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UNIVERSITY OF MASSACHUSETTS DARTMOUTH COLLEGE OF ENGINEERING EGR 101 INTRODUCTION TO ENGINEERING I This assignment is due Thursday, February 14, 2013. Use engineering paper. Show all of your steps. Present your work neatly and clearly. Box your final answers. Problem 1 a. Convert 102500000 Hz to MHz, where the prefix M stands for Mega. 0.240ms = 0.240 10-3 s 240 106 s 240 s b. Convert 0.240 ms to s. 0.240ms = 0.240 10-3 s 240 106 s 240 s c. Convert 0.00355 C to C . 0.00355C 355 105 C 3550 106 C 3550C d. Convert 375 F to mF . 375 F 375 106 F 0.375 103 F 0.375mF e. Convert 5 x 1010 Hz to THz, where the prefix T is Tera. 5 1010 Hz 0.05 1012 Hz 0.05THz f. Convert 8.5 x 102 W to kW, where the prefix k stands for kilo. 8.5 102 W 850W 0.850 103W 0.850kW 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? (1 hp = 746 W) 170hp 746 W 126820W 126.82kW hp b. What is the rated speed in rad/s? rev rad 1min rad 5500 2 575.67 min rev 60s s Problem 3 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 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. F q v B kg m m C B 2 s s 1 s kg m B 2 C m s kg B Cs 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 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. F k A V 2 F k A V 2 kg m kg m 2 s s2 k 2 2 kg 2 m kg 2 m m m 3 2 3 m m s s k 1(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 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 ? E0 E cos kx t E0 E V m What is the unit of the argument of the cosine function kx t ? kx t radians What are the units of the wave number k? k x radians k m rad k rad m What are the units of the angular frequency ? rad s Problem 6 Are the following equations dimensionally homogeneous? Ft M 2 gx . kg m m s kg (2) 2 m ? 2 s s kg m kg m ? s s YES F Mx t2 kg m kg m ? 2 s s2 . YES F MV . t2 kg m s 2 kg m s s 2 ? kg m kg m ? s 2 s3 NO F M V. t kg m 2 s kg m s ? s kg m kg m ? 2 2 s s YES 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.