Can a watch-sized electromagnet deflect a bullet? (from James Bond movie)

Transcription

1 Can a peon be blown away by a bullet? et' ay a bullet of a 0.06 k i ovin at a velocity of 300 /. And let' alo ay that it ebed itelf inide a peon. Could thi peon be thut back at hih peed (i.e. blown away)? To olve thi aue the a of the peon i, ay, 70 k. Apply conevation of linea oentu to the bullet and peon, between the point jut befoe the bullet tike the peon, and afte it ebed inide the peon (o that bullet + peon both have the ae final velocity). We have, 0.06(300) +70(0) = ( )V whee V i the velocity of the bullet + peon afte the bullet ebed in the peon. Solve fo V = 0.6 /. Thi peed i fa too low to caue the peon to be "blown away". Can a watch-ized electoanet deflect a bullet? (fo Jae Bond ovie) To analyze thi let' ay a bullet flie pat a watch a hown in the fiue below, with dienion a hown. bullet anet V l F d V h Fo exaple, let' ay the bullet ove at Vh = 300 / and we wih to deflect it a inificant aount o that it ie it ak copletely. f the intended taet of the bullet i the one weain the anetic watch then the bullet would have to deflect a eat deal to avoid hittin the taet. So let' eaonably ay the bullet would have to be deflected by an anle of 45. Thi ean that the lateal peed of the bullet (Vl) would be equal to the hoizontal bullet peed (Vh). So Vl = 300 /. Befoe the bullet pae by the watch, it lateal peed i zeo. A it pae by the watch the lateal bullet peed would have to be inceaed to 300 /. Thi ean that the anetic foce of attaction F between bullet and watch would have to be vey lae in ode to caue uch a apid lateal peed inceae in the hot tie peiod it take the bullet to pa by the watch. To

2 axiize the anetic foce the bullet would have to pa a cloe a poible to the watch, o d would have to be a all a poible. f we uppoe the watch i =.5 c in diaete, then it take the bullet 0.05/300 = 8.33x0-5 econd to pa by the watch. et' alo uppoe the a of the bullet i 0.06 k. To olve fo the foce F we can ue the ipule and oentu equation: Ft = v v, whee F i the aveae lateal foce pullin on the bullet duin the bullet pa, t i the tie duation of the pa, i the a of the bullet, v i the lateal bullet peed befoe the pa, and v i the lateal bullet peed afte the pa. Uin the vaiable iven peviouly, we have F(8.33x0-5 ) = 0.06(300) 0.06(0). Solvin fo F we et F = 6,000 N. Thi i equal to ton! Clealy a watch ized anet cannot even coe cloe to ufficiently deflectin a bullet. Note that a anetic foce vaie with the invee cube of the ditance fo the anet. Thi ean that the anetic foce F can only be hih when the bullet i in vey cloe poxiity to the watch. Thi poxiity equieent i appoxiately odeled by auin that the anetic foce F i only actin on the bullet while it pae ove the watch. n eality the anetic foce would alo be actin on the bullet while it i oe ditance away fo the watch, but in the calculation we aue that the foce i only actin on the bullet a it pae ove the watch, which i a eaonably ood appoxiation. Could a kydive whoe paachute failed to open hit a playound eeaw and end a all il flyin even toie hih, and he could till uvive? We hall aue a conevative cae whee the kydive doe not ebound off the eeaw and intead "tick" to it iht afte ipact. We can apply conevation of anula oentu to analyze thi poble between tae () and () a hown in the fiue below, with vaiable hown. The lae ball on the iht epeent the kydive. The alle ball on the left epeent the il. The anle i all, which i a ood appoxiation fo the typical eeaw.

3 JUST BEFORE MACT V () JUST AFTER MACT V () V w Apply the conevation of anula oentu equation about point, between tae () and () V Whee: V V w i the a of the kydive i the a of the il V i the velocity of the kydive jut befoe he ipact the eeaw V i the velocity of the kydive (and il) jut afte the kydive ipact the eeaw 3

4 i the ditance fo the pivot point to the end of the eeaw whee the kydive and il ae located i the otational inetia of the eeaw about point, which coincide with the cente of a of the eeaw (by auption) w i the anula velocity of the eeaw jut afte ipact Now, w = V/ fo the eoety. The above equation then becoe V V V ( V / ) Solve fo V. V V / A a eaonable appoxiation teat the eeaw a a lende od, whee () 3 whee i the a of the eeaw. t follow that V V 3 Suppoe we have V = 0 ph (appoxiate teinal peed of kydive), = 80 k, = 30 k, and = 00 k. Then fo the above equation we have V = 67 ph. The fiue below how the takeoff point of the il. Thi i tae (3). 4

5 V 3 takeoff V 3 (3) At takeoff, the il leave the eeaw at V3 = V (appoxiately). Thee i vey little tie fo the velocity of the il on the eeaw to chane beyond V iven the hih V velocity afte ipact (which quickly otate the eeaw). Thi eult in a neliible velocity chane fo the il, between the tie the ipact occu and when the il take off. Since we ae conidein a conevative cae (tickin upon ipact) then V3 i the inial takeoff velocity of the il. Now, 67 ph = 30 /, which eult in a peak heiht eached of 46 ete, auin neliible ai eitance and the il flyin taiht up (a ood appoxiation iven a all anle ). Thi heiht i uch eate than even toie o the yth i indeed poible. Howeve, unle he land oewhee oft he i unlikely to uvive the fall. Thi i in addition to the udden upwad acceleation, at takeoff, which can fatally injue he a well 5