. Physics 00 Mtin with Cnstant Acceleratin Experiment In this lab, we will study the mtin f a glider as it accelerates dwnhill n a tilted air track. The glider is supprted ver the air track by a cushin f air and can mve alng the track with almst n frictin. There is sme air resistance as the glider mves, but this is relatively small. We will verify the fllwing tw equatins f mtin fr cnstant acceleratin in ne dimensin: x x v t at + + () v v + a t () where x psitin, v velcity, t time, a acceleratin, x initial psitin, and v initial velcity. A wrd f cautin. The air tracks are expensive and easily damaged s please treat them gently. D nt place the gliders n the track unless the air supply is n, since the gliders can scratch the track. Remve the gliders frm the track befre making any adjustments t the gliders. The gliders are very easily damaged if drpped. Begin by leveling the track. With the air n, place a glider n the track, and adjust the track's feet until the glider can remain statinary n the track, nt sliding ne way r the ther. Then incline the track a precise amunt, by placing ne f the wden blcks under the ft f the air track n ne side. As shwn belw, h equals the height f the blck. Ldistance between feet h blck air track table The track is nw inclined by an angle θ, where θ sin - (h/l). h L θ h h sin θ, θ sin L L The acceleratin f gravity is g 9.80 m/s, and the directin f this acceleratin is straight dwn. The cmpnent f this acceleratin alng the directin f the track is 09/0/0
. a gsin( θ ). (3) (Yu may nt have cvered this yet in lecture, but fr nw, just ntice that when θ 0, a 0 and when θ 90, a g, as yu wuld expect.) Measure h, L, and cmpute a gsinθ g h. Nte that yu d nt have t L cmpute θ in degrees. Yu nly need sin(θ) and that equals h/l. Dn't frget units! The speed f the glider n the track will be measured with phtgate timers. A card 0.0cm lng, placed n tp f the glider interrupts a light beam in the phtgate and triggers a timer. The phtgate timer can be used t measure either the time fr the glider t travel between tw gates (when the timer cntrl is set t PULSE mde) r the time fr the card t pass thrugh ne gate (when set t GATE mde). The timer can be set t read either millisecnds (msec) r 0. msec. With 0. msec reslutin, the timer will cunt up t a maximum f sec, befre verflw. phtgates card glider air track Place the tw phtgates ver the air track s that they are a meter r mre apart and at least 0 cm frm each end f the track. Part. Test f x x + vt+ a t In this experiment, we will release the glider frm rest very clse t the first phtgate s that the initial velcity v 0.. Measure the distance (x-x ) between the tw phtgates. This can be dne mst precisely by mving the glider alng the track t see exactly where the phtgate is triggered (a red LED n the phtgate lights up) and nting the psitin f the glider with the ruler n the side f the track.. Set the timer t PULSE mde and msec (nt 0.msec). Press the RESET buttn n the timer t clear the clck and ready the phtgate. Hld the glider statinary as clse as pssible t the first gate, withut triggering the timer, and then gently release it, withut giving it any push. Recrd the time t t pass between the tw gates. Repeat several times t get an average value f t and an estimate f the uncertainty in t. Rughly, δt ( tmax tmin )/. Nw cmpute
.3 a ( x x ) t Cmpare this a with yur earlier agh/l. D the tw values f a agree within significant figures? Can yu think f any surces f errr we have nt taken accunt f? Part. Test f v v + at In this part, unlike in Part, we will nt assume that v 0. We will release the glider frm a pint uphill f the first phtgate, s that the glider has sme velcity v >0 when it passes thrugh the first phtgate. Its final velcity when it passes thrugh the secnd phtgate is v. Thrughut this part, it is imprtant nt t mve the phtgates frm their riginal psitins. Otherwise, yu will nt be able t cmpare data taken at different times and yu will have t repeat sme data-taking. As usual, d a rugh errr analysis by keeping track f significant figures. We will assume that the uncertainty is abut ± in the last place, s dn't include useless extra digits just because they cme ut f yur calculatr. With the timer in GATE mde, it will read the time that the card was in gate. The card has a length x 0.0 cm, s the average velcity f the glider in gate is x. When the READ switch is tggled, the timer displays the ttal time spent in bth gates and ( + ). S, t get and, fllw this prcedure: RESET the timer. Release the glider frm a knwn pint uphill f gate. Stp the glider after it passes gate. Read frm the timer. Tggle the READ switch and read +. Cmpute by taking the difference f the tw readings. Repeat several times, always releasing the glider frm the same initial psitin, t x get gd average values fr and. Nw cmpute vinitial v and x vfinal v. Nw we must measure the time interval that the glider spent between the gates. (This time interval is the t in the equatin v v + a t.) Set the timer t PULSE mde, hit RESET, release the glider frm the same initial pint, and recrd the displayed time. Unfrtunately, this displayed time is nt quite the same as the time that we want. The displayed time interval ' ( read "delta-t-prime") is the interval between the times when the leading edge f the card hit the phtgates. What we really want is the interval between the times when the center-f-mass f the glider passes thrugh the gates. S we need t knw the times when the glider was half-way thrugh the gates.
.4 ' Let's say t time when leading edge f card hit gate and ' t edge f card hit gate. The time interval that we want is time when leading ( t t) ( ) ' ( ) ' tfinal tinitial t + t ' + ' ' + + Make several measurements f ' t get a gd average, and then cmpute ' ( ) +. Finally cmpute the acceleratin frm a ( v v ) x x ' + ( ) Cmpare yur three values f a, a gh/l (frm Part 0), a (frm part ), and a (frm part ).
.5 Physics 00 PreLab Questins Exp. T be handed in at the beginning f yur labratry perid:. If the air track is inclined by an angle θ 7 0, what is the acceleratin "a" alng the track, frm equatin (3)? (Dn't frget units, and sig. figs!). Slve the fllwing equatin fr a. x x + v t+ at, a? 3. Explain what the phtgate timer measures when it is in PULSE mde. Explain the GATE mde 4. Explain the functin f the READ switch n the phtgate timers. 5. In part f the lab, a time interval ' (t-prime) and a time interval (n prime) are described. Describe in wrds the difference between these tw times. 6. Dry Lab (next page.)
.6 "Dry" Lab Reprt. Fr this lab, and all ther labs in this curse, we ask yu t think carefully abut what variables yu will measure, what variables yu will cmpute, and hw yu will display this infrmatin in yur reprt. Write ut a "dry" lab reprt, that is, a reprt with n actual data, but which cntains all the variables yu will measure directly and all the variables that yu will cmpute. The reprt shuld shw the apprximate frmat f the actual lab reprt, including tables and calculatins. In this dry lab, give the symbls fr all measured variables and a shrt descriptin, in wrds, f the variables. Fr cmputed variables, give the equatin fr the variable and a shrt descriptin f the variable, unless it was defined previusly. Fr tables, give the clumn headings and shw the general layut f the table. There is mre than ne way t write a dry lab reprt. In general, it shuld shw the variables, tables, and calculatins in the same rder that they will be dne during the actual lab. Strive fr a clear, clean, layut that the reader can fllw easily. If a graph is called fr in the lab, the dry lab shuld shw a graph title, axes that are prperly labeled, and a rugh sketch f the expected shape f the graph. We suggest that yu make an extra cpy f yur dry lab, s that yu can hand ne cpy in at the beginning f the lab, and use the ther as a template fr preparing yur actual reprt during the lab. Here is an example f a dry lab reprt. Suppse that the lab instructins describe an experiment in which the student measures the acceleratin f gravity g by timing the fall f a marble ver a measured distance L. g is then cmputed frm the equatin L gt. Tw different lengths L are chsen and several measurements f t are made fr each value f L. The average value f g is then cmpared with the knwn value, g 9.80m/s. The dry lab fr this part f the experiment might appear as fllws:
.7 Part : Determinatin f the acceleratin f gravity g. t time f fall f marble L distance f fall f marble Determinatin L... trial t(sec).... 3.. 4.. t avg... g L... t avg Determinatin. L... trial t(sec).... 3.. 4.. t avg... g L... t avg Cmparisn with g knwn. g g + g avg... g knwn 9.80 m/s % discrepancy g g knwn g knwn avg...