What is Newton's second law: Definition and 264 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. Lotto

    B What forces act on a bar when you do pull-ups?

    I am not sure here, even though it is probably simple. If you just hang on the bar and don't move up, you act on the bar with a force equal to your weight. But when you want to do a pull-up, I would intuitively say that you act on the bar with a higher force. But when I think about it I would...
  2. lola9

    Two blocks in contact -- find the force between them

    In this problem why do I need to use this formula? F – F12 = m1 a along the x-axis. What does F12=-F21 stand for? And I don't understand when they say to find the magnitude of the forces between the two blocks
  3. K

    I Acceleration in Newton's second law

    Hi, I was looking over one of the sample examples in Halliday and Resnick, the one about the scale in the elevator. There is something that bugs me about it, and I'd like to know if you agree. The example has to do with finding the reading of a scale that is measuring someone's weight in a...
  4. A

    Newton's Second Law (Pulley Sustem)

    Two masses, M1=4.0 Kg, and M2=20 Kg, are attached by a rope that crosses over a massless, frictionless pulley. M1 slides horizontally and experiences a kinetic frictional force due to its motion across the surface. The coefficient of kinetic friction is uk = 0.638. When solving the problem...
  5. ElectroMaster88

    Application of Newton's second law to a horizontal pulley

    I don't understand how to solve these, and I don't understand how an horizontal force can affect the friction force if it's defined by μ*N, and the additional force affect neither of those. I also don't understand how there is a range of possible forces that F can be to make the system static...
  6. C

    Explanation for Newton II giving negative mass in my Physics lab results please

    I am trying to verify Newton II. The setup I am using is, Where ##m_1 = 0.887 kg## is a cart and ##m_2 = 0.02016 kg## is a small hanging mass. There is a force sensor on ##m_1## to measure the force acting on it from the string and the acceleration of the cart. To verify Newton's Second Law...
  7. C

    General form of Newton II -- Not understanding this step in the derivation

    For this, Does someone please know how do we derive equation 9.9 from 9.8? Do we take the limits as t approach's zero for both sides? Why not take limit as momentum goes to zero? Many thanks!
  8. A

    Circular Motion - Newton's Second Law: Bead on a Rotating Hoop

    For whatever reason, I'm having a hard time conceptualizing this problem. I understand that the tangential components of all forces involved need to cancel out in order for the bead to be stationary. I also understand that there is a mgsinθ in the negative θ-hat direction. What I don't...
  9. W

    B Newton's second law -- rockets

    I am having difficulty understanding the information below. In the second line it states that F=0 as there is no external force on the system. However it later calculates acceleration of the rocket. How can Force=0 if there is acceleration? (This is the first time I have encountered the...
  10. J

    I Newton's second law and pressure wave propagation

    Imagine a long deformable rod which has just been hammered on the top end (the bottom end is clamped to Earth). Consider a time interval $dt = t_{2} - t_{1}$ in which the pressure wave is traveling somewhere within the length of the rod (meaning some portion of the object has already "felt" the...
  11. A

    B Newton's second law about cars

    The car that accelerates must enter according to the equation below the external force, while such an external force does not seem to exist. The force of friction between the car and the road is in the opposite direction of motion ؟
  12. R

    Newton's second law (My turtle named Newton being accelerated)

    https://www.khanacademy.org/science/physics/forces-Newtons-laws/Newtons-laws-of-motion/a/what-is-Newtons-second-law How do I find the horizontal right components force? It states it is 22 N but there is no reason that the left horizontal component is the same as the right. I thought the...
  13. Franklie001

    Newton's second law -- Crate sliding in the back of an accelerating truck

    Hi everyone is able to help solve this question for my assignment in university? I've draw a free body diagram for each component of the question but now i am stuck. [Mentor Note -- Poster has been reminded to show their work when starting a new schoolwork thread]
  14. curiousPep

    Confused about which forces are external when Newton's Second Law is used

    So I have a trolley of mass m that moves on a straight line. A sphere of mass m, is attached on the trolley with a light string of length a and it is left to oscillate. Just to give some idea of their positions: r_trolley = xi r_sphere = (x-asinθ)i - acosθj (θ is the angle between the string...
  15. D

    Exploring Electron Rockets for Interstellar Travel

    Hi all, Why not build an electron rocket? Why won't this idea work? Seems like someone could just hitch an electron gun onto a spaceship. Boom! Electron Rocket. I was thinking about ion thrusters. These use ions to achieve thrust. They are problematic for achieving a high delta V because...
  16. T

    Deriving Momentum From Newton's Second Law of Motion

    Hello everyone I was hoping someone could shed some light on the following:- I am trying to derive the equation of Momentum from Newton's 2nd Law. What I know is the following:- I don't know how to get from Force = Mass * Acceleration TO Momentum = Mass * Velocity. I have attempted to...
  17. B

    Newton's Second Law for Translation and Rotation

    Answer choices: N2L for Translation, N2L for Rotation, Both, Either1. You are asked to find the angular acceleration of a low-friction pulley with a given force exerted on it. My solution = N2L for rotation 2. You are asked to find the angular acceleration of a low-friction pulley due to a...
  18. Jrogers201

    Newton's second law along a line

    As I mentioned I am self tutoring myself on a subject I studied 20 years ago. I'm sure I can answer all the questions apart from question (iii). I think I'm supposed to use a simultaneous equation. But I need to answer question (iii) to answer the rest. Any help please?
  19. greenrichy

    Solving Newton's Second Law: Tension, Work and Kinetic Energy

    $$\sum F_x = T - w_x - f_k = ma_x $$ $$ T = mg\sin(\theta) + mg\cos(\theta)\mu_k + ma_x$$ $$ T = (9.8 \frac{m}{s^2}) \cdot (\sin(41^{\circ}) + \cos(41^{\circ})) + (75kg)\cdot(0.25\frac{m}{s^2}) $$ $$T = 672.91 N $$ Having found the tension force, I can find the work done by the person who's...
  20. H

    Relating the universal law of gravitation and Newton's second law

    First, I started with F_a = m_aa_a=G \frac{m_am_b}{r^2} and F_b = m_ba_b=G \frac{m_am_b}{r^2} . Solving for their respective accelerations, I got a_a=G \frac{m_b}{r^2} = 100G and a_b=G \frac{m_a}{r^2} = 100G, meaning that the initial acceleration of the two point particles are each 100G ...
  21. A

    I Alternative approach to analyzing a massless string

    Consider a massless string which can rotate about a fixed pulley (first picture). The coefficient of static friction is μ. Assuming that the motion is impending, the goal is to find the equation that describes the variation in tension of the string. ( T2/T1 = eμΦ where Φ is the subtended angle.)...
  22. R

    Is Newton's Second Law Flawed? An Exploration of Zero Force in Space

    Newton's law's of motion have been used for hundred's of years, but the second law is wrong and here is why. Newton's second says that net force equals the mass of the object multiplied by the acceleration or F∑=MA. This is fairly simple and straight forward, but is easy to prove wrong. If we...
  23. T

    Find v(t) from Newton's Second Law and Differential Equation

    <Moderator's note: Moved from a technical forum and thus no template.> Is what I have done correct ? I want to find v(t) from Sigma F = m*a. I have gravity force mg pointing downward with positive direction and resistive force R = -b*v^2 pointing upwards with negative direction are acting on a...
  24. J

    Magnetic fields, Newton's Second Law, and GR

    I have a question regarding the interactions of electromagnetic fields. Say you have two superconducting electromagnets A and B. The properties of the magnets are known such that you can tell precisely how quickly it takes each one to produce it's full strength magnetic field and how long it...
  25. C

    Body Force vs Inertial Force: What's the Difference?

    Hello everyone. This is my first time on the physics forum, but I think I'm going to be a regular here. I was reading a paper that outlined various ways to approach solving dynamic problems. The first approach outlined by the author is D'Alembert's principle of virtual work. In describing...
  26. isukatphysics69

    Newton's second law problem with friction

    1. Homework Statement i did part a,b,c but i am confused about part d.. i have a test tomorrow and will reattempt this when i wake up but i really need a hint here..so when the worker pulls upward he is decreasing the magnitude of -mg right? so if Fn and mg initially cancel each other out...
  27. M

    Newton's Second Law Rocket Problem

    Homework Statement A person whose mass is 20 kg needs to accelerate vertically from the surface of the Earth at 5.0m/s^2 and is trying to pick which rocket he should strap to his back. How much thrust does he need if each rocket has a mass of 30 kg? Homework Equations F=ma The Attempt at a...
  28. F

    Origin and demonstration of Newton's second law

    At high school, we saw without demonstration the fundamental principle of dynamics (2th Newton's law), i.e : $$\sum \vec{F}=m \vec{a}\,\,\,\,\,\,\,\,\,eq(1)$$ after, at university, we saw another expression of this 2th Newton's law : $$\sum \vec{F}= \dfrac{d\vec{p}}{dt}\,\,\,\,\...
  29. U

    How Do Sign Conventions Affect Equations in Newton's Second Law?

    Imagine we have a box suspended to the ceiling by a rope of negligible mass, the net force looks like: ∑F=T-Fg=0 T=Fg where T and Fg are equal in magnitude but opposite in direction. If we cut the rope, the box is in free fall and ∑F=Fg, and this equation is similar to T=Fg but Fg and ∑F have...
  30. Angelnomahou

    Newton's Second Law Homework: Forces, Accelerations, Angles

    Homework Statement The two forces F⃗ 1 and F⃗ 2 shown in (Figure 1) act on a 29.0-kg object on a frictionless tabletop. Suppose that F1 = 10.8 N , and F2 = 19 N . A. Determine the magnitude of the net force on the object for the diagram (a) in the figure. B.Determine the angle between the...
  31. aatari

    Newton's Second Law: Car and Rock Problem

    Hi Guys, I solved two questions below. Just need some feedback to make sure I solved them correctly. Thanks a bunch. 1. Homework Statement A car of mass 1.4 tonnes (1400 kg) traveling down the highway at 120 km/h has a F air of 1800 N acting against it. What force must be applied by the...
  32. J

    Newton's Second Law -- Accelerations in a pulley system

    Homework Statement A 20-kg block with a pulley attached slides along a frictionless ledge. It is connected by a massless string to a 5.0-kg block via the arrangement shown in Figure. (a) draw complete free body diagrams for the masses and Find (b) the acceleration of each block and (c) the...
  33. aatari

    Newton's Second law: Tension on Cable

    Hey guys is my solution correct for the question below? 1. Homework Statement Consider a 5.0 kg watermelon that is being accelerated at 2.0 m/s2 [up] by a cable. Find the tension in the cable. Homework Equations Fcable = m.a The Attempt at a Solution Fcable = m.a = 5.0 kg(2.0) = 10N
  34. aatari

    Newton's Second law: Pushing the box

    Can someone please help me solve this question below. 1. Homework Statement How much force is needed to push a 20 kg box across a floor at a constant speed of 0.5 m/s [forward] against a frictional resistance of 4 N? Homework Equations Fnet = m.a The Attempt at a Solution Since the velocity...
  35. I

    Revisiting Newton's Second Law

    I wonder why Newton second law, define force as mass x acceleration, acceleration is the second time derivative of displacement, why he didn't define the force as mass x higher order time derivatives of displacement
  36. A

    How do I interpret and graph Newton's second law data?

    Homework Statement Hi, I am doing this lab this week, but before I do it I have a few questions. ( it has to be completed in class so I want to be prepared). First, these are the three pages of the lab questions...
  37. The Lich King

    Newton's Second Law question, 3 blocks acting to each other

    Homework Statement Initially, the system of objects shown in figure is held motionless, the pulley and all surfaces and wheels are frictionless. Let the force F be zero and assume that m1 can move only vertically. https://drive.google.com/file/d/0B6xlSNQyGbU5M3FTSXpNSVdmT2c/view?usp=sharing...
  38. T

    Tension and Newton's second law

    Homework Statement A 7kg mass is hung from a 1.5 m long massless string. It is released from rest with the string displaced by an angle of 18 degrees from vertical. a) Make a free body diagram of the forces on the mass just after it is released. b) Find the tension in the string. c) Find the...
  39. brotherbobby

    Problem - Different weights on a swinging rod

    The following problem is from Sears and Zemansky's textbook. A wooden rod of negligible mass and length 80.0 cm is pivoted about a horizontal axis through its center. A white rat with mass 0.500 kg clings to one end of the stick, and a mouse with mass 0.200 kg clings to the other end. The...
  40. Vanessa Avila

    Finding the speed of a book against a vertical wall

    Homework Statement the main question asks: "If the book is initially at rest, what is its speed after it has traveled 0.400 m up the wall?" Homework Equations ∑F = m*a vf2 = vi2 + 2 * a * d , when initial velocity is 0. The Attempt at a Solution So here's my free body diagram: and out of...
  41. M

    Newton's Second Law Integral Form

    Hi PF! I was reading my book and I understand the following $$\sum \vec{F} = \frac{\partial}{\partial t} \iiint_{CV} \rho \vec{u} dV +\iint_{CS} \rho \vec{u} ( \vec{u_{rel}} \cdot \hat{n}) dS$$ ##CV## is a control volume, ##CS## is control surface, ##u## is velocity, ##u_{rel}## is velocity...
  42. Philip Robotic

    B Welcome to Physics Forums: Exploring Orbital Mechanics & Gravity

    Hi everyone! I'm really sorry if I'm using the wrong forum. It's my first time at PF. I'm pretty new to physics, as I began studying it just two years ago, but I'm really interested in the subject of astrophysics so I bought myself and started reading 'Introduction to rocket science and...
  43. Alan3030

    Newton's 2nd Law: Force, Mass, & Acceleration

    Apologies for what I assume is a rookie question. Given F=ma if you have a 1 kg object traveling in e.g. space say x @ 100m/s then F = 0 on that object. If you have another 1kg object say y sitting at 0 m/s, F=0. If they impact there must be force involved? Does negative acceleration give you a...
  44. O

    Force required to negate vertical acceleration with friction

    Homework Statement Two blocks m (16kg) and M (88kg) are as shown in the figure. If the co-efficient of friction b/w the blocks is 0.38 but the surface beneath the block is frictionless, what is the minimum force required to hold m against M? Homework Equations Fnet = ma Fs = μs*Fa The...