Physics 211: Newton s Second Law

Transcription

1 Physics 211: Newton s Second Law Reading Assignment: Chapte 5, Sections 5-9 Chapte 6, Section 2-3 Si Isaac Newton Bon: Januay 4, 1643 Died: Mach 31, 1727 Intoduction: Kinematics is the study of how objects move. Dynamics, on the othe hand, focuses upon why objects move. Ou own human expeience tells us that foces have something to do with causing motion. Aistotle developed a theoy of motion based completely upon human expeience and eason. He stated simply that all motion, even constant velocity, was caused by the existence of foces. Objects at est, accoding to Aistotle, had no foces acting upon them. Spontaneous motion, such as letting go of a ock and watching it magically pick up speed as it fell to the eath, was explained by the fact that all objects had a natual place in the univese. A ock s natual place was on the gound. Theefoe, when a peson eleased a ock fom thei gasp, it automatically etuned to its natual place. The foce aose fom the object being out of its natual place and wanting to etun to its natual place. Aistotle, howeve, neve actually veified his theoy with expeimentation. If he had, he would have found flaws in his thinking. Many people today still hold Aistotelian views. Howeve, Newtonian theoy takes a vey diffeent stance. The powe of Newton s theoies was evealed though thei ability to make detailed mathematical pedictions about the motion of objects. These pedictions have consistently been veified expeimentally. Newton hypothesized that foces cause a change in motion, not motion itself. In addition, he caefully distinguished between individual foces and the net foce acting on an object. He said that if the Net Foce acting on an object was zeo, then the object would continue to move with constant velocity. Constant velocity includes two impotant pats: constant magnitude (speed) and constant diection. [Note: 1) An object at est is a special case of the speed being equal to zeo; 2) A fame of efeence is needed to define each of these pats.] In a sense, Newton felt that moving at constant velocity was an object s natual place in the univese. Newton also caefully explained what would happen to an object that expeienced a Net Foce with a magnitude of something othe than zeo. F net = ma Potait of Isaac Newton by Si Godfey Knelle

2 This vesion of Newton s Second Law is popula because it clealy demonstates the elationship between Net Foce and Acceleation. Afte studying kinematics, acceleation is a quantity with which many students ae familia and comfotable. Similaly, most people ae familia with the concept of Foce, but many do not have a ealistic numbe sense of its magnitude expessed in newtons. Fo example, what is the magnitude of the foce povided by a Satun V ocket (i.e. Thust)? How does the foce on a basketball diffe fom the foce on a bullet when each is shot? Many people ae not awae that a bullet and a basketball each expeience appoximately the same change in momentum. Why would this be? As you pefom this lab, make some mental notes egading the size of the values that you calculate fo you answes. It is essential that you develop a good sense of what is ealistic.

3 Newton s Second Law Goals: Veify that a constant net foce causes a constant acceleation by collecting data, gaphing each vs. time, and analyzing the data duing the appopiate time inteval. Detemine the mass of an unknown object by gaphing Net Foce vs. Acceleation. Equipment List: Low Fiction Tack with cat Ultasonic motion senso Foce senso Pulley system Data Studio Excel scale balance, hanging masses, including 1-kg hook 灺 Shown at left is NASA s Satun V ocket as it blasts off on July 16th, 1969 with the cew of Apollo 11 sitting on top. The Satun V ocket was the lagest ocket eve used by NASA, and the only one able to lift the lage masses needed to land astonauts on the moon. Photo coutesy of NASA Lab Activity 1: Detemine the Mass of an Unknown Cat What is the mass of the cat (including the foce pobe) sitting on the tack at you lab station? One way to measue mass is to use a scale balance. Howeve, this method will not be available to you until the end of the lab. Theefoe, you must find it indiectly using anothe method. Newton s 2 nd Law states: if a net foce acts upon an object, then the object will espond by acceleating in the diection of the net foce. In addition, a constant net foce should esult in a constant acceleation. F net = ma

4 This method uses the motion detecto and foce pobe to measue the acceleation and net foce, espectively, acting on the cat. The net foce is caused by a mass that is hanging ove a pulley at the edge of the tack. Gavity ensues that this foce will be constant. Once this data is taken, the mass can easily be calculated. It is impotant to note, howeve, that all good expeiments ely upon moe than one data point. Theefoe, you will epeat this expeiment fo diffeent acceleations and coesponding net foces while keeping the mass (the cat) the same. All of the data will be gaphed togethe to detemine the mass. 1. Set up Data Studio to ead the data collected by the motion senso and foce pobe. Ceate gaph windows of Position, Velocity, Acceleation, and (Net) Foce vs. Time so that the data will be displayed on the sceen as each un is taken. The motion senso does not need to be calibated. Howeve, the foce senso must be calibated as befoe, using the 1-kg hook. It should also be e-zeoed often thoughout the lab. In ode to do this, fist emove all tension fom the foce senso. Then, pess the TARE button to eset the foce senso to zeo 1. Repeat this pocedue befoe each tial. 2. Place a hanging mass at the end of the sting. (Suggestion: 50g, 100g, 150g, ) 3. Release the mass and ecod you data. 4. Using the gaphs that you ceated on Data Studio, notice the time inteval duing which the cat was being feely pulled by the hanging mass. (The foce and acceleation data should be elatively constant.) Click and dag to highlight this egion on each gaph. (Note: the gaphs can be esized and enlaged.) 5. Using the Σ icon on Data Studio, pefom statistics calculations on this egion of the data fo this tial. Calculate: (1) the Acceleation and (2) the Net Foce. Hint#1: the constant net foce is the mean y-value of this egion of data on the foce vs. time gaph. 1 Calibation of the Foce Pobe See the pevious lab (Newton s Second Law. Pat I) fo instuctions on how to calibate the foce sensos.

5 Hint#2: the constant acceleation is eithe the mean y-value of this egion of data on the acceleation vs. time gaph o the slope of this egion of data on the velocity vs. time gaph. 6. Open Excel. Ceate a table in which to place the Acceleation and Net Foce data point that you detemined in step 5. Place these values in you table as one data point. 7. Repeat steps 2-6 fo at least 6 diffeent hanging masses. (Note: This will povide a set of 6 data points fom which the mass can be detemined.) Impot the Excel Acceleation and Net Foce Table containing all of you collected data into the Template. 8. Constuct a Net Foce vs. Acceleation gaph in Excel. (Impot this gaph into the Template.) What does the slope of this gaph epesent? Find the value of the slope (including units). Does you gaph pass though the oigin? If not, explain why it doesn't. 9. Measue the actual mass of the cat (including the foce pobe) using the scale povided by you instucto. 10. Calculate the % eo between the calculated and actual values fo the mass of you cat. (By what pecentage does you calculated mass diffe fom the mass measued on the scale?) Comment on the esult by including a discussion of eo in you answe. (Hint: You may wish to complete Activity 2 befoe completing this question.) Lab Activity 2: Fee Body Diagams 1. Daw a foce diagam of the cat as it is being pulled acoss the level tack. If the Net Foce does not equal zeo, then also indicate the diection of the Net Foce on the cat. 2. Daw a foce diagam of the hanging mass as it is allowed to fall feely, pulling the cat. If the Net Foce does not equal zeo, then also indicate the diection of the Net Foce acting on the hanging mass. 3. What foce does the foce pobe actually measue? (In Activity 1, it is stated at measuing the Net Foce. Is this tue? Unde what conditions?) 4. Compae the value of the Net Foce (measued by the foce pobe) in each of you 6 tials in Activity 1 to the actual weight of the hanging mass. Ae they equal? If not, which one is geate and why?