# NEWTON S SECOND LAW OF MOTION

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1 Course and Secion Dae Names NEWTON S SECOND LAW OF MOTION The acceleraion of an objec is defined as he rae of change of elociy. If he elociy changes by an amoun in a ime, hen he aerage acceleraion during his ime is aa = (1) Newon s 2 nd law of moion saes ha if a ne force F NET acs on an objec, hen he objec acceleraes and is acceleraion is proporional o he ne force applied: aa = 1 mm FF NNNNNN or FF NNNNNN = mm aa (2) The proporionaliy consan m is he ineria of he objec and is numerical alue is called he mass. Equipmen: Track, moion sensor, force sensor + hooks, car, rubber band, fan, masses, sopper PART I - PUSH ON A CART Predicion Imagine ha you hae car a one end of a leel rack. There is no fricion. 1) Suppose he car is iniially a res a one end of he rack. You push i wih a consan force unil i reaches he middle of he rack and hen le i roll freely unil i reaches he oher end. Skech he expeced elociy ersus ime cure o he righ 2) Nex gie i a shor ap wih your finger o se i ino moion. Then when he car has reached he cener of he rack you gie i anoher shor ap in he same direcion and le i roll o he end of he rack. Make a skech of he expeced elociy of he car as a funcion ime in he lef graph below. Nex, repea he aboe bu when he car reaches he middle of he rack you ap i in a direcion opposie o is moion. Make a skech of he expeced elociy as a funcion of ime in he righ graph.

2 3) Describe why you draw he cures as you did 4) Draw below hree free body diagrams of he car. One when is a res on he rack. Two, while i is moing (and no apping). Three, a he insan you ap i. Experimen Connec he moion sensor o he Pasco inerface box, open Daasudio and se he daa rae of he moion sensor o 50 Hz. Place he moion sensor a one end of he rack and he car cm from he sensor. sensor car Tap he car wih one finger o se i moing away from he sensor and hen ap i again in he same direcion when i reaches he middle of he rack. (Noe: Try o keep mos of your hand away from he car since i will inerfere wih he measuremens.) 8) Record he elociy as a funcion of ime and make a rough skech of he cure o he righ. 9) Is he cure qualiaiely like you prediced? 10) Is he elociy consan beween aps? If no, why? 11) Now ry o push he car away from he sensor wih a consan force for an exended period of ime while recording he elociy. Skech your measured cure o he righ. 12) Does he shape of he elociy ersus ime cure during he push sugges ha you were indeed pushing wih a consan force? Explain.

3 Pushing he car wih your hand wih a consan force is difficul o do. In order o mainain a more nearly consan force, you can ry o pull he car wih a rubber band while keeping he srech of he rubber band consan during he pull. (Use hin rubber bands and ie wo or hree end-o-end.). Add a mass on op of he car. Saring wih he car cm from he sensor, record he elociy while pulling wih a consan srech of he rubber band in a direcion away from he sensor. 13) Does he elociy ersus ime cure sugges ha he force is approximaely consan? 14) Now add some mass o he car and repea wih he same srech of he rubber band. Is your acceleraion larger or smaller? Is his wha you expec? 15) For each of he wo cases aboe, calculae he mass imes he acceleraion. Be sure o include he mass of he car. 16) We now wan o check numerically Newon 2 nd law. Use he force sensor o measure he force acing on he car (pull he rubber band wih he hook aached o he force sensor). Again keep he rubber band a consan srech and use four differen masses. Close Daasudio (if sill open) and open he file: Newonlaw.ds conained in he T:\Daasudio folder. You see a window wih he force s ime and elociy s ime so you can compare he alues of he force wih he acceleraion during he same ime ineral. Tare he force sensor before each measuremen (press he are buon on he side of he sensor). The force migh no appear o be consan and smooh, so ake he mean alue of i. Ge he measure of he acceleraion from he elociy s ime graph. Repor he resuls in he able below. On he las column (Check) draw a check mark if he Newon second s law is saisfied from your daa F (N) a (m/s 2 ) Mass x a (N) Check PART II - INCLINE PLANE Predicions Firs, assume ha fricion can be negleced. Suppose you shoe a car so ha i rolls up an incline plane and hen i comes back down.

4 17) Draw wo free body diagrams: as he car moes up and as i moes back down. Indicae on he diagrams also he ne force acing on he car. Up Down 18) Compare he magniudes of he ne forces. Should hey be he same? If no, which one is greaer? Skech he expeced posiion and elociy of he car as a funcion of ime. Assume he coordinae sysem proided by he moion sensor locaed he boom of he incline plane. x Now, assume ha fricion is presen 19) Draw wo free body diagrams: as he car moes up and as i moes back down. Indicae on he diagrams also he ne force acing on he car. Up Down 20) Compare he magniudes of he ne forces. Should hey be he same? If no, which one is greaer? Skech he expeced posiion and elociy as a funcion of ime. x 19) Are your prediced cures he same wih and wihou fricion? Explain.

5 Experimen Now, place somehing under he end of he rack opposie o he moion sensor o raise i by 2-3 cm. Shoe he car so ha i rolls up he incline and comes back down. Record he posiion and elociy during his ime. 18) From he elociy s ime graph, is he magniude of he acceleraion greaer when he car is moing up or down he incline? 19) How can you ell he wo acceleraions are differen by looking a he posiion s ime graph? 20) Now compare hese graphs wih your earlier predicions wih fricion. Would you say ha fricion has a noiceable effec on he shapes of he cures? Explain. I can be shown ha, in his case, he fricion force is gien by: F FRICTION m = ( aup adown ) (3) 2 21) Find he acceleraions by aking he slope of he elociy ersus ime cures a up = a down = 22) Calculae he fricion force using he equaion (3): F FRICTION = 22) Now raise by few more cenimeers he incline plane, shoe he car again, measure he acceleraions and calculae he fricion force. F FRICTION = 23) Compare he wo numerical alues of he fricional forces. Should hey be he same? 24) Is here a relaion beween F FRICTION and he slope of he incline plane? If necessary increase he slope o explore his.

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