1 f 5 P8 Lab #5 Summer 004 Experiment 5 Ballistic Pendulum In this experiment yu will aain be examinin a system that cnserves bth mmentum and enery. The ballistic pendulum is a device ften fund at well equipped shtin ranes. It is used t measure the speed f a bullet. The peratin f the ballistic pendulum is simple. A blck f wd f knwn mass is suspended frm lenth f rpe, frmin a pendulum. A bullet f knwn mass is fired hrizntally int the blck f wd, causin the blck with the imbedded bullet t rise. The heiht f the rise is measured and the speed f the bullet can be calculated. M+m m M h T calculate the speed f the prjectile ( ) the cnservatin f mmentum is used t predict the mtin f the blck immediately befre and immediately after the cllisin f the bullet with the blck. (Immediately after the cllisin the blck initially mves ff t the riht in a straiht line.) p i = p f p i = m p f = (M + m)v b m = (M + m)v b v ( M + m) = (Equatin 1) m v b T be able t calculate the speed f the prjectile the recil velcity f the blck plus the prjectile (v b ) must be knwn. T find it cnservatin f enery is used. The initial kinetic enery f the blck plus prjectile is cnverted int ravitatinal ptential enery as the pendulum bb rises.
f 5 P8 Lab #5 Summer 004 1 1 ( M + m) v b = ( M + m) h v b = h v b = h (Equatin ) Knwin v b, the initial speed f the prjectile ( ) can nw be calculated. It wuld be nice if we culd find sme independent way f verifyin the crrectness f the prjectile s speed. That is what yu will d in the secnd part f this experiment. When yu studied accelerated mtin yu prbably ran int an exercise where a ball rlled ff a hrizntal tabletp and hit the flr at sme distance frm the table. H x As the ball rlls aln the tabletp, it has nly a hrizntal cmpnent f mtin. Hwever, as it rlls ff it starts acceleratin dwnwards and acquires an ever rwin vertical velcity cmpnent. This is superimpsed nt the cnstant hrizntal velcity cmpnent and causes the parablic trajectry shwn. Our task here is t measure the initial hrizntal velcity,. (This crrespnds t the prjectile speed calculated usin Equatins 1 and fr the ballistic pendulum abve.) If the heiht f the tabletp H and the distance x frm the table the prjectile hits the flr are knwn, then if the hrizntal velcity cmpnent is cnstant: x = v t
3 f 5 P8 Lab #5 Summer 004 The time it takes fr the ball t fall t the flr is shrt and the time is difficult t measure directly. Hwever, knwin that the ball accelerates vertically under the influence f ravity we can calculate the time it takes t fall knwin nly the acceleratin f ravity and the heiht f the tabletp. 1 t H H = t = Knwin the time, the initial hrizntal velcity f the prjectile can als be calculated. x = v H Equipment: = x (Equatin 3) H Serratins Cup Pendulum Trier Prjectile Ballistic Pendulum Abve is a pht f the ballistic pendulum apparatus that yu will use fr this labratry. At the riht is a husin with a strn sprin inside, and a steel rd prjectin
4 f 5 P8 Lab #5 Summer 004 frm the husin. The prjectile is a brass sphere with a hle bred thruh its diameter. The prjectile is launched by the sprin int the cup at the bttm f the pendulum. After the prjectile is captured by the cup, the pendulum bb rises and is stpped at the tp f its rise by a ratchet mechanism enain with the serrated black strip n the elevated arm at the left f the apparatus. T lad the ballistic pendulum and prepare it fr use, place the hle in the brass sphere ver the small rd at the end f the steel rd prjectin frm the husin. Push the steel rd back int the husin until the trier lcks the cmpressed sprin and steel rd int the launch psitin. There are three pssible psitins fr launch as the sprin is successively cmpressed. Make sure that yu use the same launch psitin thruhut the lab. The sprin is als quite stiff and takes sme muscle t cck it. T launch the prjectile, simply push dwn n the trier, the sprin will release the steel rd and the prjectile will be prpelled int the cup at the bttm f the pendulum. The bb will then rise and be cauht at the tp f its rise by the ratchetin mechanism mentined abve. Prcedure: Weih the brass sphere and the pendulum. The pendulum will have t be remved frm the apparatus first. The pendulum is hun frm the ballistic pendulum frame with a pair f bearins. Detach the pendulum frm the frame by unscrewin the thumbscrew n the pendulum s suspensin bearins. Reattach the pendulum t the suspensin bearins. Place the brass prjectile nt the steel shaft and cck the sprin. Push dwn n the trier and release the prjectile. After the cup has been cauht by the ratchetin, measure the heiht the pendulum bb has risen frm its equilibrium psitin. D this fur r five times. Ntice the ratchet psitin each time the bb is cauht. It wn t be the same every time. Smetimes the ratchet will slip dwn a ntch r tw befre it finally catches the bb. Yu want t determine the hihest ntch that catches the bb mst f the time, and use this psitin t determine the heiht the bb rises. Use Equatins 1 and t calculate the prjectile s initial velcity immediately after it was launched.
5 f 5 P8 Lab #5 Summer 004 Take the ballistic pendulum apparatus and place it at the ede f the table. Measure the heiht H f the brass sphere frm the flr when the sphere is n the end f the steel rd. Cck the apparatus and launch the prjectile. Measure the distance x t where the prjectile landed n the flr frm directly under the launch psitin. Try this a few times befre cllectin data. Make sure the apparatus is psitined at the same place n the table fr each launch, and be certain that the sprin is cmpressed the same amunt fr each launch. (This shuld be the same cmpressin used in the calculatin f the prjectile s initial launch velcity abve.) After launchin the brass sphere a few times yu ll have a pretty d idea where it will land. Place a sheet f carbn paper with a sheet f white paper under it where yu ve seen the sphere land. When the sphere lands n the carbn paper it will make a mark, and yu can use this mark t measure the hrizntal rane x. Use Equatin 3 t calculate the initial launch velcity f the brass sphere frm the ballistic pendulum apparatus. Cmpare this launch velcity determined by ballistics with the launch velcity determined usin the ballistic pendulum and cnservatin f mmentum and enery. They shuld be abut the same. Calculate the percentae errr between them. The errr shuld be arund 10%. Lab Reprt: I) Recrd the masses f the brass sphere and the pendulum (m and M). Recrd the heiht t which the bb rse (h) after launchin the prjectile. Frm this data calculate the launch velcity f the brass sphere usin Equatins 1 and. II) Recrd the heiht f the launch psitin frm the flr (H), and the distance frm the table the prjectile landed (x). Frm Equatin 3 calculate the launch velcity f the prjectile. III) Cmpare the tw launch velcities and calculate the errr between them. Theretically they shuld be the same, but practically they will differ smewhat because f the errr always inherent in real equipment.