Purpose: the purpose of this lab is to apply Newton's Second Law and to understand how forces cause objects to accelerate. We limit to motion in 1-dimension and look at the affects of varying the forces exerted on a system of objects, as well as varying the mass of the system. This lab also teaches some concepts of measurement and analysis of experimental data.
In part one performs set up of experiment and measure the time it takes the glider to travel distance at two positions separated by distance. Position the track so that the pulley at the end hangs over the edge of the table as in Figure 1. Level the air track by placing the cart at the middle of the track, turning on the air blower, and adjusting the leveling screws on the legs of the air track to get minimum movement of the cart. Half a turn of the leveling screw produces a noticeable amount of acceleration of the cart. Also, measure and record the weight of the cart (with hook and flag attached) and the mass hanger, and attach the pulley from the kit to the end of the air track. Run the nylon line from the cart over the pulley and hang the mass hanger at the end. Turn on the blower. In part two, measure the acceleration of the cart due to the gravitational pull of the hanging weight , which will remain constant while we increase the weight of the cart. Take data for at least five different cart weight trials, starting with being the hanger plus 10 g, and being the cart with no additional weights. In part three, keep the system mass constant but change the force pulling the cart by transferring mass from the cart to the hanger for each trial. Start with the setup the same as your last trial for Part II: 40 g on the cart and 10 g on the hanger. Perform five trials and again take care to make good records of the mass for each trial. In part four, keep the cart mass constant and vary the hanger-mass in increments of 10 g. This way you are varying both the system mass and the force. Perform five trials and tabulate data. Part two: Constant force varying system mass
M1, mass of hanger g M2,mass of cart g Change in time, t(s) Velocity initial, m/s Velocity final,m/s Acceleration m/s^2 experimental X(m) Acceleration
Method 1 m/s^2 Change
10 207.1 1.11415 0.312216
0.6 0.4128599 0.45778
10 217.1 1.0759 0.3560563 0.772945 0.387678
0.6 0.39222323 0.416889
10 227.1 1.33146 0.288100 0.62746594 0.254881
0.6 0.25892658 0.339365
10 237.1 1.34112 0.3465113 0.75361357 0.368894 0.6 0.3601254
10 247.1 1.1243 0.338492 0.7304580 0.343845
0.6 0.349160046 0.391965
m/s^2 method 2 Average velocity(m/s) M1+m2 kg 1/a(s^2/m)
0.410878248 0.5411115 0.2171 2.433652547
0.38747932 0.561754 0.2271 2.579460274
0.254881859 0.2371 3.923399547
0.360288088 0.2471 2.710805814
0.348630259 0.2571 2.908244874
Trial 1: , a= (vf^2 –vi^2)/2x =(0.770007^2-0.312216^2)/2*0.6=0.410905 m/s^2
, a= 0.45778/1.11415 = 0.410878248 m/s^2
Question 1. Does one of the two ways methods give a more precise value for g? Hypothesize as to why this might be.
If we compare acceleration value from method one and method two , we will notice that method one gives 0.48 % error and method two gives 0.0065 % error compare to the experimental values. From this data we can conclude that method two gives more accurate data, probably this happened because in method one we use x(distance between photogates) which we measure by ruler and ruler gives more systematic error compare to photogates machine. If machine measure the distance than the error was less.
b. Checking the Constant Acceleration Assumption
Question 2. Is the system under constant acceleration according to this calculation?
According to calculations our system is near the constant accelerations .We compare the average velocity in trial one and trial two and they are near the same ( just have 2 %