Primary author: Dequan Ye
Partner: Dorothy Liu

Newton’s 2nd Law of Motion
Introduction: We verified the Newton’s second law of motion, ∑i Fi = ma, by first holding total mass m constant and confirm the relationship between the other two variable (external force F and acceleration a), and then hold external force F constant while I verify the relationship between total mass m and acceleration a, with a set of gliders on a frictionless air track.

Procedure: While we were holding total mass m constant, the relationship between external force F and acceleration a should be direct ratio, if Newton’s 2nd Law of Motion is right. While we were holding external force F constant, the relationship between total mass m and acceleration a should be inverse or the relationship between 1/m and acceleration a should be direct ratio, if Newton’s 2nd Law of Motion is right. The material we needed are an air track, two photogates, an air pulley, a scale, a 70g weight, a scissor jack, a timing card, three different gliders, tape, and some nickels. We connected the air track with the air supply and adjust the height of scissor jack to keep the air track horizontal. Then we use a scale to get the mass of three different glider with the timing card and the mass of one nickel. We considered the hanging mass as m and the mass on glider is M. In this system, all of the mass is accelerated, so the total system mass is (M + m). And the external force F is the weight of the hanging mass (mg). Our first activity is to hold total system mass (M + m) constant. We put 8 nickels on the medium size (red) glider, used tape to tie two nickel as the hanging mass, positioned the glider at the end of the track away from the air pulley, released the glider and then allowed it to pass once through both photogates. We repeated it for 6 times and got acceleration for each time. Then we took 2 nickels off the glider and added it to the hanging mass. We released the glider for 2 times and got acceleration for each time. In order to get more data from different trial while holding total system mass (M + m) constant and changing the external force F, we continued took 2 nickels off the glider and added it to the hanging mass for each trial until all the nickels on the glider were added to the hanging mass. Our second activity is to hold the external force F constant. We put the red glider on the air track, used tape to tie 10 nickels as the hanging mass, positioned the red glider at the end of the track away from the air pulley, released the glider and then allowed it to pass once through both photogates. We tried it 2 times for acceleration. However, we needed more data from different trials while holding the external force F constant and changing the total system mass (M + m). In the following trials, we kept the hanging mass of 10 nickels to be constant. Then we put the yellow glider on the air track and released it 2 times for acceleration. Also, we put the blue glider on the air track and released it 2 times for acceleration. In addition, we put the yellow glider with a 70g weight on the air track and released it 2 times for acceleration. Finally, we put the red glider with a 70g weight on the air track and released it 2 times for acceleration.

Data: Time1 and Time2 are the amount of time the timing card blocks photogate 1 and photogate 2. T is the amount of time from when gate1 is unblocked until gate2 is blocked. Pulse

Time is calculated as Pulse Time = Time1 / 2 + T + Time2 / 2. V1 and V2 are the calculated average velocity of the glider when passing through gate1 and gate2. Acceleration is equal to (V2 – V1) / Pulse Time.

Red glider: 291.2g
Mass on the glider: 40g
Hanging mass: 10g (5g per nickel)
Weight of hanging mass (external force): 0.098N

V1 (m/s)
V2 (m/s)
Time1
(s)
Time2 (s)
T
(s)
Pulse Time (s)
Acceleration (m/s2)
1
0.069
0.153
0.868
0.392
1.055
1.685
0.050
2
0.061
0.158
0.079
0.380
1.039
1.719
0.056
3
0.064
0.143
0.943
0.420
1.124