Direction fields in newtons law, Mathematics

Assignment Help:

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.


Related Discussions:- Direction fields in newtons law

Multiply 3 (x + 4) = 3x + 12 to find out the total perimeter, Jake required...

Jake required to find out the perimeter of an equilateral triangle whose sides measure x + 4 cm each. Jake realized that he could multiply 3 (x + 4) = 3x + 12 to find out the total

The shape of a graph, The Shape of a Graph, Part II : In previous we saw h...

The Shape of a Graph, Part II : In previous we saw how we could use the first derivative of a function to obtain some information regarding the graph of a function.  In this secti

Marketing, In a 2500 word report do the market analysis of China. Under thi...

In a 2500 word report do the market analysis of China. Under this you have to explain: - What are the advantages and disadvantages for foreign company to set up its business cent

Find out the volume of the solid -y = (x -1) ( x - 3)2, Find out the volume...

Find out the volume of the solid obtained by rotating the region bounded by y = (x -1) ( x - 3) 2 and the x-axis about the y-axis. Solution Let's first graph the bounded r

Transforming the base of logarithms, Suppose that we know the logarit...

Suppose that we know the logarithms of all numbers which are expressed to base 'a' and we are required to find the logarithms of all these numbers to base 'b'. We

Write the next two terms, Write the next two terms √12, √27, √48, √75.........

Write the next two terms √12, √27, √48, √75................... Ans:    next two terms √108 , √147 AP is 2 √3 , 3 √3 , 4 √3 , 5 √3 , 6 √3 , 7 √3 ......

Lognormal distribution, The Lognormal Distribution If ln(X) is a normal...

The Lognormal Distribution If ln(X) is a normally distributed random variable, then X is said to be a lognormal variable. If P1, P2, P3, ... are the prices of a scrip in per

Design a game strategy involves process of learning maths, Doing these sums...

Doing these sums initially in this way helps children see why they carry over numbers to the next column. You may like to devise some related activities now. , EI) Give activ

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd