UNIVERSITY OF MASSACHUSETTS DARTMOUTH
COLLEGE OF ENGINEERING
EGR 101 INTRODUCTION TO ENGINEERING THROUGH APPLIED
SCIENCE I

This assignment is due Thursday, September 19, 2013.
 Use engineering papers.

Show all of your steps.

Present your work neatly and clearly.

Box your final answers.
Problem 1 a.
Convert 102500000 Hz to MHz.
102.5MHz b.
Convert 0.240 ms to
 s .
240µs c.
Convert 0.00355 C to

C .
3550µC d.
Convert 375

F to mF .
0.375mF e.
Convert 5 x 10
10
Hz to THz.
0.05THz f.
Convert 8.5 x 10
2
W to kW .
0.85kW
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 ?
Use the conversion factor 1hp = 746W
(170hp)(746W/hp) = 126.82kW b.
What is the rated speed in rad / s ?
(5500rev/min)(2πrad/rev)(1min/60seconds) – 57566rad/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.


F


     sin

 q v
  sin

 kg
 m
 s
2
C
 m s
 kg
C
 s
Problem 4
Consider the relationship F
 
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.
F
 k

AV
2
     


 
V
2
 
  kg
 m
 kg m
3 s
2
 m
2  m
2 s
2
 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
 o
   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 E o
?

Volts/meter
What is the unit of the argument of the cosine function kx
  t ? radians

What are the units of the wave number k ?

 radians
 
 radians m

What are the units of the angular frequency

? radians/s
Problem 6
Are the following equations dimensionally homogeneous?

Ft

M 2 gx .
  kg
 m
 s

?
 kg

2
 s
2 s
2 m
 m
YES
Since 2 is dimensionless, the equation is dimensionally homogeneous.

F

Mx
. t
2 kg
 m s
2 t
  x

?
 kg
 m s
2
YES

F

MV t
2 kg
 m s
. t
 
V

?
 kg
 m s
2
YES
 F

M
V t
.
    t kg
 m

?
 s
2
YES kg
 m s s

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 / s
2
.
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?
Power rating of Tempra 24Plus is 18kW for 208 Volt input
Total cost = (kW)(hr)($0.114/kW-hr)
Total cost = (18kW)(40hr)($0.114/kW-hr)
Total cost = $82.08