newton's second law assignment

• Science Notes Posts
• Contact Science Notes
• Todd Helmenstine Biography
• Anne Helmenstine Biography
• Free Printable Periodic Tables (PDF and PNG)
• Periodic Table Wallpapers
• Interactive Periodic Table
• Periodic Table Posters
• Science Experiments for Kids
• How to Grow Crystals
• Chemistry Projects
• Fire and Flames Projects
• Holiday Science
• Chemistry Problems With Answers
• Physics Problems
• Unit Conversion Example Problems
• Chemistry Worksheets
• Biology Worksheets
• Periodic Table Worksheets
• Physical Science Worksheets
• Science Lab Worksheets
• My Amazon Books

Newton’s Second Law of Motion in Physics   Recently updated !

Newton’s second law of motion is one of the three fundamental laws formulated by Sir Isaac Newton. It describes how the motion of an object changes when a force is applied to it. The second law provides the quantitative relationship between force, mass, and acceleration, laying the groundwork for analyzing everything from the motion of everyday objects to the trajectories of spacecraft.

Isaac Newton formulated the second law of motion as part of his work in the late 17th century, published in Philosophiæ Naturalis Principia Mathematica (1687). Newton’s goal was providing a mathematical explanation for the motions of objects and celestial bodies, building on earlier works by scientists such as Galileo and Kepler. While Galileo had studied the acceleration of objects and the forces acting upon them, Newton formalized this relationship into a precise law.

Newton’s second law was revolutionary because it provided a framework that explained not only everyday terrestrial motion but also the motion of planets, moons, and comets. By defining force as the product of mass and acceleration, Newton introduced a quantitative way to link the concepts of force and motion, laying the foundation for classical physics.

Stating the Second Law

“The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The direction of the acceleration is in the direction of the applied net force.”

There are a few ways of stating Newton’s second law of motion:

• Force (F) equals the rate of change of momentum of an object ( d p) with respect to time ( d t). F = d p / d t
• Force (F) equal mass (m) multiplied by acceleration (a). This works when mass remains constant, as in classical mechanics. F = m·a
• Acceleration is directly proportional to force : For a constant mass, the greater the force applied, the greater the acceleration produced.
• Acceleration is inversely proportional to mass : For a constant force, a heavier object accelerates less than a lighter object.
• Force is needed to change motion : The force applied to an object determines how much its velocity (speed and direction) changes.

In SI units:

• F is the net force acting on the object (in newtons, N)
• m is the mass of the object (in kilograms, kg)
• a is the acceleration of the object (in meters per second squared, m/s²)

Relationships Between Force, Mass, and Acceleration

• If you double the force while keeping the mass constant, the acceleration doubles.
• If you halve the mass while keeping the force constant, the acceleration doubles.
• If you double the mass , the same force results in half the acceleration.

The Vector Nature of Force and Acceleration

Both force and acceleration are vector quantities, meaning they have both magnitude and direction. Keep in mind, the direction of a force is just as important as its strength..

• Vector Components : Break forces into components (e.g., horizontal and vertical forces) and analyze them using vector addition.
• Directional Implications : Acceleration always occurs in the direction of the net force. For example, if a force acts at an angle, the object accelerates in the direction of that force, which may be a combination of horizontal and vertical motion.

Importance of Newton’s Second Law

Newton’s second law is crucial because it explains how forces cause changes in motion. This lets us predict and understand the behavior of objects under different forces. It underpins much of classical mechanics and is applied across numerous fields including engineering, physics, and technology. Scientists and engineers apply this law in designing vehicles, analyzing structural forces, and predicting the motion of celestial bodies.

Practical applications include:

• Vehicle Acceleration : When designing cars, engineers use Newton’s second law in calculating how much force is needed to accelerate a vehicle to a certain speed. The heavier the car, the more force it takes for a given acceleration.
• Rocket Launch : During a rocket launch, Newton’s second law helps calculate the force produced by the engines required to accelerate the rocket’s mass against Earth’s gravitational pull.
• Sports : In sports like soccer or tennis, players use the second law intuitively to apply the right amount of force to the ball for a desired acceleration, such as a faster serve or stronger kick.

How the Second Law Differs from the Other Laws

All three of Newton’s laws apply under the condition that the objects are in inertial reference frames (i.e., not accelerating themselves). The second law, specifically, applies only when forces are net forces (the vector sum of all forces acting on the object).

• First Law (Law of Inertia) : Newton’s first law deals with objects at rest or in uniform motion. It states that without a net force, an object will not change its state of motion. The second law, in contrast, explains what happens when a net force is applied—it causes acceleration.
• Third Law (Action and Reaction) : Newton’s third law focuses on interactions between two objects. It states that for every action, there is an equal and opposite reaction. In contrast, the second law is concerned with the forces acting on a single object and the resulting acceleration.

Newton’s Second Law With Non-Inertial Frames of Reference

Working with the second law is straightforward in inertial reference frames. However, in non-inertial frames—such as those that are accelerating or rotating—there are additional forces called fictitious forces or pseudo-forces. These forces do not arise from any physical interaction, but from the observer’s acceleration within the reference frame.

For example:

• Centrifugal force in a rotating frame of reference appears to push objects outward but doesn’t exist in an inertial frame.
• Coriolis force is a fictitious force that acts on objects moving within a rotating system, such as wind patterns on Earth.

Common Misconceptions About Newton’s Second Law

• Force is Required to Keep an Object Moving : Many people mistakenly believe that a constant force is needed to keep an object moving. However, Newton’s first law states that an object in motion continues moving at constant velocity unless acted upon by a net force. The second law tells us that forces change an object’s motion (by causing acceleration) rather than maintain it.
• Mass and Weight are the Same : It’s common to confuse mass and weight . Mass is the amount of matter in an object, while weight is the force exerted on that object by gravity. The second law uses mass, not weight, for determining how an object accelerates in response to a force.
• Force and Velocity are Proportional : Some students mistakenly think that force is proportional to velocity, but this is incorrect. Force is proportional to acceleration, which is the change in velocity over time, not the velocity itself.

Example Problems

Example Problem 1: A 5 kg box is pushed with a force of 20 N. What is its acceleration?

Rearrange F = ma, solving for acceleration.

a = F / m = 20 N / 5 kg = 4 m/s 2

Example Problem 2: If the force on a 10 kg cart increases from 30 N to 60 N, how does the acceleration change?

Calculate the acceleration for both the initial and final conditions. Then, find the difference between the two values.

Initial acceleration:

a 1 = F 1 / m = 30 N / 10 kg = 3 m/s 2

New acceleration:

a 2 = F 2 /m = 60 N / 10 kg = 6 m/s 2

The acceleration doubles when the force is doubled.

Example Problem 3: If a car accelerates at 2 m/s² with a force of 1000 N, what force achieves the same acceleration with a car that is twice as heavy?

Acceleration remains constant, while mass doubles.

F 2 = ma = 2 × (1000 N) = 2000 N

More Example Problems:

• Block Sliding With Friction on a Flat Surface
• Weight in an Elevator

Derivation of Newton’s Second Law

Newton’s second law derives from the definition of acceleration and the concept of momentum.

• Start with momentum : Momentum (p) is a vector quantity that is the product of mass and velocity : p=mv
• Time rate of change of momentum : The net force on an object equals the rate of change of its momentum with respect to time: F= d p / d t
• Constant mass assumption : For most applications where the mass is constant, this simplifies to: F= m d v/ d t = ma. Thus, force equals mass times acceleration.

If the mass is not constant (as in a rocket expelling fuel), the second law still applies. However, the calculation involves momentum rather than mass times acceleration.

Example Problem:

A 1500 kg car is moving with a velocity of 20 m/s. The driver applies the brakes, producing a force of 4500 N in the opposite direction. How long does it take the car to stop?

• Initial momentum: p 0 = 1500 kg × 20 m/s = 30,000 kg⋅m/s
• Final momentum: p f = 0 (since the car stops)
• Net force: F = −4500 N

Rearrange F= d p / d t and solve for time.

t = Δp / F = 30,000 kg⋅m/s / 4500 N = 6.67 seconds

It takes about 6.67 seconds for the car to stop.

Newton’s Second Law and Relativity

Newton’s second law is a cornerstone of classical mechanics, but it requires modification when dealing with objects moving at speeds close to the speed of light , where relativistic effects come into play. In Einstein’s theory of relativity, mass increases with velocity. The relationship between force, mass, and acceleration becomes more complex.

At relativistic speeds, the momentum of an object is not simply p = mv. Instead, the equation becomes:

Here, γ is the Lorentz factor:

γ = 1 / (1 − v 2 /c 2 ) 1/2 ​

As velocity v approaches the speed of light c, the object’s mass effectively increases. Further acceleration requires a greater force. No object with mass reaches the speed of light because this requires an infinite force.

• Eisenbud, Leonard (1958). “On the Classical Laws of Motion”. American Journal of Physics . 26: 144–159. doi: 10.1119/1.1934608
• Feather, Norman (1959). An Introduction to the Physics of Mass, Length, and Time . United Kingdom: University Press.
• Frautschi, Steven C.; Olenick, Richard P.; et al. (2007). The Mechanical Universe: Mechanics and Heat (Advanced ed.). Cambridge: Cambridge University Press. ISBN 978-0-521-71590-4.
• José, Jorge V.; Saletan, Eugene J. (1998). Classical Dynamics: A Contemporary Approach . Cambridge: Cambridge University Press. ISBN 978-1-139-64890-5.
• Newton, Isaac; Chittenden, N. W.; Motte, Andrew; Hill, Theodore Preston (1846). Newton’s Principia: The Mathematical Principles of Natural Philosophy . University of California Libraries.

Related Posts

• Search forums

Follow along with the video below to see how to install our site as a web app on your home screen.

Note: this_feature_currently_requires_accessing_site_using_safari

• Fight Discussion
• UFC Discussion

Azamat Murzakanov (beat Menifield yesterday) from Nalchik in Kabardino-Balkaria, Russia

• Thread starter Robbocop
• Start date Aug 4, 2024

Purple Belt

• Aug 4, 2024

I found Murzakanov's performance against Menifield to be quite brutal, and the dude seems extremely legit. I have read Murzakanov is from Nalchik in Kabardino-Balkaria, Russia. It is a small Russian republic near Georgia, which is also almost entirely Muslim, comprised of Kabardians who are "One of the 12 Circassian tribes". This interested me because his style and appearance is similar to the many Dagestani Russian fighters of which there are too many to list. Also I am aware of Russian Muslim fighters coming from Chechnya like Chimaev, but I have never heard of fighters coming from Kabardino-Balkaria, or to be honest I was not familiar with the notion of Kabardians or Circassian tribes until I did some reading after watching Murzakanov's fight. My question is, does anyone know any info about Murzakanov, Kabardians, Circassian tribes etc? Are they pretty much very similar to Dagestanis or are they different in some distinct ways? That part of the world between Georgia and Russia seems a very interesting little area where there is some very rich culture and a lot of stuff going on. Sorry for the long post, interested in any comments from my fellow Sherdoggers. EDIT: I might just add, is there an MMA scene in Nalchik? Any other fighters from that region?  

Common Traits Across the North Caucasus:​

• Wrestling Base: Like Dagestani fighters, many athletes from Kabardino-Balkaria, Chechnya, and other North Caucasus regions have a strong background in wrestling, especially freestyle and Greco-Roman wrestling, which are popular in this area.
• Sambo and Judo: These disciplines are also commonly practiced, with many fighters transitioning from these sports into MMA, similar to their Dagestani counterparts.
• Cultural Emphasis on Combat Sports: The North Caucasus has a deep-rooted tradition of combat sports, with societal respect and support for wrestlers and fighters. This is also a key characteristic of Dagestani fighters.

Differences:​

• Ethnic and Cultural Identity: While Dagestani fighters are often Avar, Dargin, or of other Dagestani ethnicities, fighters from Kabardino-Balkaria might be Kabardian, Balkar, or Circassian. This influences their cultural identity and sometimes their fighting style, though the differences are subtle.
• Specific Training Focus: Fighters from different regions might emphasize different aspects of training due to local traditions or coaching preferences. For example, some Circassian fighters might have a strong background in traditional wrestling forms like Circassian Kuresh, which can influence their grappling approach in MMA.
• Representation in MMA: While Dagestani fighters are highly prominent in MMA (with fighters like Khabib Nurmagomedov bringing international attention to the region), fighters from Kabardino-Balkaria and Circassian tribes are less well-known but still making their mark. Azamat Murzakanov, for instance, is a fighter from Kabardino-Balkaria competing in the UFC.

Notable Fighters:​

• Azamat Murzakanov: From Kabardino-Balkaria, he has been making a name for himself in the UFC with a strong grappling and striking base.
• Imam Shamilov: A Circassian fighter with a strong wrestling and combat sambo background.

Embracing Entropy

Robbocop said: I found Murzakanov's performance against Menifield to be quite brutal, and the dude seems extremely legit. I have read Murzakanov is from Nalchik in Kabardino-Balkaria, Russia. It is a small Russian republic near Georgia, which is also almost entirely Muslim, comprised of Kabardians who are "One of the 12 Circassian tribes". This interested me because his style and appearance is similar to the many Dagestani Russian fighters of which there are too many to list. Also I am aware of Russian Muslim fighters coming from Chechnya like Chimaev, but I have never heard of fighters coming from Kabardino-Balkaria, or to be honest I was not familiar with the notion of Kabardians or Circassian tribes until I did some reading after watching Murzakanov's fight. My question is, does anyone know any info about Murzakanov, Kabardians, Circassian tribes etc? Are they pretty much very similar to Dagestanis or are they different in some distinct ways? That part of the world between Georgia and Russia seems a very interesting little area where there is some very rich culture and a lot of stuff going on. Sorry for the long post, interested in any comments from my fellow Sherdoggers. EDIT: I might just add, is there an MMA scene in Nalchik? Any other fighters from that region? Click to expand...

taugrim said: Imam Shamilov: A Circassian fighter with a strong wrestling and combat sambo background. Click to expand...

EndlessCritic

Titanium belt.

Murzakanov moves way faster than he looks. He really is a modern Fedor.  

Carrotman23

taugrim said: Obligatory ChatGPT question & response: In terms of MMA, how many fighters hail from Murzakanov, Kabardians, Circassian tribes etc? Are they pretty much very similar to Dagestanis or are they different in some distinct ways in terms of combat disciplines? Fighters from the North Caucasus region, including those from Kabardino-Balkaria, where the Murzakanov name originates, as well as Circassian tribes and other ethnic groups, are part of a broader tradition of martial arts that has produced many successful MMA athletes. While they share some similarities with fighters from Dagestan, there are also distinct differences. Common Traits Across the North Caucasus:​ Wrestling Base: Like Dagestani fighters, many athletes from Kabardino-Balkaria, Chechnya, and other North Caucasus regions have a strong background in wrestling, especially freestyle and Greco-Roman wrestling, which are popular in this area. Sambo and Judo: These disciplines are also commonly practiced, with many fighters transitioning from these sports into MMA, similar to their Dagestani counterparts. Cultural Emphasis on Combat Sports: The North Caucasus has a deep-rooted tradition of combat sports, with societal respect and support for wrestlers and fighters. This is also a key characteristic of Dagestani fighters. Differences:​ Ethnic and Cultural Identity: While Dagestani fighters are often Avar, Dargin, or of other Dagestani ethnicities, fighters from Kabardino-Balkaria might be Kabardian, Balkar, or Circassian. This influences their cultural identity and sometimes their fighting style, though the differences are subtle. Specific Training Focus: Fighters from different regions might emphasize different aspects of training due to local traditions or coaching preferences. For example, some Circassian fighters might have a strong background in traditional wrestling forms like Circassian Kuresh, which can influence their grappling approach in MMA. Representation in MMA: While Dagestani fighters are highly prominent in MMA (with fighters like Khabib Nurmagomedov bringing international attention to the region), fighters from Kabardino-Balkaria and Circassian tribes are less well-known but still making their mark. Azamat Murzakanov, for instance, is a fighter from Kabardino-Balkaria competing in the UFC. Notable Fighters:​ Azamat Murzakanov: From Kabardino-Balkaria, he has been making a name for himself in the UFC with a strong grappling and striking base. Imam Shamilov: A Circassian fighter with a strong wrestling and combat sambo background. Overall, while there are many similarities due to shared regional training practices and combat sports traditions, there are also unique cultural and stylistic elements that distinguish fighters from different North Caucasus ethnic groups. Click to expand...

Siver! said: Who? I can't even get a profile lol Click to expand...

Ashmouz is Circassian (his ancestors moved from Russia to Ottoman Empire and nowadays this territory is Israel). In other promotions I think there is Berkhamov in Bellator, Tokov brothers is Balkar through their mother, there were Dugulubgov in WSOF or PFL and founder/owner of K-Dojo gym in New Jersey is Circassian and his nephew was an mma fighter.  

I feel like Husky needs to aware of this tism that is going on in this thread.  

DoctorStoppage

I’m been very impressed with Murzakanov’s last few fights, I think he’ll make waves in the division. I believe that Circassia was a Christian kingdom on the Black Sea that got conquered by the Ottoman Empire back in the day. Think Circassia or their royalty was related to the Byzantine Empire too. I don’t feel like looking it up to be sure though.  

Carrotman23 said: Chat GPT really is good at making banal points or regurgitating outright bullshit that can be said in one or two sentences and extending it to multiple paragraphs. Literally just said " they are similar because they are from similar parts of the world that emphasize martial arts and especially wrestling." And "they are different ethnicities and there are more Dagestanis in MMA" Wow what a break through lol . Not saying this is necessarily the case here, but Chat GPT and similar AI programs have been known to just literally make shit up ha. Like when asked medical questions it can spit out fancy sounding medical advice/analysis that's actually just complete world salad bullshit with no consistently logical thread . This is because these "AI" programs aren't actually what most people would call "AI" . They are just advanced algorithms that compile information, but they have no base logic or perspective to center reality . For instance if you ask an AI "what would it take to carry the San Francisco bridge to New York" , some programs will try and answer it , obviously this is an illogical question. Nothing with "intelligence" would try and answer that question. Or if you ask it "what's the perspective of a ham sandwich" it will try and describe what it's like to be a ham sandwich lol . They are just blank input algorithms with powerful computing. That's why "AI" has become bigger as GPU's get more powerful, it's just raw data being able to be read extremely quickly, it's nothing resembling conscious intellect. Click to expand...

Most K Dojo dudes or guys cornered by Murad Keshtov are Circassians  

The Siege said: I tried now and it seemed to have gotten dumber lol I am not sure if they nerfed the algorithm on purpose to get us to upgrade the paid version, but it was getting a lot of basic things wrong. Click to expand...

EndlessCritic said: Murzakanov moves way faster than he looks. He really is a modern Fedor. Click to expand...

KavkazDominance

BJJ4Tone said: That whole Caucuses region is a hot bed for combat sports/martial arts. For years, people only knew Dagestan and only knew them for wrestling. Buvaisar Saitiev, Adam Saitiev, Abdulrashid Sadulaev, etc. But Chechnya (Tons of MMA fighters), Kabardino-Balkaria (Bibert and Albert Tumenov, Murzakanov), Ingushetia (Movsar Evloev, Musa Evloev), North Ossetia-Alania (Arsen Fadzayev, Artur Taymazov, Makharbek Khadartsev, Soslan Andiyev), Georgia (Geno Petriashvili, Levan Tediashvili), Azerbaijan (Haji Aliev, Toghrul Azgarov) and Armenia (Artur Aleksanyan, Edmond Tarverdyan ) have all produced COUNTLESS high-level athletes. Each region is very unique from the others, but the one thing they definitely have in common is their high percentage of elite combat athletes. Click to expand...

The_Renaissance

Sherdog bunceweight champion.

• Aug 6, 2024

Yellow Belt

Is he Muslim? I didnt see that mentioned in the first post and feel like that's kind of an important part of the Dagestani culture. I would have assumed he was Eastern Orthodox, And thus not similar to the Dagestani school in anyway way... But I'm still learning too. Am also a huge fan of his.  

RichardHarrow

'arrow.

WillyWill said: Is he Muslim? I didnt see that mentioned in the first post and feel like that's kind of an important part of the Dagestani culture. I would have assumed he was Eastern Orthodox, And thus not similar to the Dagestani school in anyway way... But I'm still learning too. Am also a huge fan of his. Click to expand...

Feniamin said: Ashmouz is Circassian (his ancestors moved from Russia to Ottoman Empire and nowadays this territory is Israel). In other promotions I think there is Berkhamov in Bellator, Tokov brothers is Balkar through their mother, there were Dugulubgov in WSOF or PFL and founder/owner of K-Dojo gym in New Jersey is Circassian and his nephew was an mma fighter. Click to expand...

• Aug 14, 2024

Joinho10 said: Ali Bagov in ACA MMA is one aswell. Click to expand...

Latest posts

• Latest: usernamee
• A moment ago

• Latest: Ballsaque

• Latest: Greyscale

• Latest: Dogpound2020
• 2 minutes ago

• Latest: The_Renaissance

Forum statistics

Share this page.

• This site uses cookies to help personalise content, tailor your experience and to keep you logged in if you register. By continuing to use this site, you are consenting to our use of cookies. Accept Learn more…

Poor Economic Outlook and Lack of Security Undermine Kabardino-Balkaria’s Governor