Direction fields in newtons law, Mathematics

One of the simplest physical situations to imagine of is a falling object. Thus let's consider a falling object along with mass m and derive a differential equation as, when resolved, will provide us the velocity of the object at any time, t.  We will suppose that only gravity and air resistance will act upon the object like it falls.  Below is a figure demonstrating the forces which will act upon the object.

1618_differential equation.png

Before describing all the terms in such problem we require to set some conventions. We will suppose that forces acting in the downward direction are positive forces whereas forces which act in the upward direction are negative. Similarly, we will suppose that an object moving downward that is a falling object will have a positive velocity.

Here, let's take a look at the forces demonstrated in the diagram above.

 FG is the force because of gravity and is provided by FG = mg where g is the acceleration because of gravity.  In this type of class I use g = 9.8 m/s2 or g = 32 ft/s2 based on whether we will utilize the metric or British system.

FA is the force because of air resistance and for this illustration we will suppose that this is proportional to the velocity, v, of the mass. Hence the force because of air resistance is then given through FA = -gv ,  where g > 0.  Remember that the "-" is needed to get the correct sign upon the force.  Both g and v are positive and the force is acting upward and thus must be negative.  The "-" will provide us the correct sign and thus direction for this force.

Posted Date: 4/10/2013 3:12:48 AM | Location : United States

Related Discussions:- Direction fields in newtons law, Assignment Help, Ask Question on Direction fields in newtons law, Get Answer, Expert's Help, Direction fields in newtons law Discussions

Write discussion on Direction fields in newtons law
Your posts are moderated
Related Questions
how to solve imaginary number such as like (-3v-5)² ?? Can I cancel the radical sign and the power of two ? and square the -3 and times to -5 ? hope you will answer this :) thanks

how to find x,y and z in parallelograms,rhombus etc.

Tabulated values of the dynamic and kinematic viscosity of aqueous sodium chloride solutions have been researched in the academic literature (Kestin et al 1981). The data availab

You are required to implement Kruskal's algorithm for finding a Minimum Spanning Tree of Graph.  This will require implementing : A Graph Data Type (including a display meth

find the value of 0 that makes cos 21 degrees = sin 0 statement true.

Is it possible to add two vectors of unequal magnitude and get a resultant of zero?Please explain also. Ans) no it is not possible as .. if the magnitude is diffrent then they c

can i get some triangle congruence proofs help?

Data collected from the STATS 10x class survey one semester included responses to questions on the number of different sexual partners and on the number of pairs of shoes the stude

Give the Definition of Logarithms ? A logarithm to the base a of a number x is the power to which a is raised to get x. In equation format: If x = ay, then log a x = y.

Can you help me with what goes into 54