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

Determine rank correlation coefficient, Determine Rank Correlation Coef...

Determine Rank Correlation Coefficient A group of 8 accountancy students are tested in Quantitative Techniques and Law II.  Their rankings in the two tests were as:

Exponential functions, The exponential functions are useful for descr...

The exponential functions are useful for describing compound interest and growth. The exponential function is defined as:          y = m. a x where '

Find out equation is a function, Example: Find out which of the following ...

Example: Find out which of the following equations functions are & which are not functions.                            y= 5x + 1 Solution The "working" definition of fu

Find out the center of mass, Find out the center of mass for the region bou...

Find out the center of mass for the region bounded by y = 2sin (2x), y =0 on  the interval  [0 , Π/2] Solution Here is a sketch (diagram) of the region along with the cent

Introduction to multiplication and division, INTRODUCTION :  When a Class ...

INTRODUCTION :  When a Class 5 child was given the problem 'If I paid Rs. 60 for 30 pencil boxes, how much did b pencil box cost?', he said it would be 60 x 30 = 1800. This

Inverse functions, We have seen that if y is a function of x, then fo...

We have seen that if y is a function of x, then for each given value of x, we can determine uniquely the value of y as per the functional relationship. For some f

Geometry, #question.onstruct/draw geometric shapes with specific condition....

#question.onstruct/draw geometric shapes with specific condition.

Ratio, what is the simplest form of 6:9?

what is the simplest form of 6:9?

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