<p> UNIVERSITY OF MASSACHUSETTS DARTMOUTH COLLEGE OF ENGINEERING EGR 101 INTRODUCTION TO ENGINEERING I</p><p> This assignment is due Thursday, June 13, 2013.  Use engineering paper.  Show all of your steps.  Present your work neatly and clearly.  Box your final answers.</p><p>Problem 1</p><p> a. Convert 102500000 Hz to MHz, where the prefix M stands for Mega. b. Convert 0.240 ms to m s. c. Convert 0.00355 C to mC . d. Convert 375mF to mF . e. Convert 5 x 1010 Hz to THz, where the prefix T is Tera. f. Convert 8.5 x 102 W to kW, where the prefix k stands for kilo.</p><p>Problem 2</p><p>The power of a motor is rated at 170 hp (horsepower) at a rotational speed of 5500 rpm (revolutions per minute).</p><p> a. What is the rated power in kW? (1 hp = 746 W) b. What is the rated speed in rad/s?</p><p>Problem 3</p><p>There is a magnetic force F associated with a moving charge q at speed v, whose magnitude is given by</p><p>F= qvB sin(q )</p><p> Derive the units of B using SI primary units if the equation is dimensionally homogeneous. The primary units in SI are kg for mass, s for time, m for length and C for charge.</p><p>Problem 4</p><p>Consider the relationship F= kr AV 2 , where F is force, r is density, A is area and V is speed, and k is a constant.  Derive the units of k using SI primary units if the equation is dimensionally homogeneous. The primary units in SI are kg for mass, s for time, m for length and C for charge.</p><p>Problem 5</p><p>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 </p><p>E= Eo cos( kx -w t) where x is a spatial coordinate in m and t is time in s; k and w are known as the wave number and angular frequency, respectively.</p><p> What are the units of Eo ?  What is the unit of the argument of the cosine function kx-w t ?  What are the units of the wave number k?  What are the units of the angular frequencyw ?</p><p>Problem 6</p><p>Are the following equations dimensionally homogeneous?</p><p> Ft= M2 gx .</p><p>Mx  F = . t 2</p><p>MV  F = . t 2</p><p>M  F= 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.</p>