# What is Newton's 2nd law: Definition and 135 Discussions

In classical mechanics, Newton's laws of motion are three laws that describe the relationship between the motion of an object and the forces acting on it. The first law states that an object either remains at rest or continues to move at a constant velocity, unless it is acted upon by an external force. The second law states that the rate of change of momentum of an object is directly proportional to the force applied, or, for an object with constant mass, that the net force on an object is equal to the mass of that object multiplied by the acceleration. The third law states that when one object exerts a force on a second object, that second object exerts a force that is equal in magnitude and opposite in direction on the first object.
The three laws of motion were first compiled by Isaac Newton in his Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), first published in 1687. Newton used them to explain and investigate the motion of many physical objects and systems, which laid the foundation for Newtonian mechanics.

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1. ### B How to characterize a rubber ball moving horizontally and bouncing off of a vertical wall?

So imagine we had a rubber ball and we threw it perpendicular to the surface of wall. The ball will obviously experience some “throwing” force — horizontal with respect to floor (let’s assume the ball is in perfect vacuum and there is no net torque). As it hits the wall, the normal force will...
2. ### Modeling a mass falling from one side of the Earth to the other

Then, by the 2nd Law $$F_g=\frac{Gm_1m_2}{y(t)^2}=m_1y''(t)\tag{1}$$ $$y''(t)=\frac{Gm_2}{y(t)^2}\tag{2}$$ I don't know how to solve (2) but it doesn't seem to be correct. I then thought about the following picture Consider the Earth as made up of infinitesimally small pieces of mass...
3. ### Having a hard time learning Newton's 2nd law

I'm taking college physics without calculus this semester and it's been quite the challenge to say the least. We recently covered free body diagrams and while I understand the different vectors in the FBD, making calculations is killing me. Specifically Newton's 2nd law. The problems range...
4. ### I Meaning of the terms in the formula of the net external force

The mathematical representation of the net external force on a system(obtained from Newton's second law) is ##\vec F_{net} = \frac {d\vec P}{dt}##, which is the rate of change of linear momentum of the system. If we substitute ##\vec P = m\vec v## into the formula for force and differentiate, we...
5. ### Rocket acceleration problem: confused about Newton's 2nd Law

TL;DR Summary: I approach a rocket acceleration problem using two approaches: F=d(m*v)/dt and F=ma. The resulting differential equations are different. What am I doing wrong? We have a ship with a mass-reaction rocket engine floating in space. The initial mass of the ship (including fuel) is...
6. ### Static Friction Required to Keep the System from Moving (Two Boxes)

Ok, logically, it must be that the static friction force of block A equal to the force of gravity on block B, so mass of block A is: m_A * 9.8 * 0.30 = m_B * 9.8 m_A * 2.94 = 2 * 9.8 m_A * 2.94 = 19.6 m_A \approx 6.7 kg. However, when I look at block A individually, there is one thing...
7. ### Two masses connected by a rope on a pulley on a ramp

I have no clue how to do the problem. I created a free body diagram for each block. I assume that it is simpler than I am making it out to be.
8. ### Unbalanced force to find altitude of airplane

Since the airplane is flying at a constant speed, then the lift force equals the weight of the airplane. This means that the lift force prior to acceleration is the mass * gravity constant = 29400 N. When the airplane increases horizontal speed, the lift force increases to 30 kN. This means...
9. ### Tangential velocity of rotating rod

1) ##LT\sin(\frac{\pi}{2}-\theta)-\frac{L}{2}mg\sin\theta=0\Rightarrow T=\frac{mg}{2}\tan\theta##. ##N_{x}-T=0, N_{y}-mg=0\Rightarrow N=\sqrt{N_x ^2+N_y ^2}=mg\sqrt{(\frac{\tan\theta}{2})^2 +1}## 2) ##E_{k_{fin}}=mg\frac{L}{2}[1+\cos\theta]## 3)...
10. ### Engineering Solving Moment Equations with Newton's 2nd Law: Help Needed!

So I set up 3 equation for this problem. 1st was the moment equation about point G, 2nd and 3rd were from applying Newton's 2nd law to each of the blocks. I thought once I set those equations up I could solve for alpha (angular acceleration) and then find acceleration of each block but when i...
11. ### Understanding Newton's 2nd Law

F=ma To check if this law works, we measure the left hand side and the right hand side and if they are equal then the law is working. To measure acceleration, we rapidly measure three positional measurements. Without appealing to the notion of the pull of gravity on an object, we measure the...
12. ### Is there a clever name for Newton's 2nd Law?

Summary:: We all know of the "law of inertia" nickname for Newton's 1st law, but is there a clever name for the 2nd as well? What about the 3rd? This may be the most inane question ever asked here, but I've spent some time searching and cannot find an answer. So many laws in physics and other...
13. ### Solving Newton's 2nd Law for Particle Falling in Medium

Good afternoon, I have a question regarding this derivation that I'm covering in Thornton & Marion's "Classical Dynamics of Particles and Systems". In it, we're covering the most basic equation of motion for a particle falling in a medium. I understand the process of starting with Newton's 2nd...
14. ### Newton's 2nd Law: Force, Mass and Acceleration

I´m currently studying Newtons 2nd law and I don't get how can force only depend on mass and acceleration and not on velocity.. I mean, if I punch something with my fist going at constant velocity ( acceleration=0) it stills has a force right?
15. ### Applying Newton's 2nd Law: A Scientist's Guide

Hi , How to approach the problem? Thanks
16. ### Covariance of Newton's 2nd Law under Galilean boosts

I'm reading a section in a textbook on the explanation of covariance of Newton's 2nd law under Galilean boosts. It's explained that ##\mathbf{a}=\mathbf{a'}## (where we're considering two frames ##S## and ##S'## moving inertially w.r.t. each other). Mass is assumed to not vary across the frames...
17. ### Movement contraptions that inspired Newton's 2nd law of motion

Besides gravity that always works perpendicular to Earth and thus pulls apples from apple trees towards the ground, there must have been some sort of mid 17th century human made contraption, that used a constant force, produced to move objects with or without wheels, in a direction parallel to...
18. ### Newton's 2nd Law: Pile of Books on a Table Being Moved

I drew a free body diagram for the books but it's not the same one in the correction. The static force Fs between the books and the table must be opposite to the motion but the correction does not the same and puts that vector in the same direction as the motion. Here's a drawing of the...
19. ### Understanding Newton's 2nd Law of Motion

Hello all I am trying to understanding Newton's 2md Law of Motion which states:- Force = Mass * Acceleration If I had a force of 10Newtons pushing an object along the ground (assume no friction) in a perfectly horizontal direction that has a Mass of 10kg then the objects acceleration would be...
20. ### External force on three blocks stacked

The figure is shown above. In order to facilitate solution, I need to separate each block and draw the free-body diagram (FBD) with all the forces acting on it. 1. Let me start with the lowest block. Let me put its FBD as shown below. For forces in the vertical direction, ##N_3 = N_2 + m_3 g...
21. ### Debate over the experimental procedure for Newton's 2nd Law

Hi, I'm currently having an ongoing debate with some teachers regarding a practical for Newton's Second Law. The prac involves a cart attached to some weights via a string on a pulley. The protocol as it stands has students add increasing mass to the end of the string (not changing the mass of...
22. ### Newton's 2nd law with oscilations

Homework Statement a car moving to the left with constent accelration. a ball is hanging from the ceiling held in 90 degrees to the ceiling until t=0, then it is realesed and start to swing. find the max angle. Homework Equations Newton's second law The Attempt at a Solution...
23. ### How Does the Chain Rule Apply to Newton's Second Law in Calculus?

Hello, I'm new to the language of calculus. I am learning about Newtons second law and I'm trying to understand it's forms in calculus. Excuse my notation, just trying to keep it as simple as possible. F=m * dV/dt I know V= dx/dt My textbook says you can 'apply chain rule' to obtain the...
24. ### Relationship between mass and acceleration

Hi. I am currently working on an assessed science experiment write-up. The experiment is about whether or not if mass of a pendulum bob affect the oscillation time for a simple pendulum. Obviously, the answer is no but I am struggling to write a concise and accurate explanation to why this is. I...
25. ### Using Newton's 2nd Law to find acceleration

So this is my first time posting on here and I hope I'm doing right! 1. Homework Statement A 75-kg snowboarder has an initial velocity of 5.0 m/s at the top of a 28 ∘ incline. After sliding down the 110-mlong incline (on which the coefficient of kinetic friction is μk = 0.18), the snowboarder...
26. A

### Determining what the y-intercept means in a force lab

Homework Statement In lab, we put a glider on an airtrack and used a pulley to move the glider. The mass on the pulley was changed with each iteration. I have created a graph to find the mass of the glider, but I don't know what the y-intercept is supposed to mean. The graph I have is linear...
27. ### Experiment Investigating Newton's 2nd Law

Homework Statement We were given two methods to look into Newton's 2nd Law and evaluate them by looking at where sources of error may have come from. They both involved accelerating a car across a table. A plastic track was used to guide the car along a straight path to make sure it went...
28. ### Galilean invariance: Newton's 2nd Law of motion

Consider a frame S' moving with speed u along +ve x direction with respect to another frame S. Consider a body moving with speed v along +ve x direction with respect to frame S . Both frame are inertials. here,force acting in S frame on the body is $$F\hat x=\frac {dp} {dt}\hat x,$$...
29. ### Understanding Newton's 2nd Law

I have a problem which reads: A frictionless pulley with zero mass is attached to the ceiling, in a gravity field of 9.81 m/s2 . Mass M2 = 0.10 kg is observed to be accelerating downward at 1.3 m/s2 and I have a solution which tells me to solve the problem use Newton's 2nd law: m1a1 = T1 -...
30. ### Newton's 2nd Law Problem, Angle exerted on block by surface

Homework Statement Problem: A 12.0-kg block is pushed to the left across a rough horizontal surface by a force that is angled 30.0◦ below the horizontal. The magnitude of the force is 75.0 N and the acceleration of the block as it is pushed is 3.20 m/s^2 . What angle does the force exerted on...
31. ### Why not use the product rule to expand Newton's 2nd law?

Hi! I was reading the Wikipedia article on Newton's laws of motion. I read there that when mass is a variable function of time as well as velocity, one cannot use the product rule of derivatives to expand d/dt(mv) It said that d/dt(mv)=mdv/dt+vdm/dt is WRONG I don't know why that is wrong. The...
32. ### Exploring Newton's 2nd Law: Rope on a Frictionless Table

Homework Statement A rope of mass M and length ##l## lies on a frictionless table, with a short portion ##l_0##, hanging through a hole. Initially the rope is at rest. Find the length of the rope through the hole as a function of time. Homework EquationsThe Attempt at a Solution So I know...
33. ### Newton's 2nd Law Problem: Finding Force and Direction of Travel

Homework Statement A 0.25 kg particle moves in an xy plane according to x(t) = -15 + 2t - 4t3 and y(t) = 25 + 7t - 9t2, with x and y in meters and t in seconds. Find formulas at time t<35 sec for the (a) the magnitude and (b) the angle (relative to the positive direction of the x axis) of the...
34. ### Dynamics -- Newton's 2nd law with acceleration

Homework Statement A sleigh with a mass of 150 kg from rest is horizontally towed to the left . This is done using a rope that makes an angle of 30 ° with the horizontale. The tensile force is 200 N. (Neglect friction forces.) a. What is the horizontal component of the force? b. What...
35. ### Problem using Newton's 2nd Law F= m x A

Homework Statement A ball whirling on the end of a string, length L Maximum tension in string before it breaks: T sub break Find an equation for the maximum speed of the ball , V sub max, in terms of the ball's mass, M, the breaking tension T sub break, and the gravitational acceleration g...
36. ### Newton's 2nd law for Massless Particles in SR

I think I have never seen a force equation for massless particles, I wonder if such thing exist or if not why not?
37. ### What is the flaw in my logic for solving this Newton's 2nd law problem?

Homework Statement http://postimg.org/image/z9uzlyt3p/ Homework Equations F=MA W=MG The Attempt at a Solution the force on the block must be gravity *its mass (weight) since it hangs, but because of the pulley and other box pulling the other way, creating an T, the force on the hanging block...
38. ### Understanding the Impact of Mass on Falling Objects: Applying Newton's 2nd Law

I am trying to explain why a small object falling from a short distance on another object does not have the same impact as a bigger object falling from the same height on another object by using Newton's 2nd Law but I get stuck all the time. Can somebody please help me?
39. ### Easy university problem Newton's 2nd law

The question is basically, a block with a mass "m" is sliding up and down on a incline plane with an angle of inclination that is β. The leaving velocity (Start velocity v_i) is v0 and the frictionskoefficient is between the plane and the block is μ. Determine the velocity "v" when the block...
40. ### Newton's 2nd law question -- pushing a block up an inclined ramp....

If a constant force is applied to an object and the force is pushing the object up a inclined ramp with constant velocity what is the acceleration if mass is unknown? F=ma F=m (1m/s^2) If i apply this equation then acceleration is 1m/s^2. Am i applying this formula correctly? thanks
41. ### Show that Newton's 2nd Law is *Not* valid in a reference frame

Homework Statement Show that Newton's Second Law is NOT valid in a reference frame moving past the laboratory frame of problem 1 with a constant acceleration? Problem 1: In a laboratory frame of reference, an observer notes that Newton's Second Law is valid. Show that it is also valid for an...
42. ### Show that Newton's 2nd Law is Not valid in accelerating reference frame

Homework Statement Show that Newton's Second Law is NOT valid in a reference frame moving past the laboratory frame of problem 1 with a constant acceleration? Problem 1: In a laboratory frame of reference, an observer notes that Newton's Second Law is valid. Show that it is also valid for an...
43. ### Expressing Newton's 2nd law in terms of momentum

Homework Statement Show that ##\Sigma \vec F = \frac {d \vec p}{dt} ## Homework Equations ##\Sigma \vec F = m \vec a ## ## \vec a = \frac {d \vec v}{dt} ## ## \vec p = m \vec v ## The Attempt at a Solution We need to prove that ## \frac {d \vec p}{dt} = m \vec a ##. When I physicists...
44. ### What is the acceleration of a car with a hanging mass at an angle of 23 degrees?

The problem states that a 3.4 kg object hangs at one end of a rope that is attached to a support on a car. The car and cruisin' and is accelerating, when it does this, the rope makes an angle of 23 degrees with the vertical. Acceleration of gravity is 9.8 m/s/s and the question is asking for the...
45. ### Chain problem to do with Newton's 2nd law.

Hello, I have a problem to do with a chain. You have a table with infinite drop and a chain of length l. The chain is let off at the end of the table. Assuming a frictionless table, calculate an expression for the speed of the chain. Could anyone help with this please? Best wishes...
46. ### How to get transfer function (freq. domain) from Newton's 2nd Law Eqn

Homework Statement I am given the following dynamic system. I want to find the transfer function, θ1(s)/T(s). The main body of the satellite, J1, acts like a large mass flying through space; space is essentially without friction and therefore no damping is imparted on the main body...
47. ### Newton's 2nd law for open mass systems

Sorry, but this will be a long post. This isn't homework, I'm reviewing physics after many years of neglect. Halliday & Resnick, 4th Ed., section on variable mass and rockets, refers the interested reader to an article, "Force, Momentum Change, and Motion," Martin S. Tiersten, Am. J...
48. ### Solving a Physics Problem: FBD and Newton's 2nd Law

Homework Statement Attached Homework Equations Attached The Attempt at a Solution 2ac + 3 = 0 => ac = 1.5m/s^2 upwards For FBD of C, Newton's 2nd law 2T - 200g = 200*1.5 => T = 1131N For FBD of the beam, Take moments about A, and assume beam is rigid (CCW positive): 2.5T - 3T -...
49. ### Understanding Newton's 2nd Law & Drude Assumption for Conductivity

I can't derive it properly even though it should be easy: From Newtons 2nd law: m dv/dt = -eE => v(t) = -meEt + v(0) (the latter will average out when taking average) Now the Drude assumption: An electron will on average travel a time τ before being scattered and starting its motion...
50. ### Different Forms of Newton's 2nd Law

I’m supposed to prove that if ΣF(v) = -Av^2, where A is a constant, then Δx = m/A * ln (v0/v) by using Newton’s second law in the form ΣF = m dv/dt. I can solve the problem by using the form ΣF = mv dv/dx; however, it’s specifically stated that I’m not allowed to use the law in that form...