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In a similar investigation where the mass is kept constant, but the applied force is varied, you will find that the bigger the force is, the faster the object will move. The acceleration of the trolley is therefore directly proportional to the resultant force. In mathematical terms:

a F

Rearranging the above equations, we get a F m OR F = m a

Newton formulated his second law as follows:

Newton's Second Law of Motion

If a resultant force acts on a body, it will cause the body to accelerate in the direction of the resultant force. The acceleration of the body will be directly proportional to the resultant force and inversely proportional to the mass of the body. The mathematical representation is:

F = m a .

Khan academy video on newtons laws - 2

Applying newton's second law

Newton's Second Law can be applied to a variety of situations. We will look at the main types of examples that you need to study.

A 10 kg box is placed on a table. A horizontal force of 32 N is applied to the box. A frictional force of 7 N is present between the surface and the box.

  1. Draw a force diagram indicating all the horizontal forces acting on the box.
  2. Calculate the acceleration of the box.
  1. We only look at the forces acting in a horizontal direction (left-right) and not vertical (up-down) forces. The applied force and the force of friction will be included. The force of gravity, which is a vertical force, will not be included.

  2. We have been given:

    Applied force F 1 = 32 N

    Frictional force F f = - 7 N

    Mass m = 10 kg

    To calculate the acceleration of the box we will be using the equation F R = m a . Therefore:

    F R = m a F 1 + F f = ( 10 ) ( a ) 32 - 7 = 10 a 25 = 10 a a = 2 , 5 m · s - 1 towards the left

Two crates, 10 kg and 15 kg respectively, are connected with a thick rope according to the diagram. A force of 500 N is applied. The boxes move with an acceleration of 2 m · s - 2 . One third of the total frictional force is acting on the 10 kg block and two thirds on the 15 kg block. Calculate:

  1. the magnitude and direction of the frictional force present.
  2. the magnitude of the tension in the rope at T.
Two crates on a surface
  1. Always draw a force diagram although the question might not ask for it. The acceleration of the whole system is given, therefore a force diagram of the whole system will be drawn. Because the two crates are seen as a unit, the force diagram will look like this:

    Force diagram for two crates on a surface
  2. To find the frictional force we will apply Newton's Second Law. We are given the mass (10 + 15 kg) and the acceleration (2 m · s - 2 ). Choose the direction of motion to be the positive direction (to the right is positive).

    F R = m a F applied + F f = m a 500 + F f = ( 10 + 15 ) ( 2 ) F f = 50 - 500 F f = - 450 N

    The frictional force is 450 N opposite to the direction of motion (to the left).

  3. To find the tension in the rope we need to look at one of the two crates on their own. Let's choose the 10 kg crate. Firstly, we need to draw a force diagram:

    Force diagram of 10 kg crate

    The frictional force on the 10 kg block is one third of the total, therefore:

    F f = 1 3 × 450

    F f = 150 N

    If we apply Newton's Second Law:

    F R = m a T + F f = ( 10 ) ( 2 ) T + ( - 150 ) = 20 T = 170 N

    Note: If we had used the same principle and applied it to 15 kg crate, our calculations would have been the following:

    F R = m a F applied + T + F f = ( 15 ) ( 2 ) 500 + T + ( - 300 ) = 30 T = - 170 N

    The negative answer here means that the force is in the direction opposite to the motion, in other words to the left, which is correct. However, the question asks for the magnitude of the force and your answer will be quoted as 170 N.

Questions & Answers

anyone know any internet site where one can find nanotechnology papers?
Damian Reply
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
many many of nanotubes
what is the k.e before it land
what is the function of carbon nanotubes?
I'm interested in nanotube
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Maths test. OpenStax CNX. Feb 09, 2011 Download for free at http://cnx.org/content/col11236/1.2
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