Newtons Second Law - Lab Report Example

Friction Newton’s second law was put up to investigate the relationship between massforce and acceleration. Finding coefficient of static friction, µs and the coefficient of kinetic friction, µk. requires set formulae to determine the acceleration of a body in relation to the force and mass of an object. It is widely believed that the natural state of an object is when it is at rest. Forces are responsible for the movement of a body. To test Newton’s law, various experiments can be conducted on the acceleration and proportionality of an object. A proof of an increase or decrease in mass of the Newton’s experiment is determined by the force and acceleration achieved from the experiment. Goals: The goal of the experiment is to verify the existence of Newton’s second law by finding the coefficient of static friction, µs and the coefficient of kinetic friction, µk. using the experiment stated below. Introduction: Have you wondered the make-ups of mechanics? Well Newton’s second law breaks it down into simple understandable terms by providing a means of translating directly between the acceleration and force acting towards a given mass or object. Theoretical background: The experiments are based on the concepts of force and Newton’s Laws of Motion, particularly Newton’s Second Law which states that: the acceleration of a body is directly proportional to the net force acting on the body, and inversely proportional to the mass of the body. From this definition, the equation Net Force = Mass x Acceleration (Fnet = mass x acceleration) is derived. Air tracks were used to reduce friction; the little amount of friction that remains in the system is negligible in the data. The suspended mass was subject to gravity which has a constant acceleration of -9.81 m/s2. The variables were solved to include: acceleration of the sled, velocities of the sled at each photo-gate, net force acting on the string, and the time taken from release to the first photo-gate and between the photo-gates. Acceleration was calculated using the formula: Acceleration= Velocity/ Time. The experiment is commonly used in mechanics fields to determine the acceleration acting towards a given mass or object. Theory: The variables to be used in the experiment and their explanation involves F used to show the force, m used to show the mass being used and a used to show the acceleration of the object. The variables used by Newton’s lay emphasis on the net force used exerted on the experiment in question. The relationship between force and motion was initially discussed by Aristotle (384-332B.C). He proposed that the natural state of an object was during rest, and force was required to put an object into motion, therefore, a continuous force was necessary to keep the body in motion. Galileo Galilei (1564-1642) argued that a body at rest is a unique case of a more broad case of constant motion. He noted that in the absence of friction acting on a body to slow it down, the body might continue to move in a straight line forever. He proposed that bodies remain at rest or in a state of constant motion unless an external force acts on them to change this motion. Frictional force is a force unlike other forces which accelerate or slows down a moving body (Lerner & Lawrence, page 51). Isaac Newton (1642-1727) sanctified the relationship between force and motion by proposing that the acceleration of a body is directly proportional to the net force acting on it and inversely proportional to the mass of the body. This law is summarized by the formula F=ma which is verified quantitatively in this experiment. Work done i.e. physical work defined in terms of physical quantities is expressed as a product of positional change multiplied by the component of force Fx in the displacement direction dx. W = Fx ?x = F?xcos? Where ? is the angle between the direction of displacement and the direction of force. This relationship can be written in the vector dot product form W = F??x The equations of uniform acceleration resulting from a constant force can be rewritten as: 2 1/2mvf2 – 1/2mvi2 = W = F??x This shows the relationship between work done and the resultant change in kinetic energy known as the work-energy theorem. This theorem is only valid given that W is the total work done on the object i.e. work done by all forces acting on the object. Experimental Procedure Description of apparatus: The sketch in the figure below shows the essential elements of the apparatus. The experiment was done using a low-friction sled on a flat, smooth level track. Due to the extremely low friction of the sled and the pulley, any mass hung on the string created a horizontal force that pulled the sled along the track. By changing either the amount of extra mass loaded on the sled or the amount of suspended mass placed on the weight hanger, the acceleration of the glider is consequently varied. Static friction The amount of suspended mass was gradually increased until the sled started moving. The experiment was repeated for different total masses on the sled. A graph of frictional force versus the normal force was plotted, and coefficient of static friction was determined from the slope. Kinetic friction A force was applied on the string connected to the suspended mass. The applied force and the mass of the string was varied, whereas the photo-gates and timer were used to record time The measurements of time for five different driving masses were measured and recorded. Each value of time was measured three times and the average value recorded. The acceleration was calculated from the values of measured distances and time. This acceleration was less than that in the absence of frictional force due to the frictional force. The frictional force was calculated from the decrease in acceleration. Data: Part A: Mass (g) Plastic surface m (g) Cork surface m (g) 250+92.70 50 100 500+92.70 100 170 750+92.70 130 240 1000+92.70 150 350 1250+92.70 190 450 Part B: M (g) m (g) a f 250+92.70=342.7 300 17.4973 10.955 500+92.70=592.7 300 17.4973 15.362 750+92.70=842.7 400 17.4973 20.654 1000+92.70=1092.7 500 17.4973 23.178 1250+92.70=1342.7 700 17.4973 27.349 d (cm) 20 30 40 50 60 t (s) 0.4488 0.5554 0.6045 0.6815 0.7753 ts (s2) 0.2014 0.3085 0.3654 0.4644 0.6011 d (cm) 20 30 40 50 60 t (s) 0.6350 0.7321 0.0377 0.4399 0.7560 ts (s2) 0.4032 0.5360 0.0014 0.1935 0.5715 d (cm) 20 30 40 50 60 t (s) 0.7330 1.0423 1.1547 1.7579 2.0386 ts (s2) 0.5373 1.0864 1.3333 3.0902 4.1559 d (cm) 20 30 40 50 60 t (s) 1.2205 1.4016 1.7880 1.8194 2.3204 ts (s2) 1.4896 1.9645 3.1613 3.3102 5.3843 d (cm) 20 30 40 50 60 t (s) 0.9500 1.2200 1.3045 1.2227 1.3239 ts (s2) 0.9025 1.4884 1.7017 1.4950 1.7527 Results/calculations: The results obtained show that when the mass of the suspended mass was increased it resulted in a greater force and acceleration to pull the glider. When the mass on the sledge was increased it decelerated. The data collected is a prediction of what would happen and is relatively accurate. The timing from start to the first photo-gate may not be so accurate because it was collected using a stop watch susceptible to human error. This data supports Newton’s second law of motion since acceleration was proportional to the mass when the net force was maintained at a constant. Static friction Graph 1 vertical axis: m (g) horizontal axis: M (g) slope: kinetic friction Kinetic friction µk = (1343-592.7)/(190-100) = 0.120 Kinetic friction Vertical axis: d (cm) horizontal axis: ts (s2) slope: a/2 a = 2slope = 2*(60-30)/(5.3843-1.9545) = 17.4937 Conclusion/discussion: In conclusion, the above results demonstrate the presence of Newton’s law in action as the acceleration was inversely proportional to the total time. The graphs give a clear indication that the data used, indeed supported Newton’s second law in action. This is evidenced from the sled since it does not move with equal velocity and acceleration as the accelerating masses. The experiment compares to Newton’s second law because acceleration was proportional to the mass when the net force was maintained at a constant since the laws states that to verify the existence of Newton’s second law acceleration depends directly on the force of an object. The errors in the result could be associated to the use of stopwatches which might have led to glitches in the time spent in the experiment. Work Cited Lerner, Lawrence S, and Lawrence S. Lerner. Physics: For Scientists and Engineers ; Modern Physics : for Scientists and Engineers. Boston [etc.: Jones and Bartlett, 1996. Print. Read More