# UNIVERSITY OF MASSACHUSETTS DARTMOUTH COLLEGE OF ENGINEERING

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.

b.

102.5MHz

Convert 0.240

ms

to 

s

. c.

d.

240µs

Convert 0.00355

C

to 

C

.

3550µC

Convert 375 

F

to

mF

. e.

0.375mF

Convert 5 x 10 10

Hz

to

THz.

f.

0.05THz

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

b.

(170hp)(746W/hp) = 126.82kW

What is the rated speed in

/

s

?

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

Problem 4

kg C

s

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    

###  

A

   

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

?

What are the units of the wave number

k

?

 

What are the units of the angular frequency  ?

Are the following equations dimensionally homogeneous? 

Ft

M

2

gx

 . 

kg

m

s s

2  ?

kg

 2 

m s

2 

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