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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.*

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 **