# UNIVERSITY OF MASSACHUSETTS DARTMOUTH COLLEGE OF ENGINEERING

```UNIVERSITY OF MASSACHUSETTS DARTMOUTH
COLLEGE OF ENGINEERING
EGR 101 INTRODUCTION TO ENGINEERING THROUGH APPLIED
SCIENCE I
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This assignment is due Thursday, September 19, 2013.
Use engineering papers.
Present your work neatly and clearly.
Problem 1
a. Convert 102500000 Hz to MHz.
b. Convert 0.240 ms to  s.
c. Convert 0.00355 C to  C .
d. Convert 375 F to mF .
e. Convert 5 x 1010 Hz to THz.
f. Convert 8.5 x 102 W to kW.
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?
b. What is the rated speed in rad/s?
Problem 3
On the following webpage http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html
it is claimed that 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 metric primary units if the equation is dimensionally
homogeneous. The primary units in metric 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 metric primary units if the equation is dimensionally
homogeneous. The primary units in metric 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
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t2
 F
MV
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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.
Problem 7
The following website advertises tankless water heaters
http://www.e-tankless.com/products.php
http://www.e-tankless.com/electric-tankless-how-it-works.php
 Based on the first link what is the power rating of the Tempra 24 Plus?
 What is the electricity cost for a total usage of 40 hours if the electric service is
208V and the rate is \$0.114/kW-hr?
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