Linear motion and vectors
Linear motion and vectors
There are three Newton’s laws of motion and vectors classified according to the variables of kinematics. They are the first law, second law and third law depending on the situation under investigation. The variables that are always used in linear motion are velocity, displacement and time. The classifications of Newton’s laws rely on these variables e. g. the first law discusses the relationship between velocity and time. This law is the simplest of all the three laws to understand.
The second law discusses the relationship between displacement and time; the third law explores the relationship between velocity and displacement, independent of time while the acceleration is constant. The first and second laws are best understood in real life situation as the acceleration is a constant depending on the force that is acting on an object. These laws can be written in equation form for mathematical reasons and proper understanding of the basic concepts involved in the underlying physics.
The first law is written as v = u ± at, where v is the final velocity, u is the initial velocity, at is the rate of change of velocity. The second law deals basically with displacement and is written as d = s ± 1/2at^2, where d is the final displacement, s is the initial displacement and at is the rate of change of displacement. The third law as earlier mentioned only deals with velocity and displacement and is written as v^2= u^(2 )± 2as, where v is the final velocity, u the initial velocity and (as) is the rate of change of velocity.
The purpose of this report is to investigate the application of Newton’s laws of linear motion in real life situations. These laws can be best understood when applied to real life scenarios. The case scenario in this context is the falling of apples from a tree. Initial Observation Initial observations from the scenario indicate that the apples while still on the tree are at rest. All the variables are at an initial value of zero. Though, there is a force that acts perpendicularly on the apples. This is the force of gravity causing the apples to fall at a constant acceleration. Initial Explanation
Explanations on this scenario have three parts involving all the three laws of linear motion. Scenario1: An apple falling from a tree. According to Newton anything falling experiences the force of gravity which is a constant of value 9. 8 ms^(-2). This is a constant acceleration. At this point we have established that the initial parameters; u which is the initial velocity is zero and s which is the initial displacement is zero. Thus the Newton’s laws of linear motion are reduced to v = ± gt for the first law and d = ± 1/2gt^2 and finally v^2 =± 2gs, this depends on the direction of the falling apples.
It is more than evident from the initial explanations that we can be able to determine the final velocity and time taken for the apples to fall from the trees to the ground using the laws of motion. Detailed Observations and Documentation Scenario1: First law From the First law of kinematics. It is assumed that the apples are falling under a constant acceleration of 9. 8 ms^(-2) i. e. the force of gravity. The only variables that can be determined in this scenario are time and velocity. It is therefore established that we can determine time taken for the apples to fall if we know the final velocity.
It is the reverse if we know the time taken. Scenario 2: Second law Using the second law it is already predetermined that the acceleration is a constant. Using the equation d = ± 1/2gt^2 . In this case we are able to determine the displacement of the apples from the trees, provided we know the time taken for the apples to fall. As in the first case we can also determine time if given the displacements of the apples from the trees. Scenario 3: Third law Here we use the equation v^2 =± 2gs. We can determine the displacements in relation to the velocities of the apples.
The same applies the other way round. Discussion and Analysis From our observation, it is evident that the apples will not fall at the same point but different places around the tree. This will give rise to different displacements, velocities and time variables. But to estimate the value of these variables, it is important to calculate their averages in order to come up with a common value on each variable. Conclusion The three Newton’s laws of motion basically try to explain realistic situations.
These equations of motion are valid only when acceleration is constant and motion is constrained to a straight line. In the real world this is an unrealistic notion. No object has ever traveled in a straight line with constant acceleration anywhere in the universe at any time. However it would be wrong to dismiss this section outright or as useless. In many instances, it is useful to assume that an object did or will travel along a path that is essentially straight and with an acceleration that is nearly constant. That is, any deviation from the ideal motion can be essentially ignored.
Motion along a curved path may also be effectively one-dimensional if there is only one degree of freedom for the objects involved. References Crowell, Benjamin, (2000), Newtonian Physics, (2000, Light and Matter), ISBN 0-9704670-1-X, 9780970467010 Galili, I. & Tseitlin, M. (2003). “Newton’s first law: text, translations, interpretations, and physics education. “. Science and Education 12 (1): 45–73. Newton, Isaac, “Mathematical Principles of Natural Philosophy”, 1729 English translation based on 3rd Latin edition (1726), volume 1, containing Book 1
University/College: University of California
Type of paper: Thesis/Dissertation Chapter
Date: 6 November 2016
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