What is Newton’s Second Law of Motion

Newton’s Second Law of Motion Definition   

Newton’s Second Law of Motion states that when a resultant force acts on a body, the body’s acceleration due to the resultant force is directly proportional to the force.

As an equation, we write,

\sum\vec{F}=m\vec{a}

The summation sign, \Sigma, indicates that one needs to add all the forces using vector addition and find the resultant (or the net) force. According to Newton’s second law of motion, the resultant force is proportional to acceleration. This means that if the resultant force acting on a body is doubled, then the body’s acceleration would also double. If the resultant force is halved, the acceleration will also be halved and so on.

An alternative way to express Newton’s second law of motion is to use momentum. In this definition, the resultant force experienced by a body is equal to the rate of change of momentum of the body

\sum\vec{F}=\frac{\mathrm{d}\vec{p}}{\mathrm{d}t}

If we take the case of a body whose mass stays constant, since \vec{p}=m\vec{v}, this expression becomes:

\sum\vec{F}=m\frac{\mathrm{d}\vec{v}}{\mathrm{d}t}=m\vec{a}

Now, let’s look at a simple example of Newton’s second law of motion.

Newton’s Second Law of Motion Example

Two pirates tug at a treasure chest, which has a mass of 55 kg. One pirate pulls it towards the Sea with a force of 18 N while the other pulls it away in the opposite direction with a force of 30 N. Find the acceleration of the treasure chest.

The two forces given by the two pirates are in the opposite directions, so the resultant force is (30-18) = 12 N away from the Sea. Now, using Newton’s second law, we have a=\frac{m}{\sum F}=\frac{55}{18}=\mathrm{3.05 \:N} away from the Sea.

How to Solve Newton’s Second Law Problems

Problems Involving Lifts (Elevators)

To conclude this article, we will look at a classic physics problem involving the reaction force on a person in a lift. Suppose a person with mass  m is standing inside a lift. Forces acting on the person are the weight mg acting downwards and the reaction force R from the floor of the lift acting upwards.

Newton's Second Law of Motion Example

 First, let’s take the case when the lift is still. The forces on the person are balanced. i.e. R=mg.

Now, suppose the lift is accelerating downwards. In this case, there is a resultant force acting downwards on the person. The resultant force gives an acceleration a. Then, taking downwards direction to be positive, we have

mg-R=ma\Rightarrow R=m(g-a).

Suppose the lift now travels upwards, with an acceleration of the same magnitude. In this case,

mg-R=-ma\Rightarrow R=m(g+a).

So, the person experiences a larger reaction force when the lift is accelerating upwards. This makes intuitive sense: as the floor of the lift is rushing up to meet the person, they should feel a larger force than when the floor is trying to “fall away” from them. The lower reaction force experienced as the lift accelerates downwards is what often makes you feel lighter when you take a lift.

About the Author: Nipun


Related pages


what is an example of a nonpolar moleculetransmittance vs absorbancesimilarities between command and market economywhat is meant by valencyhow are frankenstein and the monster differentmass number and atomic mass differencewhat does seize to amaze me meandifference between a solute and a solventdefinition of inverting amplifierwhat are the differences between myths and legendsdifference between myth and legendnoninverting amplifierdefinition cytosinethe difference between thermoplastic and thermosetting plasticprotoplasm functiontax free threshold definitionhow to analyze a poemthe difference between bipolar and borderline personality disorderdefine subordinate conjunctionkinds of descriptive adjectivesstoma or stomataboarding expenses meanswhat is kinetochoreto believe synonymwhat is the difference between fructose and glucosetime difference between edt and estchemical symbol for nitratewhat are the differences between light and electron microscopesdenotation examples for kidsexamples of melodramaswhat is the difference between a panther and a jaguarexamples of irony and sarcasmfamous medieval writerselocution speechconnotations and denotations examplesdefinition of nonvasculardifferentiate between gymnosperms and angiospermsdifference between wallaby and kangaroodifference between a pail and a bucketexamples of allomorphs in englishdifference between budding and fissionmetaphor personificationcolloids and suspensionsfigurative language deftulsi botanical namehow do you write a cinquain poemsynonym for stupidstanza in literatureacculturation examplesare baking soda and bicarbonate of soda the same thinggreetings letter to a frienddieing vs dyingdada surrealismdada and surrealismmonozygotic twins definechemistry of chromyl chloride testdint or dentwhat is the difference between archaeology and anthropologyedible and eatablewhat is the difference between overweight and obesedifference between laying and lyingtofu is paneerwhat is the difference between impedance and resistancecystitis and pyelonephritisshort story with summary and moral lessonisotonic solution definitiondifference between concentration and molaritydefine charging by inductionyorkie or silkydifference between starch and sugarwhat is the difference between a biscuit and a sconefructose aldose or ketoseincidence pluralxanthan gum chemical formulaare homologous chromosomes identicalwhat is the difference between pride and egodutch hound dogmarginal costing definition accountingtetrad in meiosisendocytosis definition biologydifferentiate saturated and unsaturated hydrocarbonspoured fondant cakephagocytosis definewhat are fixtures and fittings in accountingdifference agnostic atheist