# 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.
Present your work neatly and clearly.
Problem 1
a. Convert 102500000 Hz to MHz, where the prefix M stands for Mega.
0.240ms = 0.240 10-3 s  240 106 s  240 s
b. Convert 0.240 ms to  s.
0.240ms = 0.240 10-3 s  240 106 s  240 s
c. Convert 0.00355 C to  C .
0.00355C  355 105 C  3550 106 C  3550C
d. Convert 375 F to mF .
375 F  375 106 F  0.375 103 F  0.375mF
e. Convert 5 x 1010 Hz to THz, where the prefix T is Tera.
5 1010 Hz  0.05 1012 Hz  0.05THz
f. Convert 8.5 x 102 W to kW, where the prefix k stands for kilo.
8.5 102 W  850W  0.850 103W  0.850kW
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)

170hp   746

W
  126820W  126.82kW
hp 
b. What is the rated speed in rad/s?
rev 

 5500
 2

  575.67
min 
rev  60s 
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.
 F    q v  B 
 kg  m 
m

  C     B
2
 s

s
1
s  kg  m 
 B    
 

2
 C  m  s

kg
 B 
Cs
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.
 F    k    A V 2 
F 
k  
   A V 2 
kg  m
kg  m
2
s
s2

k  
2
2
 kg  2  m 
 kg  2  m 
m
m


 3
 2 
 3   
m 
m 
s
s 
 k   1(dim ensionless)
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.
 What are the units of Eo ?
 E0    E  cos  kx  t 
 E0    E  
V
m
 What is the unit of the argument of the cosine function kx  t ?
kx  t   radians
 What are the units of the wave number k?
 k  x   radians
 k   m    rad 
k  
m
 What are the units of the angular frequency  ?
  
s
Problem 6
Are the following equations dimensionally homogeneous?
 Ft  M 2 gx .
 kg  m 
m

  s    kg  (2)  2   m  ?
2
 s

s 
 kg  m   kg  m 


?
 s   s 
YES
 F
Mx
t2
 kg  m   kg  m 
?


2
 s

 s2  .
YES
 F
MV
.
t2
 kg  m 
 s 2  
 kg  
m

s
s 
2
?
 kg  m   kg  m 
?
 s 2  
 s3 
NO
 F
M
V.
t
 kg  m 


2
 s

 kg  
m

 s ?
s
 kg  m   kg  m 


?
2
2
 s
  s

YES
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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