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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. Convert 0.240 ms to s. c. Convert 0.00355 C to C . d. Convert 375 F to mF . e. Convert 5 x 1010 Hz to THz. f. Convert 8.5 x 102 W to kW. 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? 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. Problem 4 Consider the relationship F k AV 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. 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 Eo cos kx 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 Eo ? What is the unit of the argument of the cosine function kx t ? 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 . F Mx . t2 F MV . t2 F M V. t 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 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?