161 Spring 2016 Exam1A Name: No cell phones or electronic devices (except scientific calculators). = 4 3 = = =

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1 161 Spring 2016 Exam1A Name: No cell phones or electronic devices (except scientific calculators). = 4 3 = = = = 4 =! h$%h&! ' = ( = ± 4, 2. = 2 / = 01'2 = 2 1 kg = 2.20 lbs 1609 m = 1 mi 12 in = 1 ft 60 s = 1 min 1000 g = 1 kg 2.54 cm = 1 in 1 cc = 1 cm = 1 ml 60 min = 1 hr 100 cm = 1 m 1 cm = 10 mm 1 yard = 3 ft 3600 s = 1 hr 1 km = 1000 m 1 furlong = 220 yards 5280 ft = 1 mi 24 hrs = 1 day 1 rev = 2 rad = 360 % = 9.80 m s P = RSSN m kg V W = X Pa 1 ev = RS[ J 1 N = 1 kg m s 1 J = 1 N m 1 Pa = 1 ( ] = ( ' +_ ' & & _ ] = _ ' +2 (! _ ] = _ ' + & = a( +b sin ±d! c dec = dcosf gh ic deci = dsinf gh = sincosd ±cossind _c k +_c = _c k = cosfm +sinfn fo = sinfm +cosfn /kp = q Σtc = uc N m cos±d! = coscosd sinsind = _ = r c = + /kp fo c =!+ /kp fo v xy z{ = 1 2 u_ { = 1 2 }r ~ 1 = V = 1 2 ( ~ = PV = u%h ' +pprp / ] ~ = = tc c ' = ] { = k /pk ] = t cosf = t = t ( t = ( ~(! 'p/ = & = t c _c k = & = ˆ &$u c= Šc = tc & Šc = u_c ( Œ = u S( S +u ( u S +u ( Œ = ( u u Žc = c tc ΣŽc = }qc ec = }rec 'p/ = Žc rec = f _ = r /kp = q = _ = r } k' = } Œ +u } = } +} } = u V = t t = W V k = V k V k 'p/ d = ] 2' % S _ S = _ Vh! = V W +%h V _ +%h = constant = V t = Δ_ 8 Δb When appropriate will also include moment of inertia table as found in chapter 10 showing various shapes and axes. Prefix Abbreviation? Prefix Abbreviation? Giga G 10 [ milli m 10 R Mega M 10 micro μ 10 R kilo k 10 nano n 10 R[ centi c 10 R pico p 10 RS femto f 10 RSX

2 ( massless rod basketball } 2'š = 1 2 u } /'p = u } /'p = 1 k/ 12 u } p/ = u( k } 'k = 2 5 u } 2'š = 1 4 u } /'p = u } /'p = 1 k/ 12 u +! } '2 = 2 5 u } /'p = u 'p

3 A thin plate of metal is formed by removing a ¼-circle from a right triangular plate as shown. The dimensions of the triangle are length and height. The radius of the ¼-circle is. The density of the plate is and the total mass of the plate is. **1) Determine an algebraic expression for the thickness of the plate in terms of the given variables. Note: put your final answer in the box when one is provided. 1 *2) A Joule (J) is a unit of energy. Ten tons of TNT stores an amount of energy slightly more than GJ. Convert GJ to J. Write your final answer in scientific notation with correct sig figs. 2 **3) The peak water flow rate at the Oroville Dam spillway last week was 100,000 of œ ž Ÿ. Determine the amount flowing over the dam. You may assume the density of water is 1000 «. Round your final answer to three sig figs and answer with correct scientific notation. ª 3

4 Two track stars run on a track. Jaime runs with constant speed _ for several laps. At some instant Jaime passes Loren at the starting line. Loren starts from rest and accelerates at constant rate until reaching a speed 40% greater than Jaime. From that point on, Loren runs the remainder of the race with constant speed. Jaime reaches the finish line time & before Loren. _ 40% %& &hy _ *****4) How long (what distance) was the race? Answer in terms of, _, and &. 4

5 The displacement vector between random points A and B is given by c = 2m 3n 4 o A force vector is tc = 5m +6 o Note: assume the units on ec are meters ( ) and the units on ēec are Newtons ( ). I expect you to include units on your final answers as appropriate. **5a) Write down a unit vector pointing in the same direction as c. Answer in Cartesian form and with 3 sig figs for each term. *5c) Determine the angle between c and the positive ±-axis. Express your result as a number between 0 and 180. ***5d) Torque is defined as Žc = c tc. Determine the torque using the given vectors. Answer in Cartesian form. 5a 5b 5c

6 I watched Dr. Strange (the movie). Somewhere in that movie a particle initially located 8.00 m to the left of the origin had a velocity given by the unusual function _ = 24.0 /«²S.W. Note: assume positive numbers indicate motion in the +m direction. Also, assume time is in seconds, position in meters, and velocity is in meters/second. *6a) Determine the units assumed on the number *6b) Determine the units assumed on the number ***6c) Determine the position of the particle as a function of time. Note: for this part only you need not include units on any numbers. *6d) True or False: Dr. Strange was a bad movie. Write answer in the box. 6a 6b 6c 6d

7 A student walks into her room and throws a ball upwards at 45 above the horizontal. Point A indicates just after the ball has left the woman s hand. The ball then reaches max height at point B. Point C indicates just before impact. For ease of communication, call the horizontal velocity components _ g, _ h, and _ 0, at points A, B, & C respectively. Similarly, call the vertical velocity components _ g, _ h, and _ 0, at points A, B, & C respectively. Air resistance is negligible. Figure not to scale. A B C 7a) Rank the horizontal velocity components from smallest to greatest clearly indicating any ties. Note: assume zero is larger than any negative number for this problem. 7b) Rank the vertical velocity components from smallest to greatest clearly indicating any ties. Note: assume zero is larger than any negative number for this problem. 7c) Are any of the components listed equal to zero? If so, list the component or components equal to zero. If none are equal to zero, write none are equal to zero. 7d) At which point is speed the greatest? If it is a tie, list all points that have the greatest speed. 7e) At which point or points is acceleration the greatest? If it is a tie, list all points that have the greatest acceleration.

8 An xt-plot for a taco is shown below. Use this plot to answer the questions below. x (m) t (s) a) Over what time interval (or at what time) is the taco at rest? 8b) Over what time interval (or at what time) is the taco moving forwards? 8c) Over what time interval (or at what time) is the taco speeding up? 8d) Estimate the displacement of the taco between & = 1.00 s and & = 3.00 s. 8e) Estimate the velocity of the taco at & = 3.00 s. Show clear work and get within 10% for full credit on this part. 8f) Estimate the distance traveled by the taco during the entire 4.00 s of travel shown in the plot.

9 *****9) Choose your own adventure: You can do this problem either algebraically or with numbers (# s provided at end of problem statement). A ball is launched from negligible initial height. The ball travels distance ( horizontally and impacts the top of a post of height. The ball was launched with known initial speed _. Determine all possible launch angles. If you use numbers assume _ = 20.0 ª, ( = 18.0 m, = 15.3 m, and % = 9.80 ª ³. Suggestion: keep all intermediate answers to 5 sig figs to avoid rounding error. Round final answers to 3 sig figs. 9

10 Extra Credit: A projectile is launched from the origin with initial speed _ W at an angle of 60.0 above the horizontal. The terrain immediately to the right of the launch point can be modeled by the sine wave b(! = sin (. Assume = 1.00 m and = 1.50 m RS. Figure not to scale. _ W *EC1a) First write out the relevant equations required for determining the impact location. Then describe a method for solving your system of equations. Do not actually solve them. Note: points are awarded for describing the method of solution, not for writing the equations. *EC1b) Explain why this problem is physically unreasonable if = 1.00 m and = 2.00 m RS.

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