Newton's Second Law of Motion

E104: NEWTON’S SECOND LAW OF MOTION

METHODOLOGY
In Part A of the experiment (Constant Mass, Changing Net Force), place the dynamics track on the laboratory table. Make sure that it is horizontal by placing the dynamics cart on the track. If the dynamics cart does not move, then the track is already horizontal. Otherwise, make the necessary adjustments. Get the mass of the dynamics cart. Write this under m1 in Table 1. Set the first photogate at the 20-cm mark of the dynamics track and the second photogate at the 70-cm track. This is the distance in which the cart can travel. Write this under S in Table 1. Plug the first photogate to the number 1 slot of the smart timer and the second photogate to the number 2 slot. Ask for help from your instructor if you have difficulty in setting up the photogates and the smart timer. Set the smart timer by pressing the “Select Measurement” button until it shows “Time:”. Set the mode by pressing the “Select Mode” button until it shows “Time: Two Gates”. Tie one end of the string to the cart and the other end to the weight hanger. Set the dynamics cart on one end of the track and the weight hanger over the pulley. Refer to setup. (See Figures 2 and 3). For the first trial, use a total mass of 20g for the hanging weight. Write this under m2 in Table 1. Release the cart. Read the time of travel from the smart timer. Write the time of travel under t in Table 1. Repeat procedures 1-8 using masses of 40g, 60g, 80g, and 100g. Write the data in appropriate spaces in Table 1. Compute the accepted value of the acceleration using Equation 5. Compute the experimental value of the acceleration using Equiation 6. Compute the percentage error for each trial. From your data draw the acceleration (experimental value) vs. Net force graph.

In Part B of the experiment (Changing Mass, Constant Net Force), repeat Part A using a mass of 100g for the hanging weight. Write this under m2 in Table 2. For the first trial, get the mass of the cart and write this under total mass of cart m1. Release the cart. Read the time of travel from the smart timer. Write the time of travel under t in Table 1. For trials 2-5, add masses of 100g, 200g, 300g, and 400g to the cart and write this under total mass of cart m1. Compute the accepted value of the acceleration using Equation 5. Compute the experimental value of the acceleration using Equation 6. Compute the percentage error for each trial. From your data draw the acceleration (experimental value) vs. mass graph.

In Part C of the experiment (Changing Mass, Changing Net Force, repeat Part A changing the mass of the cart and the hanging weight for each trial. Use the following masses:

Trial | m1 | m2 | 1 | mass of cart | 20g | 2 | mass of cart + 100g | 40g | 3 | mass of cart + 200g | 60g | 4 | mass of cart + 300g | 80g | 5 | mass of cart + 400g | 100g |

The dynamics track serves as the path for the motion of the dynamics cart. The dynamis cart is the object being observed as it accelerates on the dynamic track. The string is used to tie the end of the dynamics cart and the weight hanger. The photogates are used for detecting the motion in which the cart passed from photogate 1 to photogate 2. The smart timer is used to record the time of travel of the cart from photogate 1 to photogate 2. The set of weights are for changing the mass of the track and the net force. The weight hanger holds the weights. The pulley is a tool for pulling the cart as the weight hanger falls.

DATA AND RESULTS
Table 1. Constant Mass, Changing Net Force trial | m1 (kg) | m2 (kg) | net force (N) | a (av) (ms2) | time (s) | a (ev) (ms2) | % error | 1 | 0.52 | 0.02 | 0.20 | 0.36 | 1.80 | 0.31 | 14.43 | 2 | 0.62 | 0.04 | 0.39 | 0.60 | 1.42 | 0.50 | 16.51 | 3 | 0.72 | 0.06 | 0.59 | 0.76 | 1.22 | 0.67 | 10.75 | 4 | 0.82 | 0.08 | 0.78 | 0.87 | 1.09 | 0.85 | 3.01 | 5 | 0.92 | 0.1 | 0.98 | 0.96 | 1.01 | 0.98 | 1.74 | mass of cart, m1 = 0.51814 kg distance traveled, s = 0.5 m trial | total hanging mass (kg) | net force (N) | a (av) (ms2) | time (s) | a (ev) (ms2) | % error | 1 | 0.02 | 0.20 | 0.36 | 1.87 | 0.29 | 21.22 | 2 | 0.04 | 0.39 | 0.70 | 1.21 | 0.68 | 2.72 | 3 | 0.06 | 0.59 | 1.02 | 0.90 | 1.23 | 20.82 | 4 | 0.08 | 0.78 | 1.31 | 0.83 | 1.44 | 9.77 | 5 | 0.1 | 0.98 | 1.59 | 0.74 | 1.82 | 14.91 |

Table 2. Changing Mass, Constant Net Force
Total hanging mass, m2 = 0.1 kg distance traveled, s = 0.5 m
Net Force, m2g = 0.98 N trial | mass of cart + mass added (kg) | a (av) (ms2) | time (s) | a (ev) (ms2) | % error | 1 | 0.52 | 1.59 | 0.74 | 1.82 | 14.91 | 2 | 0.62 | 1.36 | 0.85 | 1.39 | 1.71 | 3 | 0.72 | 1.20 | 0.92 | 1.17 | 2.39 | 4 | 0.82 | 1.07 | 0.98 | 1.05 | 1.47 | 5 | 0.92 | 0.96 | 1.05 | 0.91 | 5.03 |

Table 3. Changing Mass, Changing Net Force distance traveled, s = 0.5 m]

SAMPLE COMPUTATION a=2st2= 2(0.5m)(0.98s)2=1.04 m/s2

DISCUSSION
This experiment is for me not difficult to conduct because this experiment is based from previous experiments (same materials, same setup, the only thing new is the pulley at the end of the track with a string). I and my groupmates have to be careful in the weights we hang on the hanger. I have to catch the motion of the dynamics cart after passing from the second photogate so that the cart will not collide with the pulley. If I did not caught the cart after passing from the second photogate then the cart will collide with the pulley which may cause damage. The gathering and recording of data was easy because we just have to measure the distance between the two photogates and the time of travel the cart moved from the first photogate to the second photogate. The computation of the data gathered was not hard because the formulas provided are simple in form. The design of the experiment was overall understandable.

In Part A of the experiment, the mass of the dynamics cart is constant but the net force from the weight hanger is changing. My hypothesis was that as the net force is increased, the acceleration of the dynamics cart will also increase. The net force produced is increased by the weights put on the hanger starting from 0.02 kg up to 0.1 kg (trials 1 to 5). The higher the mass on the weight hanger, the higher the acceleration is produced by the gravity. With the string connected from the weight hanger to the dynamics cart, the dynamics cart will also accelerate with the help of the pulley. The graph in Table 1 shows that acceleration is directly proportional to the net force provided that the net force is increasing and the mass of the cart is constant. Thus my hypothesis was correct.

In Part B of the experiment, the mass of the dynamics cart is changing while the net force is constant. My hypothesis is that the higher the mass of the dynamics cart, the lower will be its acceleration on the dynamics track. This is because of the increased mass on the cart that impedes its acceleration. The time of travel as a result of lower acceleration will be longer than that of Part A. The mass of the dynamics cart was increased from 0.52 kg to 0.92 kg (from trials 1 to 5). The increased mass of the dynamics cart with the effect of gravity makes a strong force downward perpendicular to the dynamics track. As a result of this, the pull of gravity on the weight hanger given that there is a constant net force on it will have a reduced effect in accelerating the dynamics cart which has an increased mass. The graph in Table 2 shows that the acceleration is inversely proportional to the net force provided that the net force is constant and the mass of the cart is increasing. Thus my hypothesis was correct.

CONCLUSION
The principle being explored on this experiment is that the acceleration is dependent on the net force acting on the object and the mass of the object. If there exists an acceleration on the object then there must be a net force action on the object which is also known as an unbalanced force. I conclude that the acceleration is directly proportional to the net force acted upon the object and that the acceleration is inversely proportional to the object’s mass.

ACKNOWLEDGMENT
I thank my groupmates for uploading the pictures of the experiment and their cooperation during the conduct of the experiment.

REFERENCES [1] Surname, F., Title of the paper, Title of the journal, Vol., No., Year [2] http://www.physicsclassroom.com/class/newtlaws/u2l3a.cfm