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PHYSICS SAMPLE LAB WRITE-UP Title - Newton’s 2nd Law Objective In this experiment we will attempt to confirm the validity of Newton’s 2nd Law by analyzing the motion of two objects (glider and hanging mass) on a horizontal air-track. First, we will calculate the theoretical acceleration by applying Newton’s 2nd Law (Fnet = MA), neglecting friction, to the glider and hanging mass. Next, we will calculate the experimental acceleration of the glider by applying the kinematic equations of motion as it moves between two markers (photogates) on the track. We will then compare the experimental acceleration to the theoretical acceleration.
Theory a) Acceleration using Newton’s 2nd Law Apparatus Setup V1
Photogates
V2
glider
M1
d
+X Airtrack
M2
+Y
hanging mass
Free-Body Diagram N T T
M1 M1g
M2 M2g
Apply Newton’s 2nd Law to mass M1 and M2. Mass ‘M1’ ΣFx = T = M1a Mass ‘M2’
b) Acceleration using Kinematic Equations Using the kinematic equation V22 = V12 + 2a ( x − x0 ) we will calculate the experimental acceleration of the glider as it moves between the two photogates. We will take the origin of our coordinate system at the first photogate. d = distance between photogates V1 = (s/t1) velocity of the glider through photogate 1 V2 = (s /t2) velocity of the glider through photogate 2 s = diameter of small flag on glider t1 = time for small flag to go trough photogate 1 t2 = time for small flag to go trough photogate 2
a exp =
V22 − V12 2d
Apparatus Refer to theory section for apparatus setup One air track(#21), blower(#2), blower hose and power supply One digital photogate(#2C) and one accessory photogate(#2A) One glider(#1B) One flat accessory box(#22A) String Electronic pan balance(#1) Vernier Calypers (#12c)
Procedure 1. 2. 3. 4. 5.
Measure the mass of the glider and hanging mass. Setup the air track and blower as indicated by instructor. Measure the distance between photogates. Measure the diameter of the small flag on glider with vernier calipers. Release glider 10 cm away from photogate 1 and record times trough both photogates. 6. Repeat step (5) four more times. 2
Data M1= 4750 g M2=50.00 g g = 9.80 m/s2 d = 60.65 cm s = 1.01 cm Run #
Conclusion 1. The theoretical acceleration using Newton’s 2nd Law was 10.21 cm/s2 and the average experiment acceleration using the kinematic equations was 10.10 cm/s2. The percent error between experiment and theory was only 1%. Although the percent error was small, there were still systematic and random errors present. 2. Based on the relative small % error of 0.98% we can conclude that the objective of confirming Newton’s 2nd Law was accomplished. 3. In measuring the velocity of the gliders through the photogates we used the average velocity instead of the instantaneous velocity. This resulted in the average velocity always being smaller than the instantaneous velocity. This will V 2 − V12 then cause a exp = 2 to be consistently smaller than atheo which resulted in a 2d systematic error. A second systematic error was that in applying Newton’s 2nd Law to derive atheo of the glider we neglected the frictional force. The resulting equation should have been atheo = (M2g – fk)/(M1 + M2). Neglecting friction on the atheo equation should result in atheo being consistently larger than aexp. The data shows this to be true with the exception of one data point. 4. In addition to the random errors involved due to the uncertainty of the measuring devices, other random errors involved in the experiment include: a) Not releasing the glider from same initial point every run. b) Trying to balance the air track. c) Having the hanging mass M2 swinging when releasing M1 from rest. All these random errors contributed to the uncertainty in the final results for the accelerations. These random errors also contributed to the 0.98% error in the final results.
