303b Reducing the impact (Accelerometer & Light gate)

Transcription

1 Senor: Logger: Accelerometer High g, Light gate Any EASYSENSE capable of fat logging Science in Sport Logging time: 1 econd 303b Reducing the impact (Accelerometer & Light gate) Read In many porting activitie there i the potential to generate very large change of force. If the change of force take place over too hort a period of time the energy change created can be damaging, and many cae fatal. The invetigation will ue a model of a colliion to how the force during a colliion and then alter the condition at colliion to reduce the force and duration of force to a afer level. Think of everal porting activitie and decribe how afety meaure in the port are ued to reduce the potentially fatal high force of a colliion e.g. gravel trap in motor racing, flexible fencing in downhill kiing. You are to invetigate the ize and duration of the force (the impule) involved in a colliion. The model ue a cart in colliion with a fixed barrier. The peed of the cart i recorded uing a Light gate and force in the colliion by an Accelerometer. Thi information will be ued to create and tet crumple zone that will dilute the force involved in the colliion. You are to deign and make crumple zone of different hape and material which will be fitted to the front of a dynamic cart. Each crumple zone will then be teted to meaure it effectivene. From the reult you will compare the effectivene of your crumple zone. A tandard colliion without the crumple zone will be ued for comparion. 303b - 1

2 What you need 1. An EASYSENSE logger capable of fat logging. 2. A Smart Q High g Accelerometer et to y-axi range mounted vertically on the Dynamic cart. 3. A Smart Q Light gate 4. Dynamic cart with fitted with ingle interrupt card. 5. Track fitted with fixed barrier at it end. 6. Material for making crumple zone - paper traw, ticky tape, corrugated paper, paper glue (glue gun are ueful). 7. Large block or adjutable upport pillar for the track. 8. Retort tand or bracket to hold Light gate in poition and to keep Accelerometer enor wire out of the way. 9. Balance reading to ±0.001 kg. What you need to do The Light gate need to be poitioned to meaure the velocity jut before the impact begin. Each crumple zone hould be teted with an impact at the ame velocity. To enure the ame impact velocity, releae the trolley from the ame point on the ramp for each tet. The Light gate i ued to confirm that the velocitie are the ame for each tet. 1. Aemble the apparatu a hown. Meaure the length of the interrupt card, and attach it to the cart. Attach the Accelerometer ecurely to the cart. 2. Connect the Accelerometer enor to input 1, and the Light gate to input Arrange the Light gate to meaure the velocity of the cart jut before impact. Check that the interrupt card will cut the light beam and it will pa completely through before the cart tart to make contact with the end barrier. 4. Meaure the total ma of the trolley and attachment (thi hould be done before each run and certainly before a run where the additional crumple area ha been modified). 5. Find (by trial and error) the appropriate tarting poition and the lope needed. Make ure that the bottom of the ramp cannot move (you may need to clamp it or butt the end againt a wall). 6. From the EaySene oftware Home creen elect Open Setup (or File, Open Setup). Open the file Data Harvet Invetigation (Edition 2) \ Setup file \ V2 \ 303b Impact accelerometer 7. Click on Start to begin recording. 8. Mark a releae point on the ramp e.g. a thin bracket (each releae mut be from the ame point to give a contant comparable velocity of colliion). Releae the trolley from thi mark. 9. Select Overlay. Click on Start and repeat everal time to allow a calculation of average of value in the colliion. You will need to record the maximum g meaured, the time the g wa applied for, and the area of g v. time (the impule). See the ection on reult and analyi for detail. 10. Repeat the experiment with the deigned crumple zone() attached to the front of the cart. You will need to record the ame data a you collected in the normal colliion. 303b - 2

3 Reult analyi Theory:- The effectivene of a crumple zone can be aeed by conidering the following quantitie:- Colliion time, t (). Average rate of change of momentum, and hence the average colliion force. Maximum colliion force. A crumple zone i deigned to maximie the colliion time making the average and maximum colliion force a low a poible. The vehicle hould be brought to a top without rebounding. Cart ma, m =... kg. Interrupt card, (l) =... m. 1. Ue the Zoom function to elect an area uitable for analying the g/t graph. 2. Ue the Value tool, to find the time that the Light gate reached 50% on it riing and it falling edge. The riing edge time will be T 1 and the falling edge time will be T 2 3. Ue the Area tool to obtain a value for the area under the g/t graph. Thi i the impule. For each crumple zone made (you can add column if you have made more than three crumple zone), read off the following value and fill in the table. t 1 and t 2 at the beginning and the end of the light beam interrupt. t 3 and t 4 at the beginning and end of the colliion with the Accelerometer. l = length of the interrupt card. Quantity Unit No crumple Crumple 1 Crumple 2 Crumple 3 t 2 t 1 (time interval of interrupt card in Light gate) Length of interrupt card l m l Velocity v = t 2 t 1 m -1 Area under graph (colliion) P = mv Impule = Change in momentum Ft = Δmv Force = ma g. kgm kgm Colliion time t c (t 3 - t 4 ) = Δmv AveF = N t c Maximum colliion force (from graph) N 303b - 3

4 Evaluation Evaluate the effectivene of the crumple zone you have made. In your evaluation you need to refer to:- Colliion time. Average colliion force. Maximum colliion force. Momentum and impule The momentum of a body i equal to it ma multiplied by it velocity. Momentum i meaured in N (newton econd, kg m/). Note that momentum i a vector quantity, in other word the direction i important. The impule of a force (alo meaured in N ) i equal to the change in momentum of a body which a force caue. Thi i alo equal to the magnitude of the force multiplied by the length of time the force i applied. Impule = change in momentum = force time Calculation Take care with the unit being ued. Quantity Symbol / abbreviation Unit Ma m kg (kilogram) Ditance l m (metre) Time t (econd) Change, difference Δ Time from the graph i recorded in m (milliecond = 10-3 of a econd). The calculation require. Ma value are in kg. Ditance value are in metre. Formula / equation Meaning Additional note F = ma Force i equal to ma x acceleration F = mg Force i equal to ma x the acceleration due to gravity p = mv Momentum = ma x velocity Momentum i a vector quantity, direction i important. Momentum ha quantity and direction. v = /t Velocity i equal to the ditance moved divided by the time taken for the movement i ued in phyical cience to indicate diplacement. Diplacement i the ditance from point. Ditance i the total ditance travelled to reach a point Note for the calculation ued in thi practical Force i defined a the ma x the acceleration. F = ma Gravity, g, i the force required to accelerate an object by 9.81 m//. We can ubtitute g directly into a force calculation a g = a, the definition then become F = mg 303b - 4

5 Calculation of Impule Δmv (change in momentum) You will need to find the time the interrupt card wa blocking the Light gate and the width of the interrupt card. v = width of interrupt card/time or l v = t 1 t 2 v = where = diplacement or ditance, not econd. t Where l = the width of the interrupt card and t 1 and t 2 at the beginning and the end of the light beam interrupt. Ue the calculated velocity x the ma of the cart to produce the momentum of the cart immediately before the colliion. Worked example An experiment wa conducted a decribed. Ma of cart (cart, Accelerometer, fixing bracket, ecuring crew, etc) wa kg. Interrupt time wa found to be (29.2 m). Interrupt card width wa 0.04 m (40 mm). To calculate momentum uing ma of cart and velocity..04 Velocity = = m momentum = mv. 1 mv = = 0.604mkg 0 1 To calculate change in momentum (impule) uing the area of graph when the enor i et to record data a g Impule = area of the colliion graph x g x ma of cart. Impule = x 9.81 x = mkg -1 To calculate change in momentum (impule) uing the area of graph when the enor i et to record data a m// Impule = area of the colliion graph x g x ma of cart. Impule = x = mkg -1 Where did the 9.81 come from? In the calculation we are finding the force. Force i defined a the ma x the acceleration. g i a hort hand for repreenting the acceleration equivalent to 9.81m//. When data i collected from the Accelerometer in g we are recording multiple of i introduced in the calculation to convert the unit g into acceleration in the form of m//. Note how the calculated theoretical impule / change in momentum i higher than the value derived from experimentation. Where are the error in the experiment? Analye the experiment and the data collected to create an error lit. Indicate which error you could eliminate or reduce. 303b - 5