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