PASCO scientific 012-02149B 모델 SF-9214에대한 9/91 사용설명서및실험가이드 정밀도 2.0 m 의에어트랙 Copyright January 1988 $5.00 1
장비 서론 PASCO 모델 SF-9214 에어트랙은 2.0m 길이로, 전체길이에대해 0.04mm 이내의범위까지진직도 (straightness) 가보증된다. 트랙은벽두께가 3mm인커다란사각알루미늄압출성형제품으로구성되어있으며, 벽은받침용 U자채널에의해한층더보강되어있다. 한쪽끝에는있는단일받침대와다른쪽끝에는있는이중받침대는에어트랙이 옆으로길게수평을이룰수있도록해준다. 개봉과설치 SF-9214 에어트랙은트랙이들어있는커다란튜브하나와부속품이들어있는 판지상자하나에담겨배송된다. 에어트랙이들어있는튜브의한쪽끝을천천히제거한다. 부착되어있는정렬용 빔과함께튜브에서트랙을조심스럽게당긴다. 주의 : 트랙의상부표면이긁히거나칼자국이나지않도록주의한다. ( 상부 표면에는공기구멍이있다.) 상부표면의융기는글라이더의운동을방해할수 있다. 구성품목 : 2 m 길이의에어트랙 부속품 : 봉투 : 깃발 (100 mm) 2 장 상부층 : 부속품트레이 1 개 2
에어트랙 봉투 상부충 중간층 하부층 부속품상자 3
중간층 : 글라이더 2개 설치용금속기구류 ( 단일지주 (leg) 나사 2개, 이중지주나사 2개, 4mm용렌치 (1), 5mm용렌치 (1)) 하부층 : 단일지주 1개 이중지주폭 (w)/ 조절용발 1개 정지장치 2개 필요한추가장비 : 공기공급장치 (Model SF-9416) 부속품트레이 바나나플러그가 부착되어있는도르래 1 개 50g 의글라이더용 추가질량체 (4PL) 바나나플러그가부착되어있는 고무밴드완충장치 (3PL) 정지장치설치용 나사 (4PL) 질량체걸이와질량체세트1개바나나플러그가부착되어있는후크연결장치 바나나플러그가부착되어있고왁스가채워져있는실린더 1개 바나나플러그와니들이부착되어있는 (needle on) 실린더 바나나플러그와완충장치날이부착되어있는실린더 (2PL) 4
장비설치 에어트랙조립하기 1. 제공된나사와앨렌렌치를이용하여그림 2 에서와같이에어트랙의 U 자형 채널에단일수평받침대 (foot) 와이중수평받침대를부착한다. 4mm 용앨렌렌치 조절용받침대 단일받침대 5mm 용앨렌렌치 브래킷 그림 2 수평받침대부착하기 2. 부속품트레이에포함되어있는설치용나사를이용하여에어트랙의양끝에 정지장치를설치한다. 정지장치 그림 3 정지장치설치하기 에어트랙의수평맞추기 5
에어트랙을평평하고안정된테이블위에올려놓고에어트랙이최대한수평이될 때까지 2 개의조절용받침대를돌린다. 공기방울수평계를이용하여트랙의수평을 대략적으로맞출수도있다. 그러나최종적으로수평을맞출때에는다음의방법으로맞추어야한다 : 1 에어트랙을에어공급장치에연결하고에어공급장치의전원을켠다. 2 초속 ( 初速 ) 이없는트랙가운데에글라이더를놓는다. 3 글라이더가어느방향으로도가속하지않고최초의위치에계속있을때까지수평나사를조절한다. 주의 : 글라이더가제자리에서약간진동할수도있다. 이러한움직임은트랙의 공기구멍으로들어오는기류에의해발생하는것이므로정상적인것으로간주한다. 에어공급장치조절하기 PASCO 모델 SF-9216 에어공급장치는트랙의한쪽끝에있는에어용부속품에의해에어트랙에연결되어있다. 글라이더가트랙위에거의떠있도록송풍기의출력을조절하여야한다. 과도한기압은가속력이없을때까지도트랙에서글라이더를벗어나게할수있다. 에어공급장치는에어트랙을약간가열시켜에어트랙을팽창시킨다. 에어 공급장치를 5 분간작동시킨후따뜻해졌을때, 트랙의진직도가 +/- 0.04 mm 가 되도록, 트랙아래에는조절용빔이설치되어있다. 6
부속품 글라이더 양극처리된흑색알루미늄글라이더의질량은 180 g ± 1 g 이고길이는 129 mm ±1 mm 이다. 글라이더의질량을증가시키려면, 글라이더의양측면에튀어나와있는 강철핀에질량체를올려놓기만하면된다. 추가질량체 각 50 g 주의 : 질량체는항상대칭으로부착시켜야한다 ( 각측면에동일한수의질량체를 부착시켜야한다 ). 그렇게하지않으면글라이더가제대로작동하지않는다. 고무밴드완충장치와같은글라이더부속품은글라이더의각끝부분에있는구멍 중하나에설치한다. 주의 : 대부분의경우, 부속품은포토게이트의작동을방해하지않도록아래쪽 구멍에설치하여야한다. 이들부속품은글라이더의질량을증가시키므로, 모든계산시반드시고려해야 한다. 7
중요 : 글라이더의한쪽끝에부속품 ( 완충판과같은부속품 ) 을올려놓았으면, 반대쪽에도동일한질량의부속품 ( 완충장치나완충판과같은부속품 ) 을올려놓아야한다. 이렇게하면글라이더는에어트랙위에서계속수평을유지하며, 글라이더자체가어느한방향으로쏠리지않게된다. 깃발 포토게이트를이용하여글라이더의속도를측정할때에는각글라이더의상부 표면에 100 mm 의깃발을꽂아포토게이트의빔을차단한다. 글라이더자체를 깃발 로이용할수도있다. 서로다른길이의깃발이필요한 경우에는간단하게얇은판지나알루미늄을적당한길이로잘라서글라이더의상부 표면에테이프로붙이면된다. 주의 : 다음의부속품들은 4 mm 표준플러그를이용해에어트랙정지장치나글라이더에설치한다. 도르래를제외한각부속품의중량은약 10 g이다. 글라이더는항상각끝부위에는한개의부속품만을설치하여대칭이되게올려놓아야한다. 고무밴드완충장치 고무밴드완충장치는글라이더가다른글라이더나끝부분에충돌할때충돌을 완화시키고글라이더의진동을없애준다. 8
고무밴드완충장치를정지장치에설치하면글라이더발사장치로도이용할수있다 : 완충장치의끝부분에있는너트에닿을때까지글라이더를뒤로당긴다. 글라이더를놓는다. 고무밴드를완충장치에있는다른홈으로옮겨글라이더에가해지는추진력을변경한다. 완충판 9
이판은글라이더의끝부분에설치하며고무밴드완충장치와충돌하도록 설계되어있다. 왁스튜브와니들 왁스튜브는비탄성충돌이있는경우를대비해글라이더의끝부분에설치한다. 수 차례의충돌후에니들과적절한점착력을유지할수있도록튜브안에왁스를 집어넣는다 (be pressed). 니들은두번째글라이더의끝부분에설치한다. 니들은 2 개의글라이더가충돌할 때다른글라이더의왁스튜브에꽂혀 2 개의글라이더를단단하게결합시킬수 있게배치하여야한다. 주의 : 니들에는작은보호용코르크가끼워져있다. 니들을부속품트레이에 보관할때에는코르크를니들에다시끼워놓은다. 후크 후크는글라이더의끝부분이나윗부분에설치할수있다. 후크는글라이더에 스트링을연결할때사용한다. 10
도르래 도르래는에어의주입과는반대로, 정지장치하단의구멍에설치한다. 글라이더에 연결되어도르래를지나다른쪽끝부분에매달려있는질량체에연결된스트링을 이용하면글라이더를가속시킬수있다. 주의 : 글라이더를보호하려면, 정지장치에부딪히게해서는안된다. 11
고무밴드완충장치 이곳혹은이곳 에어트랙용질량체 / 걸이세트 2 g 의질량체걸이 2 g 의질량체 ( 플라스틱 ) 10 g 의질량체 ( 금속 ) 5 g 의질량체 ( 금속 ) 1 g 의질량체 ( 플라스틱 ) 12
유지보수 에어트랙 별다른유지보수작업없이에어트랙의표면을청결히하고긁히거나흠이나지않도록하면된다. 장치를보관할때에는반드시에어트랙의표면을훼손시킬수있는것이없는지확인한다. 트랙에흠이나서표면의융기가글라이더의자유로운움직임을방해하게되면, 줄이나사포로융기된표면을조심스럽게갈아낸다. PASCO 에어트랙은공장에서일직선으로조정되어출하되기때문에, 선형도 (linearity) 의편차는 ±0.04 mm이하이다. 장치의구조는트랙이다년간이사양범위내에서유지가되도록설계되었다. 그러나트랙에과도한힘을가하면, 일직선으로정렬된상태에서벗어날수있다. 이렇게되면글라이더가트랙을따라이동할때속도를고르지않게한다. 글라이더는트랙에생긴굴곡을가로지를때속도가빨라졌다느려진다. 이의가제기될만한제품을이용하여글라이더의운동이고르지않다면, 반드시에어트랙을재조정하여야한다. 에어트랙을재조정하는절차에는특수한시험도구가필요하다. 따라서자사는에어트랙을조정할수있도록 PASCO로장치를반송할것을권장한다. 에어트랙을반송하는데정보가필요한경우 PASCO scientific으로연락하도록한다. 글라이더 글라이더는에어트랙위에서마찰없이운동이유지될수있도록조심스럽게다루어야한다. 트랙에서글라이더가떠있는표면에긁힌자국이나흠이생기면, 줄이나사포로제거해야한다. 글라이더를떨어뜨리거나글라이더가구부러져있는경우에는글라이더의측면과에어트랙의측면이일치하도록글라이더를바로잡아야한다. 글라이더의양측사이의각이너무작으면글라이더가트랙에붙게된다. 또각이너무크면글라이더는트랙위를이동할때흔들리게된다. 고무밴드완충장치 고무밴드는시간이경과함에따라질이나빠질수있다. 고무밴드는바람직한 발사력과 탄력성 을발생시킬수있는신축밴드로교체할수있다. 13
주의 : 고무밴드의수명을연장시키려면, 사용하지않는때에는고무밴드 완충장치에서고무밴드를빼놓는다. 또한고무밴드를과도하게다루면고무코팅에 사용되는보호용분말이제거될수있다. 실험 에어트랙에서실시되는실험의특성은이용되는시간측정장치의작용이다. 그러므로, 실험은 PASCO 로부터구입이가능한다양한시간측정장치를포함한다. 다음의 PASCO 제품에제공되는사용설명서를참조하도록한다 : ME-9218 에어트랙과자급식포토게이트장치 ME-9394 에어트랙과컴퓨터포토게이트장치 (Apple II) ME-9363A 에어트랙과컴퓨터포토게이트장치 (IBM PC와호환가능 ) ME-9336 에어트랙과컴퓨터음파레인저장치 (Apple II) ME-9391 에어트랙과컴퓨터음파레인저장치 (IBM PC와호환가능 ) ME-9226 에어트랙과스파크타이머장치 ME-9206A 포토게이트타이머 ME-9215A 기억장치가내장된포토게이트타이머 PI-8025 카운터 / 타이머 / 주파수측정기 SF-9297 결합조화진동자 14
Includes Teacher s Notes and Typical Experiment Results Instruction Manual and Experiment Guide for the PASCO scientific Model ME-9215B 012-06379B PHOTOGATE TIMER
012-06379B Photogate Timer Table of Contents Page Copyright, Warranty and Technical Support... ii Introduction... 1 Operation... 2 Accessories for the Photogate Timer... 4 10 Copy-Ready Experiments:... 4 Experiment 1: Instantaneous vs Average Velocity... 5 Experiment 2: Kinematics on an Inclined Plane... 7 Experiment 3: Speed of a Projectile... 9 Experiment 4: Newton's Second Law... 11 Experiment 5: The Force of Gravity... 13 Experiment 6: Conservation of Momentum... 15 Experiment 7: Kinetic Energy... 17 Experiment 8: Conservation of Mechanical Energy... 19 Experiment 9: Elastic-Kinetic Energy... 21 Experiment 10: Pendulum Motion... 23 Teachers Guide... 27 Maintenance... 39 i
Photogate Timer 012-06379B Copyright, Warranty and Technical Support Copyright Notice The PASCO scientific 012-06379B Instruction Manual is copyrighted with all rights reserved. Permission is granted to non-profit educational institutions for reproduction of any part of this manual, providing the reproductions are used only in their laboratories and classrooms, and are not sold for profit. Reproduction under any other circumstances, without the written consent of PASCO scientific, is prohibited. Limited Warranty For a description of the product warranty, see the PASCO catalog. Technical Support For assistance with any PASCO product, contact PASCO at: Address: PASCO scientific 10101 Foothills Blvd. Roseville, CA 95678-9011 Phone: 916-786-3800 (worldwide) 800-772-8700 (U.S) FAX: (916) 786-3292 Web www.pasco.com email: support@pasco.com ii
012-06379B Photogate Timer Introduction The PASCO ME-9215B Photogate Timer is an accurate and versatile digital timer for the student laboratory. The ME-9215B memory function makes it easy to time events that happen in rapid succession, such as an air track glider passing twice through the photogate, once before and then again after a collision. The Photogate Timer uses PASCO s narrow-beam infrared photogate (see Figure 1) to provide the timing signals. An LED in one arm of the photogate emits a narrow infrared beam. As long as the beam strikes the detector in the opposite arm of the photogate, the signal to the timer indicates that the beam is unblocked. When an object blocks the beam so it doesn t strike the detector, the signal to the timer changes. The timer has several options for timing the photogate signals. The options include Gate, Pulse, and Pendulum modes, allowing you to measure the velocity of an object as it passes through the photogate or between two photogates, or to measure the period of a pendulum. There is also a START/STOP button that lets you use the timer as an electronic stopwatch. An important addition to your Photogate Timer is the ME-9204B Accessory Photogate, which must be ordered separately. It plugs directly into the Photogate Timer and triggers the timer in the same manner as the built-in photogate. In Pulse Mode, the Accessory Photogate lets you measure the time it takes for an object to travel between two photogates. In Gate mode, it lets you measure the velocity of the object as it passes through the first photogate, and then again when it passes through the second photogate. LED: Lights when beam is blocked Detector Plug in RJ12 connector from Photogate timer Infrared beam LED: Source of infrared beam Figure 1: The PASCO Photogate Head NOTES: The Photogate Timer can be powered using the included 7.5 V adapter. It will also run on 4 C-size, 1.5 Volt batteries. Battery installation instructions are in the Appendix. Ten ready-to-use experiments are included in this manual, showing a variety of ways in which you can use your Photogate Timer. The equipment requirements vary for different experiments. For many of the experiments, you will need an air track (dynamics carts will also work). Many also require a ME-9204B Accessory Photogate in addition to the Photogate Timer. Check the equipment requirements listed at the beginning of each experiment. 1
Photogate Timer 012-06379B Operation Photogate Head Photogate beam Plug in RJ12 connector from timer Clamp screw: loosen to adjust photogate angle or height 7.5 volt power port Photogate port Rear panel Accessory photogate port 7.5 volt power adapter to 120 VAC, 60 Hz or 220/240 VAC, 50 Hz Figure 2: Setting Up the Photogate Timer To Operate the Photogate Timer: Plug the RJ12 phone connector from the timer into the RJ12 phone jack on the Photogate Head. Plug the 7.5 volt power adapter into the small receptacle on the rear of the timer and into a standard 110 VAC, 60 Hz (or 220/240 VAC, 50 Hz) wall outlet. Position the Photogate Head so the object to be timed will pass through the arms of the photogate, blocking the photogate beam. Loosen the clamp screw if you want to change the angle or height of the photogate, then tighten it securely. If you are using a ME-9204B Accessory Photogate, plug the stereo phone plug of the Accessory Photogate into the large receptacle (see Figure 2) on the rear of the timer. Slide the mode switch to the desired timing mode: Gate, Pulse, or Pendulum. Each of these modes is described below. Switch the MEMORY switch to OFF. Press the RESET button to reset the timer to zero. As a test, block the photogate beam with your hand to be sure that the timer starts counting when the beam is interrupted and stops at the appropriate time. Press the RESET button again. You are ready to begin timing. Timing Modes Gate Mode: In Gate mode, timing begins when the beam is first blocked and continues until the beam is unblocked. Use this mode to measure the velocity of an object as it passes through the photogate. If an object of length L blocks the photogate for a time t, the average velocity of the object as it passed through the photogate was L/t. Pulse Mode: In Pulse mode, the timer measures the time between successive interruptions of the photogate. Timing begins when the beam is first blocked and continues until the beam is unblocked and then blocked again. With an Accessory Photogate plugged into the Photogate Timer, the timer will measure the time it takes for an object to move between the two photogates. Pendulum Mode: In Pendulum mode, the timer measures the period of one complete oscillation. Timing begins as the pendulum first cuts through the beam. The timer ignores the next interruption, which corresponds to the pendulum swinging back in the opposite direction. Timing stops at the beginning of the third interruption, as the pendulum completes one full oscillation. Manual Stopwatch: Use the START/STOP button in either Gate or Pulse mode. In Gate mode the timer starts when the START/STOP button is pressed. The timer stops when the button is released. In Pulse mode, the timer acts as a normal stopwatch. It starts timing when the START/STOP button is first pressed and continues until the button is pressed a second time. TIMING DIAGRAMS The following diagrams show the interval, t, that is measured in each timing mode. In each diagram, a low signal corresponds to the photogate being blocked (or the START/STOP button pressed). A high signal corresponds to the photogate being unblocked (and the START/STOP button unpressed). MODE GATE PULSE PENDULUM DIAGRAM t t t t t t t t t t t 2
012-06379B Photogate Timer TIMING SUGGESTION Since the source and detector of the photogate have a finite width, the true length of the object may not be the same as the effective length seen by the photogate. This parallax error may be minimized by having the object pass as close to the detector side of the photogate as possible, with the line of travel perpendicular to the beam. To completely eliminate the parallax error in experimental data, determine the effective length of the object as follows: With the Timer in Gate mode, push the object through the photogate, along the path it will follow in the experiment. When the photogate is triggered (the LED on top of the photogate comes ON), measure the position of the object relative to an external reference point. Continue pushing the object through the photogate. When the LED goes OFF, measure the position of the object relative to the same external reference point. The difference between the first and second measurement is the effective length of the object. When measuring the speed of the object, divide this effective length by the time during which the object blocked the photogate. Memory Feature When two measurements must be made in rapid succession, such as measuring the pre- and post-collision velocities of an air track glider, use the memory function. It can be used in either the Gate or the Pulse mode. NOTE: If additional photogate interruptions occur after the second time is measured, and before the MEMORY switch is flipped to READ, they too will be measured by the timer and included in the cumulative time. Figure 3: Timing an Air Track Glider SPECIFICATIONS Detector rise time: 200 ns max. Fall Time: 200 ns max. Parallax error: For an object passing through the photogate, within 1 cm of the detector, with a velocity of less than 10 m/s, the difference between the true and effective length of the object will be less than 1 millimeter. Infrared source: Peak output at 880 nm; 10,000 hour life. To use the memory: Turn the MEMORY switch to ON. Press RESET. Run the experiment. When the first time (t 1 ) is measured, it will be immediately displayed. The second time (t 2 ) will be automatically measured by the timer, but it will not be shown on the display. Record t 1, then push the MEMORY switch to READ. The display will now show the TOTAL time, t 1 + t 2. Subtract t 1 from the displayed time to determine t 2. Figure 4: Photogate Timing a Pendulum 3
Photogate Timer 012-06379B Accessories for the Photogate Timer The following accessories are available to help extend the utility of your model ME-9215B Photogate Timer. All the accessories work equally well with either model. See the current PASCO catalog for more information. ME-9204B Accessory Photogate The stereo phone plug of the ME-9204B Accessory Photogate plugs into the phone jack on the rear of the Photogate Timer, giving you two identical photogates operating from a single timer. With the timer in Gate mode, you can measure the velocity of an object as it passes through one photogate, then again as it passes through the second photogate. With the timer in Pulse mode, you can measure the time it takes for an object to pass between the two photogates. (Many of the experiments in this manual are most easily performed using a Photogate Timer with an Accessory Photogate.) ME-9207B Free Fall Adapter For easy and accurate measurements of the acceleration of gravity, the ME-9207B Free Fall Adapter is hard to beat. The Free Fall Adapter plugs directly into the phone plug on the rear of the Photogate Timer. It comes with everything you need, including two steel balls (of different size and mass), a release mechanism, and a receptor pad. The release mechanism and the receptor pad automatically trigger the timer, so you get remarkably accurate measurements of the free fall time of the steel ball. ME-9259A Laser Switch This highly collimated photodetector is identical to a photogate, except that you use a laser (not included) as the light source. You can now time the motion of objects that are far too big to fit through a standard photogate. Measure the period of a bowling ball pendulum or the velocity of a car. The Laser Switch operates in all three timing modes (Gate, Pulse, and Pendulum). 10 Copy-Ready Experiments The following 10 experiments are written in worksheet form. Feel free to photocopy them for use in your lab. NOTE: In each experiment, the first paragraph is a list of equipment needed. Be sure to read this paragraph first, as the equipment needs vary from experiment to experiment. This manual emphasizes the use of an air track, but the air track experiments can also be performed with dynamics carts. Many also require a ME-9204B Accessory Photogate in addition to a Photogate Timer. Collision experiments, such as experiments 6 and 7, require four times to be measured in rapid succession and are therefore most easily performed using two Photogate Timers. 4
012-06379B Photogate Timer Experiment 1: Instantaneous Versus Average Velocity EQUIPMENT NEEDED: - Photogate Timer with Accessory Photogate - Air Track System with one glider. Introduction An average velocity can be a useful value. If you know you will average 50 miles per hour on a 200 mile trip, it s easy to determine how long the trip will take. On the other hand, the highway patrolman following you doesn t care about your average speed over 200 miles. He wants to know how fast you re driving at the instant his radar strikes your car, so he can determine whether or not to give you a ticket. He wants to know your instantaneous velocity. In this experiment you ll investigate the relationship between instantaneous and average velocities, and see how a series of average velocities can be used to deduce an instantaneous velocity. Procedure D x 0 D/2 D/2 Set up the air track as shown in Figure 1.1, elevating one end of x the track with a 1-2 cm support. 1 Choose a point x 1 near the center of the track. Measure the position of x 1 on the air track metric scale, 1-2 cm support and record this value in Table 1.1. If you are using an air track without a scale, use a meter stick to Figure 1.1: Setting Up the Equipment measure the distance of x 1 from the edge of the upper end of the track. Choose a starting point x 0 for the glider, near the upper end of the track. With a pencil, carefully mark this spot on the air track so you can always start the glider from the same point. Place the Photogate Timer and Accessory Photogate at points equidistant from x 1, as shown in the figure. Record the distance between the photogates as D in Table 1.1. Set the slide switch on the Photogate Timer to PULSE. Press the RESET button. Hold the glider steady at x 0, then release it. Record time t 1, the time displayed after the glider has passed through both photogates. Repeat steps 6 and 7 at least four more times, recording the times as t 2 through t 5. Now repeat steps 4 through 9, decreasing D by approximately 10 centimeters. Continue decreasing D in 10 centimeter increments. At each value of D, repeat steps 4 through 8. Cardboard D Figure 1.2: Measuring Velocity in Gate Mode 5
Photogate Timer 012-06379B Optional You can continue using smaller and smaller distances for D by changing your timing technique. Tape a piece of cardboard on top of the glider, as shown in Figure 1.2. Raise the photogate so it is the cardboard, not the body of the glider, that interrupts the photogate. Use just one photogate and place it at x 1. Set the timer to GATE. Now D is the length of the cardboard. Measure D by passing the glider through the photogate and noting the difference in glider position between where the LED first comes on, and where it goes off again. Then start the glider from x 0 as before, and make several measurements of the time it takes for the glider to pass through the photogate. As before, record your times as t 1 through t 5. Continue decreasing the value of D, by using successively smaller pieces of cardboard. Data and Calculations For each value of D, calculate the average of t 1 through t 5. Record this value as t avg. Calculate v avg = D/t avg. This is the average velocity of the glider in going between the two photogates. Plot a graph of v avg versus D with D on the x-axis. x 1 = Table 1.1 Data and Calculations D t 1 t 2 t 3 t 4 t 5 t avg v avg Questions Which of the average velocities that you measured do you think gives the closest approximation to the instantaneous velocity of the glider as it passed through point x 1? Can you extrapolate your collected data to determine an even closer approximation to the instantaneous velocity of the glider through point x 1? From your collected data, estimate the maximum error you expect in your estimated value. In trying to determine an instantaneous velocity, what factors (timer accuracy, object being timed, type of motion) influence the accuracy of the measurement? Discuss how each factor influences the result. Can you think of one or more ways to measure instantaneous velocity directly, or is an instantaneous velocity always a value that must be inferred from average velocity measurements? 6
012-06379B Photogate Timer Experiment 4: Newton s Second Law EQUIPMENT NEEDED: -Photogate timer with Accessory Photogate (or two Photogate Timers) -Air TrackSystem with one glider -Masses -Pulley -Pulley Mounting Clamp -Universal Table Clamp Introduction There s nothing obvious about the relationships governing the motions of objects. In fact, it took around 4,000 years of civilization and the genius of Isaac Newton to figure out the basic laws. Fortunately for the rest of us, hindsight is a powerful research tool. In this experiment you will experimentally determine Newton s second law by examining the motion of an air track glider under the influence of a constant force. The constant force will be supplied by the weight of a hanging mass that will be used to pull the glider. By varying the mass of the hanging weight and of the glider, and measuring the acceleration of the glider, you ll be able to determine Newton s second law. Procedure Counter Photogate Set up the air track as shown in Figure Balance x 0 Timer Hook 4.1. Level the air track very carefully by Glider String adjusting the air track leveling feet. A glider should sit on the track without accelerating in either direction. There may be some small movement of the glider due to unequal air flow beneath the glider, but it should not accelerate Figure 4.1: Equipment Setup steadily in either direction. Measure the effective length of the glider, and record your value as L in Table 4.1. Mount the hook into the bottom hole of the cart. To counterbalance its weight, add a piece of similar weight on the opposite end as shown on Fig. 4.1. Add 50-60 grams of mass to the glider using 10 or 20 gram masses. Be sure the masses are distributed symmetrically so the glider is balanced. Determine the total mass of your glider with the added masses and record the total as m in Table 4.1. Place a mass of approximately 5-10 grams on the weight hanger. Record the total mass (hanger plus added mass) as m a. Set your Photogate Timer to GATE mode. Choose a starting point x 0 for the glider, near the end of the track. Mark this point with a pencil so that you can always start the glider from this same point. Press the RESET button. Hold the glider steady at x 0, then release it. Note t 1, the time it took for the glider to pass through the first photogate, and t 2, the time it took for the glider to pass through the second photogate. Repeat this measurement four times. Take the average of your measured t 1 's and t 2 's and record these averages as t 1 and t 2 in Table 4.1. panel Set the Photogate Timer to PULSE mode. 11 Press the RESET button. Accessory Photogate Tableclamp Pulley Mounting Rod m a 11
Photogate Timer 012-06379B 12 Again, start the glider from x 0. This time measure and record t 3, the time it takes the glider to pass between the photogates. Repeat this measurement four more times and record the average of these measurements as t 3 in Table 4.1. 13 Vary m a, by moving masses from the glider to the hanger (thus keeping the total mass, m + m a, constant.) Record m and m a and repeat steps 5 through 11. Try at least four different values for m a. 14 Now leave m a constant at a previously used value. Vary m by adding or removing mass from the glider. Repeat steps 5-11. Try at least four different values for m. Calculations For each set of experimental conditions: Use the length of the glider and your average times to determine v 1 and v 2, the average glider velocity as it passed through each photogate. Use the equation a = (v 2 - v 1 )/t 3 to determine the average acceleration of the glider as it passed between the two photogates. Determine F a, the force applied to the glider by the hanging mass. (F a = m a g; g = 9.8 m/s 2 = 980 cm/s 2 ) Analysis Draw a graph showing average acceleration as a function of applied force, F a,. Draw a second graph showing average acceleration as a function of the glider mass with M a being held constant. Examine your graphs carefully. Are they straight lines? Use your graphs to determine the relationship between applied force, mass, and average acceleration for the air track glider. Discuss your results. In this experiment, you measured only the average acceleration of the glider between the two photogates. Do you have reason to believe that your results also hold true for the instantaneous acceleration? Explain. What further experiments might help extend your results to include instantaneous acceleration? Glider Length, L = Table 4.1 Data and Calculations m m a t 1 t 2 t 3 v 1 v 2 a F a 12
012-06379B Photogate Timer Experiment 5: The Force of Gravity EQUIPMENT NEEDED: -Photogate timer with Accessory Photogate Introduction -Air Track System with one glider. In this experiment, you will use Newton s Second Law (F = ma) to measure the force exerted on an object by the Earth s gravitational field. Ideally, you would simply measure the acceleration of a freely falling object, measure its mass, and compute the force. However, the acceleration of a freely falling object is difficult to measure accurately. Accuracy can be greatly increased by measuring the much smaller acceleration of an object as it slides down an inclined plane. Figure 5.1 shows a diagram of the experiment. The gravitational force F g can be resolved into two components, one acting perpendicular and one acting parallel to the motion of the glider. Only the component acting along the direction of motion can accelerate the glider. The other component is balanced by the force from the air cushion of the track acting in the opposite direction. From the diagram, F = F g sin θ, where F g is the total gravitational force and F is the component that accelerates the glider. By measuring the acceleration of the glider, F can be determined and F g can be calculated. Force of air cushion pushing glider away from air track Glider Figure 5.1: Forces Acting on the Glider Procedure Set up the air track as shown in Figure 5.2. Remove the block and level the air track very D carefully. L Measure d, the distance between the air track support legs. Record this distance in the space on the following page. h{= Place a block of thickness h under the support d leg of the track. Measure and record h on the Figure 5.2: Equipment Setup following page. (For best results, measure h with calipers.) Measure and record D, the distance the glider moves on the air track from where it triggers the first photogate, to where it triggers the second photogate. (Move the glider and watch the LED on top of the photogate. When the LED lights up, the photogate has been triggered.) Measure and record L, the effective length of the glider. (Move the glider slowly through a photogate and measure the distance it travels from where the LED first lights up to where it just goes off.) Measure and record m, the mass of the glider. Set the Photogate Timer to GATE mode and press the RESET button. Hold the glider steady near the top of the air track, then release it so it glides freely through the photogates. Record t 1, the time during which the glider blocks the first photogate, and t 2, the time during which it blocks the second photogate. Use the memory function to determine each time. Repeat the measurement several times and record your data in Table 5.1. You needn t release the glider from the same point on the air track for each trial, but it must be gliding freely and smoothly (minimum wobble) as it passes through the photogates. ϑ F g Component of F g perpendicular to air track 13
Photogate Timer 012-06379B Change the mass of the glider by adding weights and repeat steps 6 through 8. Do this for at least five different masses, recording the mass (m) for each set of measurements. (If you have time, you may also want to try changing the height of the block used to tilt the track.) Data and Calculations d = D = θ = h = L = Table 5.1 Data and Calculations m t 1 t 2 v 1 v 2 a a avg F g Calculate θ, the angle of incline for the air track, using the equation θ = tan -1 (h/d). For each set of time measurements, divide L by t 1 and t 2 to determine v 1 and v 2, the velocities of the glider as it passed through the two photogates. For each set of time measurements, calculate a, the acceleration of the glider, using the equation v 2 2 - v 1 2 = 2a(x 2 -x 1 ) = 2aD. For each value of mass that you used, take the average of your calculated accelerations to determine a avg. For each of your average accelerations, calculate the force acting on the glider along its line of motion (F = ma avg ). For each measured value of F, use the equation F = F g sin θ to determine F g. Construct a graph of F g versus m, with m as the independent variable (x-axis). Analysis Does your graph show a linear relationship between F g and m? Does the graph go through the origin? Is the gravitational force acting on the mass proportional to the mass? If so, the gravitational force can be expressed by the equation F g = mg, where g is a constant. If this is the case, measure the slope of your graph to determine the value of g. g = Questions In this experiment, it was assumed that the acceleration of the glider was constant. Was this a reasonable assumption to make? How would you test this? The equation v 2 2 - v 2 1 = 2a(x 2 -x 1 ) was used to calculate the acceleration. Under what conditions is this equation valid? Are those conditions met in this experiment? (You should be able to find a derivation for this equation in your textbook.) Could you use the relationsip F g = mg to determine the force acting between the Earth and the Moon? Explain. 14
012-06379B Photogate Timer Experiment 6: Conservation of Momentum EQUIPMENT NEEDED: -Air track system with two gliders Introduction -Two Photogate Timers. When objects collide, whether locomotives, shopping carts, or your foot and the sidewalk, the results can be complicated. Yet even in the most chaotic of collisions, as long as there are no external forces acting on the colliding objects, one principle always holds and provides an excellent tool for understanding the dynamics of the collision. That principle is called the conservation of momentum. For a two-object collision, momentum conservation is easily stated mathematically by the equation: p i = m 1 v 1i + m 2 v 2i = m 1 v 1f + m 2 v 2f = p f ; where m 1 and m 2 are the masses of the two objects, v 1i and v 2i are the initial velocities of the objects (before the collision), v 1f and v 2f are the final velocities of the objects, and p i and p f are the combined momentums of the objects, before and after the collision. In this experiment, you will verify the conservation of momentum in a collision of two airtrack gliders. Procedure Photogate 1 Photogate 2 Set up the air track and Glider 1 photogates as shown in Glider 2 Figure 6.1, using bumpers on the gliders to provide an elastic collision. Carefully level the track. Measure m 1 and m 2, the m 1 m 2 Figure 6.1: Equipment Setup masses of the two gliders to be used in the collision. Record your results in Table 6.1. Measure and record L 1 and L 2, the length of the gliders. (e.g., push glider 1 through photogate 1 and measure the distance it travels from where the LED comes on to where it goes off again.) Set both Photogate Timers to GATE mode, and press the RESET buttons. Place glider 2 at rest between the photogates. Give glider 1 a push toward it. Record four time measurements in Table 6.1 as follows: t 1i = the time that glider 1 blocks photogate 1 before the collision. t 2i = the time that glider 2 blocks photogate 2 before the collision. (In this case, there is no t 2i since glider 2 begins at rest.) t 1f = the time that glider 1 blocks photogate 1 after the collision. t 2f = the time that glider 2 blocks photogate 2 after the collision. IMPORTANT: The collision must occur after glider 1 has passed completely through photogate 1 and, after the collision, the gliders must be fully separated before either glider interrupts a photogate. NOTE: Use the memory function to store the initial times while the final times are being measured. Immediately after the final times are recorded, the gliders must be stopped to prevent them from triggering the photogate again due to rebounds. 15
Photogate Timer 012-06379B Repeat the experiment several times, varying the mass of one or both gliders and varying the initial velocity of glider 1. Try collisions in which the initial velocity of glider 2 is not zero. You may need to practice a bit to coordinate the gliders so the collision takes place completely between the photogates. Data and Calculations For each time that you measured, calculate the corresponding glider velocity. (e.g., v 1i = ±L 1 /t 1i, where the velocity is positive when the glider moves to the right and negative when it moves to the left. Use your measured values to calculate p i and p f, the combined momentum of the gliders before and after the collision. Record your results in the table. Questions Table 6.1 Data and Calculations L 1 = L 2 = m 1 m 2 t 1i t 2i t 1f t 2f v 1i v 2i v 1f v 2f p i p f (m 1 v 1i + m 2 v 2i ) (m 1 v 1f + m 2 v 2f ) Was momentum conserved in each of your collisions? If not, try to explain any discrepancies. If a glider collides with the end of the air track and rebounds, it will have nearly the same momentum it had before it collided, but in the opposite direction. Is momentum conserved in such a collision? Explain. Suppose the air track was tilted during the experiment. Would momentum be conserved in the collision? Why or why not? Optional Equipment Design and conduct an experiment to investigate conservation of momentum in an inelastic collision in which the two gliders, instead of bouncing off each other, stick together so that they move off with identical final velocities. If you are using a PASCO airtrack, replace the bumpers with the wax and needle. Otherwise, velcro fasteners can be used with most gliders. 16
012-06379B Photogate Timer Experiment 7: Conservation of Kinetic Energy Introduction EQUIPMENT NEEDED: -Two Photogate Timers -Air Track System with two gliders. Momentum is always conserved in collisions that are isolated from external forces. Energy is also always conserved, but energy conservation is much harder to demonstrate since the energy can change forms: energy of motion (kinetic energy) may be changed into heat energy, gravitational potential energy, or even chemical potential energy. In the air track glider collisions you ll be investigating, the total energy before the collision is simply the kinetic energy of the gliders: 2 E k = (1/2)mv 1 + (1/2)mv 22. In this experiment you ll examine the kinetic energy before and after a collision to determine if kinetic energy is conserved in air track collisions. Procedure Photogate 1 Photogate 2 Bumpers Glider Set up the air track and 1 Glider 2 photogates as shown in m Figure 7.1, using bumpers 1 m 2 on the gliders to provide an elastic collision. Carefully level the track. Figure 7.1: Equipment Setup Measure m 1 and m 2, the masses of the two gliders to be used in the collision. Record your results in Table 7.1. Measure and record L 1 and L 2, the length of the gliders. (e.g., push glider 1 through photogate 1 and measure the distance it travels from where the LED comes on to where it goes off again.) Set both Photogate Timers to GATE mode, and press the RESET buttons. Place glider 2 at rest between the photogates. Give glider 1 a push toward it. Record four time measurements in Table 7.1 as follows: t 1i = the time that glider 1 blocks photogate 1 before the collision. t 2i = the time that glider 2 blocks photogate 2 before the collision. (In this case, there is no t 2i since glider 2 begins at rest.) t 1f = the time that glider 1 blocks photogate 1 after the collision. t 2f = the time that glider 2 blocks photogate 2 after the collision. IMPORTANT: The collision must occur after glider 1 has passed completely through photogate 1 and, after the collision, the gliders must be fully separated before either glider interrupts a photogate. NOTE: Use the memory function to store the initial times while the final times are being measured. Immediately after the final times are recorded, the gliders must be stopped to prevent them from triggering the photogate again due to rebounds. 17
Photogate Timer 012-06379B Repeat the experiment several times, varying the mass of one or both gliders and varying the initial velocity of glider 1. Try collisions in which the initial velocity of glider 2 is not zero. You may need to practice a bit to coordinate the gliders so the collision takes place completely between the photogates. Data and Calculations For each time that you measured, calculate the corresponding glider velocity (e.g., v 1, = L 1 /t 1i ). Use your measured values to calculate E ki and E kf, the combined kinetic energy of the gliders before and after the collision. Record your results in the table. Table 7.1 Data and Calculations L 1 = L 2 = m 1 m 2 t 1i t 2i t 1f t 2f v 1i v 2i v 1f v 2f E ki E kf Questions Was kinetic energy conserved in each of your collisions? If there were one or more collisions in which kinetic energy was not conserved, where did it go? Optional Equipment Design and conduct an experiment to investigate conservation of kinetic energy in an inelastic collision in which the two gliders, instead of bouncing off each other, stick together so that they move off with identical final velocities. If you are using a PASCO air track, replace the bumpers with the wax and needle. Otherwise, velcro fasteners can be used with most gliders. 18
012-06379B Photogate Timer Experiment 8: Conservation of Mechanical Energy EQUIPMENT NEEDED: -Photogate timer and Accessory Photogate -air track system with one glider -block of wood of known thickness (approximately 1-2 cm). Introduction Though conservation of energy is one of the most powerful laws of physics, it is not an easy principle to verify. If a boulder is rolling down a hill, for example, it is constantly converting gravitational potential energy into kinetic energy (linear and rotational), and into heat energy due to the friction between it and the hillside. It also loses energy as it strikes other objects along the way, imparting to them a certain portion of its kinetic energy. Measuring all these energy changes is no simple task. This kind of difficulty exists throughout physics, and physicists meet this problem by creating simplified situations in which they can focus on a particular aspect of the problem. In this experiment you will examine the transformation of energy that occurs as an airtrack glider slides down an inclined track. Since there are no objects to interfere with the motion and there is minimal friction between the track and glider, the loss in gravitational potential energy as the glider slides down the track should be very nearly equal to the gain in kinetic energy. Stated mathematically: ΔE k =Δ(mgh)=mgΔh; 2 where Ek is the change in kinetic energy of the glider [ ΔE k = (1/2)mv 2 - (1/2)mv 12 ] and Δ(mgh) is the change in its gravitational potential energy (m is the mass of the glider, g is the acceleration of gravity, and Δh is the change in the vertical position of the glider). Procedure D Level the airtrack as accurately as possible. L Measure d, the distance between the air track support legs. Record this distance in Table 8.1. h{= Place a block of known thickness under the d support leg of the track. For best accuracy, the thickness of the block should be measured with calipers. Record the thickness of Table 8.1: Data and Calculations the block as h in Table 8.1. Setup the Photogate Timer and Accessory Photogate as shown in Figure 8.1. Measure and record D, the distance the glider moves on the air track from where it first triggers the first photogate, to where it first triggers the second photogate. (You can tell when the photogates are triggered by watching the LED on top of each photogate. When the LED lights up, the photogate has been triggered.) Measure and record L, the effective length of the glider. (The best technique is to move the glider slowly through one of the photogates and measure the distance it travels from where the LED first lights up to where it just goes off.) Measure and record m, the mass of the glider. Set the Photogate Timer to GATE mode and press the RESET button. Hold the glider steady near the top of the air track, then release it so it glides freely through the 19
Photogate Timer 012-06379B photogates. Record t 1, the time during which the glider blocks the first photogate, and t 2, the time during which it blocks the second photogate. (If you have an ME-9215A Photogate Timer, the memory function will make it easier to measure the two times. If not, someone will need to watch the timer during the experiment and quickly record t1 before the glider reaches the second photogate.) Repeat the measurement several times and record your data in Table 8.1. You needn t release the glider from the same point on the air track for each trial, but it must be gliding freely and smoothly (minimum wobble) as it passes through the photogates. 11 Change the mass of the glider by adding weights and repeat steps 7 through 10. Do this for at least five different masses, recording the mass (m) for each set of measurements. (If you have time, you may also want to try changing the height of the block used to tilt the track or the distance between the photogates.) Table 8.1 Data and Calculations d = h = D = L = m = m θ t 1 t 2 v 1 v 2 E k1 E k2 Δ(mgh) Data and Calculations Calculate θ, the angle of incline for the air track, using the equation θ = arctan (h/d). For each set of time measurements: Divide L by t 1 and t 2 to determine v 1 and v 2, the velocity of the glider as it passed through each photogate. Use the equation E k = (1/2)mv 2 to calculate the kinetic energy of the glider as it passed through each photogate. Calculate the change in kinetic energy, ΔE k = E k2 - E k1. Calculate Δh, the distance through which the glider dropped in passing between the two photogates ( Δh = D sin θ, where θ = arctan h/d). Compare the dimetic energy gained wiht the loss in gravitational potential energy. Was mechanical energy conserved in the motion of the glider? 20