 gx .
 F
Mx
.
t2
 F
MV
.
t2
 F
M
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.
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