solutionshomework3(2014) - 'i i l i ‘l 3i w ‘4 ‘4 l y...

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Unformatted text preview: 'i i l i ‘l 3i w ‘4 ‘4 l y 53W: Jan. 31, 2014 Homework #3 Due: Friday, Feb 7 Read Chapter 3 Please pass in solutions to 7 problems; 6 of the 7 problems are written below, and 1 of the 7 problems is in this week’s Supplemental Homework in "MasteringPhysics". Each problem will be weighted equally. Note: Except for one problem, this week’s MasteringPhysics assignment is still for practice (weights will be 0-points). There are many problems accompa— nying Chapter 3, so you may not have time to try them all. A number of these are "tutorials", which may be helpful. 1. Recently, there has been considerable discussion about how to alleviate concussions occurring among football players, particularly professionals who continue to play for many years. There is mounting evidence that repeated concussions have long-term consequences, such as early—onset dementia and de— pression. Football helmet manufacturers have responded by proposing new de- signs to soften the blow. The key parameter determining the extent of the brain damage in collisions is the displacement d of the helmet padding as a player’s head decelerates from a top speed of (typically) 10 m/s, to zero, in a head—on collision. Larger helmets have room for thicker and squishier padding, which allows for larger (1. I Using a model of constant acceleration (in this case constant deceleration) for simplicity, what is the deceleration experienced by a player’s head for a typical value of d = 2.0 cm? Express your answer in "g’s" (multiples of 9.8 m/s2.) How will this change if the padding is made thicker and softer, so that for the same collision d = 4 cm? What is the maximum thickness of the padding in a helmet above which players will look so silly wearing them that people will no longer tune-in to watch football? 2. The maximum range for a projectile launched at an angle 90 with speed v0 from a flat surface, in the absence of air friction, is given by 2 . R = 110 $13200) (1) This expression can be derived by combining the equation giving the horizontal displacement versus time, :12 = mg + newt + 5amt2, with the equation giving the vertical displacement versus time, 1 2 y=y0+voyt+§ayt. You know that am = O, cry 2 —g, because gravity only affects the motion in the y—direction. You bring the launch angle into the picture by resolving the launch velocity 60 into its a: and y components , 00$ = 710 cos 60 and my = no sin 60. You then have to figure out how long it takes for the object to return to the ground by setting y = 0 and solving for t. Substituting this time into the equation for a: will tell you how far the object travels in the a: — direction before it hits the ground. To put your result into the form above, you should make use of the trig. identity for the sine of the sum of two angles, sin (0: + fl) : sina cos fl + cos oz sin [3, and let both angles a and ,8 be equal to 60. Assuming that you can follow these steps, your assignment is as follows: (a) Derive eq. (1) while carefully following the instructions above. (b) Repeat the derivation without looking at the instructions, using a clean sheet of paper. (0) Keep repeating the derivation until you can do it in less than 5 minutes! None of your work for steps (a—c) needs to be passed in. But now that you are up to speed, here is something that you should do, to be passed in as the ‘ answer to this problem: (d) Derive what would be the modification of the range formula (1) for the ‘ case where the projectile is launched from the top of a building of height h. 3. In the 1991 World Track and Field Championships in Tokyo, Mike Powell jumped 8.95 m, breaking the 23—year old long-jump record set by Bob Beamon in Mexico City. Assume that Powell’s speed on takeoff was 9.5 m/s, and that g = 9.80 m/s2 in Tokyo. How much less was Powell’s range than the maximum possible range for a particle launched at the same speed? 4. A football can be kicked at an initial speed of 25 m/s. What are the (a) least and (b) greatest elevation angles at which the football can be kicked to score a field goal from a point 50 m' in front of goalposts whose horizontal bar is 3.44 m above the ground? 5. A ball is thrown horizontally from a height of 20 m, and hits the ground with a speed that is three times its initial speed. (a) What is its initial speed? (b) What is its angle of impact with the ground? (Take straight down to be 90 degrees.) 6. For women’s volleyball, the top of the net is 2.24 In above the floor, and the court. measures 9.0 m by 9.0 m on each side of the net. Using a jump serve, a player strikes the ball at a point that is 3.0 In above the floor and a horizontal distance of 8.0 m from the net. If the initial velocity of the ball is horizontal, (a) what minimum magnitude must it have if the ball is to clear the net, and (b) what maximum magnitude can it have if the ball is to strike the floor inside the back line on the other side of the net? ,_ V, ,, ,V V , ,V ,, A, ,_ w , 7 fl ,. , , ,__ _ V V ,, V, I, p Champ-l- mng Mr ‘E I: FWJLa‘m. Wfffwyflmflwmfimwm.»N.___W_m-w, fl 1 - “ww ~~~~~~~~~ Maw/RZZAJ‘LMK ‘+~ i_:“ipgalwwfiikwiiMLnfi%mmpmwm& ‘W’M " ‘ E #1 x 554, WWW wfimiwmmimh'W,,,Wmm_,-,.__, ‘ Mm,M" fimwgg-...--#m-.mmxm.wmflw 11L,.hg.mm)h3.§j&Mimi/59MOW JAMEAQQIEE);3-”.fln.qwm____mfi gm-“ WM.__W“WW”_.. A._Xmm.u_“_imfiafimcfmbflj3%,ergwqgffl flgWMW/MM2744WULWM WM ______..~r - W’zr._ wwwém ‘ .H” _. ._ __ w- ,v -M- _, kaa—afiffm/JB -_~:M€;_zmmwa_ég:42LaiiillmW_____v_fl__ iguwwwwmflmmwflmwgfi%iflmwmwmmNWWMWMWWWA M ,‘ , A ,_ ,, ,, ,V ,_ FMA.VV,,,-.MM,WWV.¢ M,m._,_wmm~ m M WW M M_M_W N. A “W.” V.“ _ mm “fl w- , ‘ w ,_ _ a l I Z {W i\ ‘\ § 1,, w H g: i g‘ 5” M 2‘ i i, E; L. N r- fi__ E1 _, _, 4 , ,_ , ,, ,, 'l in 00576 M“W‘“"“’”‘**"’“"""‘*‘““”‘”‘“f"I;:fiigfégiéflr15Lfl—«w—w~~ WA * ~ » kg ayw'm~fi #____M ____________________________________________ mm -flvo WM _. “Am..- Mm _ N W- w_ m -“WW W. 4. E1; thHJ/Uken 134M filfiLLLML£~LW._W mmmmmmmmmmmmm ____./ #WM M m "m M A wwwww "— WTWs'gW—wwa—MQM Tm“ M m PM_M W, _. m“ NM“ W M “fl m¥tmwm}v ;§_m: ”" g; :Zw __________ ___.__Ar _ W m NM # m m Bufiflxjmél ngrmijem, __ _____________________________________________ V, n. ——w~— «MVu/wfi » MM—mw m -I»- WW.,__,_.-_M_Mf__w.awmkmwxbaam,M"EmilMrugabmmmffjflarmg. m-mm“WWWV,.-__My~__s:,ofl_.:__1 ..... “7%.;3 "1: 17: 53:3: A _.W..-WWWWWWWWM “mflmwmmbgn :42) {km ,m:$.m4%w,L’lmmgmgawb“_4_7:wha_}_m_g_ww“MAW _ r a, wwfl M,“ _Aff_,._,ibiisiwizmgkmfihgm,,_4‘,..::flgymcz[“J4;,_ fl,_- __# __ w w- N. w - a “ ##Xw: A/yaivéfltgfé V ...
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