<< Chapter < Page Chapter >> Page >

Step 3. Once a free-body diagram is drawn, Newton’s second law can be applied to solve the problem . This is done in [link] (d) for a particular situation. In general, once external forces are clearly identified in free-body diagrams, it should be a straightforward task to put them into equation form and solve for the unknown, as done in all previous examples. If the problem is one-dimensional—that is, if all forces are parallel—then they add like scalars. If the problem is two-dimensional, then it must be broken down into a pair of one-dimensional problems. This is done by projecting the force vectors onto a set of axes chosen for convenience. As seen in previous examples, the choice of axes can simplify the problem. For example, when an incline is involved, a set of axes with one axis parallel to the incline and one perpendicular to it is most convenient. It is almost always convenient to make one axis parallel to the direction of motion, if this is known.

Applying newton’s second law

Before you write net force equations, it is critical to determine whether the system is accelerating in a particular direction. If the acceleration is zero in a particular direction, then the net force is zero in that direction. Similarly, if the acceleration is nonzero in a particular direction, then the net force is described by the equation: F net = ma size 12{F rSub { size 8{ ital "net"} } = ital "ma"} {} .

For example, if the system is accelerating in the horizontal direction, but it is not accelerating in the vertical direction, then you will have the following conclusions:

F net x = ma size 12{F rSub { size 8{"net x"} } = ital "ma"} {} ,

F net y = 0 size 12{F rSub { size 8{"net y"} } =0} {} .

You will need this information in order to determine unknown forces acting in a system.

Step 4. As always, check the solution to see whether it is reasonable . In some cases, this is obvious. For example, it is reasonable to find that friction causes an object to slide down an incline more slowly than when no friction exists. In practice, intuition develops gradually through problem solving, and with experience it becomes progressively easier to judge whether an answer is reasonable. Another way to check your solution is to check the units. If you are solving for force and end up with units of m/s, then you have made a mistake.

Section summary

  • To solve problems involving Newton’s laws of motion, follow the procedure described:
    1. Draw a sketch of the problem.
    2. Identify known and unknown quantities, and identify the system of interest. Draw a free-body diagram, which is a sketch showing all of the forces acting on an object. The object is represented by a dot, and the forces are represented by vectors extending in different directions from the dot.
    3. Write Newton’s second law in the horizontal and vertical directions and add the forces acting on the object. If the object does not accelerate in a particular direction (for example, the x size 12{x} {} -direction) then F net x = 0 size 12{F rSub { size 8{"net x"} } =0} {} . If the object does accelerate in that direction, F net x = ma size 12{F rSub { size 8{"net x"} } = ital "ma"} {} .
    4. Check your answer. Is the answer reasonable? Are the units correct?

Problem exercises

A 5 . 00 × 10 5 -kg size 12{5 "." "00" times "10" rSup { size 8{5} } "- kg"} {} rocket is accelerating straight up. Its engines produce 1 . 250 × 10 7 N size 12{1 "." "250" times "10" rSup { size 8{7} } " N"} {} of thrust, and air resistance is 4 . 50 × 10 6 N size 12{4 "." "50" times "10" rSup { size 8{6} } " N"} {} . What is the rocket’s acceleration? Explicitly show how you follow the steps in the Problem-Solving Strategy for Newton’s laws of motion.

An object of mass m is shown. Three forces acting on it are tension T, shown by an arrow acting vertically upward, and friction f and gravity m g, shown by two arrows acting vertically downward.

Using the free-body diagram:

F net = T f m g = ma size 12{F rSub { size 8{"net"} } =T - f= ital "ma"} {} ,

so that

a = T f mg m = 1 . 250 × 10 7 N 4.50 × 10 6 N ( 5.00 × 10 5 kg ) ( 9. 80 m/s 2 ) 5.00 × 10 5 kg = 6.20 m/s 2 size 12{a= { {T` - `f` - ` ital "mg"} over {m} } = { {1 "." "250" times "10" rSup { size 8{7} } " N" - 4 "." "50" times "10" rSup { size 8{"6 "} } N - \( 5 "." "00" times "10" rSup { size 8{5} } " kg" \) \( 9 "." "80 m/s" rSup { size 8{2} } \) } over {5 "." "00" times "10" rSup { size 8{5} } " kg"} } ="6" "." 20" m/s" rSup { size 8{2} } } {} .

Questions & Answers

What is the law of demand
Yaw Reply
price increase demand decrease...price decrease demand increase
Mujahid
ıf the price increase the demand decrease and if the demand increase the price decrease
MUBARAK
all other things being equal, an increase in demand causes a decrease in supply and vice versa
SETHUAH
yah
Johnson
how is the economy of usa now
Johnson
What is demand
jude Reply
Demand is the quantity of goods and services a consumer is willing and able to purchase at various prices over a given period of time.
Yaw
yea
SETHUAH
Okay congratulations I'll join you guys later .
Aj
yes
MUBARAK
calculate elasticity of income exercises
HABANABAKIZE Reply
If potatoes cost Jane $1 per kilogram and she has $5 that could possibly spend on potatoes or other items. If she feels that the first kilogram of potatoes is worth $1.50, the second kilogram is worth$1.14, the third is worth $1.05 and subsequent kilograms are worth $0.30, how many kilograms of potatoes will she purchase? What if she only had $2 to spend?
Susan Reply
cause of poverty in urban
DAVY Reply
QI: (A) Asume the following cost data are for a purely competitive producer: At a product price Of $56. will this firm produce in the short run? Why Why not? If it is preferable to produce, what will be the profit-maximizing Or loss-minimizing Output? Explain. What economic profit or loss will the
Falak Reply
what is money
DAVY Reply
money is any asset that is generally acceptable for the exchange of goods and for the settlement of debts
Mnoko
what is economic
Stephen Reply
economics is the study of ways in which people use resources to satisfy their wants
Falak
what is Price mechanism
Dhany Reply
what is Economics
ERNESTINA
The study of resource allocation,distribution and consumption.
Emelyn
introduction to economics
Uday Reply
welfare definition of economics
Uday
examine the wealth and welfare definitions of economics
Uday
read book by ml jhingan
Anand
What do we mean by Asian tigers
Aeesha Reply
Dm me I will tell u
Shailendra
Hi
Aeesha
hi
Pixel
What is Average revenue
KEMZO
How are u doing
KEMZO
it is so fantastic
metasebia
uday
Uday
it is a group of 4 countries named Singapore, South Korea, Taiwan and Hong Kong because their economies are growing very faster
Anand
fyn
EDWARD
Please, average revenue is an amount of money you gained after deducted your total expenditure from your total income.
EDWARD
what's a demand
Edward Reply
it is the quantity of commodities that consumers are willing and able to purchase at particular prices and at a given time
Munanag
quantity of commodities dgat consumers are willing to pat at particular price
Omed
demand depends upon 2 things 1wish to buy 2 have purchasing power of that deserving commodity except any from both can't be said demand.
Bashir
Demand is a various quantity of a commodities that a consumer is willing and able to buy at a particular price within a given period of time. All other things been equal.
Vedzi
State the law of demand
Vedzi
The desire to get something is called demand.
Mahabuba
what is the use of something should pay for its opportunity foregone to indicate?
Random Reply
Why in monopoly does the firm maximize profits when its marginal revenue equals marginal cost
astrid Reply
different between economic n history
Falma Reply
A soccer field is a rectangle 130 meters wide and 110 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is that distance, to the nearest tenths place.
Kimberly Reply
Jeannette has $5 and $10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
August Reply
What is the expressiin for seven less than four times the number of nickels
Leonardo Reply
How do i figure this problem out.
how do you translate this in Algebraic Expressions
linda Reply
why surface tension is zero at critical temperature
Shanjida
I think if critical temperature denote high temperature then a liquid stats boils that time the water stats to evaporate so some moles of h2o to up and due to high temp the bonding break they have low density so it can be a reason
s.
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play




Source:  OpenStax, Abe advanced level physics. OpenStax CNX. Jul 11, 2013 Download for free at http://legacy.cnx.org/content/col11534/1.3
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Abe advanced level physics' conversation and receive update notifications?

Ask