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

Converting mixed numbers to improper fractions, Q. Converting Mixed Numbers...

Q. Converting Mixed Numbers to Improper Fractions? Ans. Converting a mixed number to an improper fraction is easy. A single multiplication, and then a single addition:

Determine if r is equivalence relation or a partial ordering, Let R be the ...

Let R be the relation on the set of ordered pairs of positive integers such that ((a, b), (c, d)) ∈ R if and only if ad = bc.  Determine whether R is an equivalence relation or a p

Quantitative, A lobster catcher spends $12 500 per month to maintain a lobs...

A lobster catcher spends $12 500 per month to maintain a lobster boat. He plans to catch an average of 20 days per month during lobster season. For each day, he must allow approx

probability that they are both the same color, Consider two bags, A and B,...

Consider two bags, A and B, with the following contents a)    A single marble is drawn from each bag. What is the probability of getting a white marble out of Bag A and a red marb

Find the distance of the bird from the girl, A boy standing on a horizontal...

A boy standing on a horizontal plane finds a bird flying at a distance of 100m from him at an elevation of 300. A girl standing on the roof of 20 meter high building finds the angl

Earth Day Bags, #question.I headed into Target in Webster, NY for an advert...

#question.I headed into Target in Webster, NY for an advertized free Earth Day Bag in (local newspaper and on your entrance store doors) and at 10:30 a.m. on Sunday, April 22nd, th

Formulas, A house painter uses the formula, c = $110.50 + $39.50h, where c ...

A house painter uses the formula, c = $110.50 + $39.50h, where c is the total cost and h is the number of hours he works, to determine how much he charges his customers. How much s

How do you find the second minimum spanning tree of a graph, How do you fin...

How do you find the second minimum spanning tree of a graph?  Find the second minimum spanning tree of the following graph.  Ans: The second minimum spanning tree is acq

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