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.

Present your work neatly and clearly.

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 ?

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

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 .

  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