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**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

*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*

**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*

?

**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 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 **