UNIVERSITY OF MASSACHUSETTS DARTMOUTH

COLLEGE OF ENGINEERING

EGR 101 INTRODUCTION TO ENGINEERING THROUGH APPLIED SCIENCE I

Ø  This assignment is due Thursday, September 19, 2013.

Ø  Use engineering papers.

Ø  Show all of your steps.

Ø  Present your work neatly and clearly.

Ø  Box your final answers.

Problem 1

a.  Convert 102500000 Hz to MHz.

102.5MHz

b.  Convert 0.240 ms tos.

240µs

c.  Convert 0.00355 C to.

3550µC

d.  Convert to.

0.375mF

e.  Convert 5 x 1010 Hz to THz.

0.05THz

f.  Convert 8.5 x 102 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

Ø  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.

Problem 4

Consider the relationship, where F is force, is density, A is area and V is speed, and k is a constant.

Ø  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.

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

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.

Ø  What are the units of?

Volts/meter

Ø  What is the unit of the argument of the cosine function?

radians

Ø  What are the units of the wave number k?

Ø  What are the units of the angular frequency?

radians/s

Problem 6

Are the following equations dimensionally homogeneous?

Ø  .

Since 2 is dimensionless, the equation is dimensionally homogeneous.

Ø  .

Ø  .

Ø  .

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/s2.

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

Ø  Based on the first link what is the power rating of the Tempra 24 Plus?

Ø  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