Lab Report 1 Newtons Secondlawofmotion-phys101l.docx

INTRODUCTION We know objects can only accelerate if there are forces on the object. Newton's second law tells us exactly how much an object will accelerate for a given net force. Newton's second law of motion pertains to the behavior of objects for which all existing forces are not balanced. The second law states that the acceleration of an object is dependent upon two variables - the net force acting upon the object and the mass of the object. The acceleration of an object depends directly upon the net force acting upon the object, and inversely upon the mass of the object. As the force acting upon an object is increased, the acceleration of the object is increased. As the mass of an object is increased, the acceleration of the object is decreased. In this experiment we have verified the relationship between a body’s acceleration and net force and between acceleration and mass.

ANALYSIS The second law explains how the velocity of an object changes when it is subjected to an external force. The law defines a force to be equal to change in momentum (mass times velocity) per change in time. Newton also developed the calculus of mathematics, and the "changes" expressed in the second law are most accurately defined in differential forms. For an object with a constant mass m, the second law states that the force F is the product of an object's mass and its acceleration a:

𝐹 = 𝑚𝑎

For an external applied force, the change in velocity depends on the mass of the object. A force will cause a change in velocity; and likewise, a change in velocity will generate a force. The equation works both ways. In this experiment, motion of the objects moves along a straight line and is therefore classified as a one-dimensional motion. The moving object or the dynamics cart will be represented as a particle in kinematics and the dynamic cart is considered moving along the x-axis.

OBJECTIVES The main objectives of this experiments are to:  To verify the direct proportionality of acceleration and net force if the mass of the body is constant and  To verify the inverse proportionality of acceleration and mass if the net force is constant.

MATERIALS The materials used in the experiment were provided for by Mapua UniveristyDepartment of Physics. The materials and apparatus that were provided for by the school were.  1 pc. Dynamics Track with pulley  1 pc. Dynamics cart  2 pcs. Photogates  1.5 m String  1 pc. Smart Timer  1 pc. Meter stick  1 pc. Set of weights  1 pc. Weights hanger

The use of the dynamics tracks and carts in the experiment will act as a demonstration of all the laws of motion. The smart timer and two photogates were used in determination of time traveled of the dynamic cart between the photogates. In order for the photogates to record the time travel, a picket fence will be placed in the dynamic cart and will act as a detection tool for the photogates. In the first part of the experiment, the students must verify the direct relationship of the acceleration and net force given constant mass of the body. Before being able to achieve this goal, the students must first follow the lab manual that was provided for by the instructor on how to set-up the apparatus properly. The positions of the first and second photogates, the dynamics track, and the pulley was set up according to the exact positions indicated in the manual. The string in the hook will be tied to the dynamics cart and will be put on the pulley wheel. The time of travel

and acceleration was computed. These will be used to either prove or disprove the first objective of this experiment. For the results of the first part of the experiment wherein the mass of the cart was at a constant mass of 0.5192 kg, the first trial had a hanging weight of 20 g or 0.0200 kg with a net force of 0.196 N, the travel time recorded was 1.7977seconds, and the computed experimental value of acceleration was 0.3094 𝑚〖/𝑠〗^(−2) thus getting a margin of error of 14.8831%. The second trial had a hanging weight of 60 g or 0.0600 kg with a net force of 0.5880 N, the travel time recorded was 1.0203 seconds, and the computed experimental value of acceleration was 0.9606 𝑚〖/𝑠〗^(−2) thus getting a margin of error of 11.9119%. Lastly, the third trial had a hanging weight of 100 g or 0.1000 kg with a net force of 0.980 N, the travel time recorded was 0.7953 seconds, and the computed experimental value of acceleration was 1.5810 𝑚〖/𝑠〗^(−2) thus getting a margin of error of 0.1074%. The second part of the experiment, students need to verify if there will be an inverse relationship of the acceleration and mass given that the net force or the hanging mass is constant. The same set-up was done with the first part, but the difference is that the net force, which is the hanging mass, will be constant at 0.980 kg. For the result of the second part of the experiment wherein the hanging mass was constant at 100 g or 0.100 kg and the net force at a constant 0.9800 N, the first trial had the mass of the cart at 519.2 g or 0.5192 kg (no weights added) and the time travel recorded was 0.7953 seconds and the computed experimental value for acceleration was 0.1074 𝑚/𝑠^(−2) thus getting a margin of error of 0.1074%. The second trial had the mass of the cart at 619.2 g or 0.6192kg ,100 g of weights added, and the time travel recorded was 0.0.9241 seconds and the computed experimental

value for acceleration was 1.7110 𝑚/𝑠^(−2) thus getting a margin of error of 14.0613%. Lastly, the third trial had the mass of the cart at 819.2 g or 0.8192 kg , 300 g of weights is weight added, and the time travel recorded was 1.0375 seconds and the computed experimental value for acceleration was 0.9290 𝑚/𝑠^(−2) thus getting a margin of error of 12.8599 %.

GUIDE QUESTIONS From the results of part A, how would you relate the acceleration of the cart to the total hanging weight?  Newton’s second law states that the net force is equal to the product of mass and acceleration. Base on the results of part A, the total hanging weight and the cart are directly proportional. The net force applied is the total hanging weight to the object with a mass that will make the object accelerate. From the results of part B, how would you relate the acceleration of the cart to its total mass?  From the results of part B, as the cart increases with mass having the net force constant, the cart slows down or the acceleration decreases. Therefore the acceleration is indirectly proportional to the total mass. The cart with the greater mass needs greater amount of net force to accelerate just like as stated in newtons second law of motion. List down the possible sources of errors in this experiment  Human error

 Dynamics track and the dynamics cart  Photogates  Smart timer.

CONCLUSION

Therefor I conclude:  That the objective of this experiment was achieved; to prove that the theory of newton is correct and accurate.  That the magnitude of acceleration is directly proportional with the net force acting upon the object  That the magnitude of the acceleration is inversely proportional to the mass if the object being accelerated.  That when the mass increases then the time decreases, hence it is inversely proportional.  That there were some errors that will occur at some point because of human errors and because of the materials used. Newton’s 2nd law states that the acceleration of an object is dependent upon two variables - the net force acting upon the object and the mass of the object. In the experiment it was proven that the acceleration of the dynamic cart has a direct relationship with the net force, the hanging mass, given that the mass is constant. In the graphs provided, the greater the force applied on the object, the faster

acceleration, meaning that the magnitude of acceleration is directly proportional with the net force acting upon the object. In the second experiment, it was also proven that the acceleration of the dynamic cart has an indirect/inverse relationship with the mass of the dynamic cart if the hanging mass is constant. Meaning, • That when the mass increases then the time decreases, hence it is inversely proportional. Less mass, faster acceleration. The margin of error for some trials were greater than 10 % and some were close to 1%. We can consider some human error like the slight push on the release od the dynamics cart can greatly affect the results especially when we are talking about difference in milliseconds. Also, we were advised by our professor to put the cart closes to the first photogate to ensure that the initial velocity of the cart will be zero.