110 Spring 2018 Exam 1 Version A Name: No cell phones or electronic devices (except scientific calculators). = 4 3 = = =

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1 110 Spring 2018 Exam 1 Version A Name: No cell phones or electronic devices (except scientific calculators). = 4 3 = = = =4 = h h = = ± 4 2 =2 = = m=1 mi 12 in=1 ft 60 s=1 min 1000 g=1 kg 2.54 cm=1 in 1 cc=1 cm =1 ml 60 min=1 hr 100 cm=1 m 1 cm=10 mm 1 yard=3 ft 3600 s=1 hr 1 km=1000 m 1 furlong=220 yards 5280 ft=1 mi 24 hrs=1 day 1 rev=2 rad=360 =9.8 m s = N m kg = Pa 1 ev= J 1 N = 1 kg m s 1 J = 1 N m 1 Pa = 1 = = cos = +2 = + = + = sin N m sin ± =sin cos ±cos sin + = =cos +sin = sin +cos cos ± =cos cos sin sin Prefix Abbreviation? Prefix Abbreviation? Giga G 10 milli m 10 Mega M 10 micro μ 10 kilo k 10 nano n 10 centi c 10 pico p 10 femto f 10 M =mass=kg L 2 =area=m 2 T =time=s L T 2 =acceleration=m s 2 L =length=m L 3 =volume=m 3 L T =velocity=m s L M T 2 =force=kg m s 2 =N

2 You are told = N and = N. **1a) Compute +. Answer in engineering notation with appropriate prefix and correct sig figs. **1b) Compute. Answer in engineering notation with appropriate prefix and correct sig figs. 1a 1b **2) You are told an equation exists such that = where is position, is velocity, is time, is acceleration, is a distance, and is an unknown constant. Determine the units of the unknown constant. The answer may look pretty unusual. Only fully simplified answers will receive credit. 2 An acceleration is given as = *3a) Determine the number of sig figs in. ***3b) Convert the acceleration to units. Write your final answer with correct sig figs and scientific notation. 3a 3b

3 A circular brass plate has a square hole cut from it. The circle has diameter and the square hole has side length. The mass of the plate, after the square piece is removed, is. The thickness of the plate is. Figure not to scale. *****4) Determine an algebraic expression for the density. Write the answer as a number with three sig figs times. 3 4

4 A drone, initially at the origin is repositioned using three displacements. The first displacement, shown in black, moves the drone m heading south of east. The second displacement, shown in grey, moves the drone upwards 7.25 m. The final position of the drone, shown in white, is in the plane defined by the east-west axis and the vertical axis with the angle shown in the figure. The final distance from the origin is 5.00 m. Up (+ ) N (+ ) **5a) Write down the 1 st displacement in Cartesian form with four sig figs. **5b) Write down the final position vector in Cartesian form with four sig figs. **5c) What 3 rd displacement vector was required to give the drone the stated final position? Answer in Cartesian form with three sig figs. W 5a S E (+ ) 5b 5c

5 A position vector is given as = You may assume the units on this position vector are meters. A linear momentum vector is given by = The assumed units on the momentum vector are kg. 6a Angular momentum ( ) is defined by the equation = *6a) Determine the units appropriate for angular momentum. ***6b) Determine the angle between the position vector and the linear momentum vector. **6c) Determine the angular momentum vector by computing the cross-product. Answer in Cartesian form and keep three sig figs on all components. Don t forget to include the units you determined in part a!!! 6b 6c

6 For this problem we will ignore the units. An electric field vector is = a) Determine the magnitude of the electric field vector. Tip: when the problem statement is written with decimals, that implies you should answer with as a decimal with the same number of sig figs. 7b) Determine a unit vector describing the direction of the electric field. Each term should have a decimal number with three sig figs. **7c) Determine the angle between the electric field and the positive -axis. Again, assume I want three sig figs for final answer. 7a 7b 7c

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