What is F=ma: Definition and 192 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. tharindu_

    B Why don't cars accelerate according to F = ma?

    If the engine is constant, then the wheels of the car exerts a constant force on the floor. And F = ma, So the car should be accelerating rather than maintaining the same speed. What is going on here?
  2. latos

    Coefficient of kinetic friction of a block sliding across the ceiling

    I first found the force of friction by setting the force in the x direction (horizontal component of force applied - friction) = ma. I then thought the normal force would be equal to vertical component of the force applied because of Newton's 3rd Law, which states that for every action, there is...
  3. L

    Scarf modelled as a pulley system / F=ma exercise

    My teacher gave the above answer as a solution. However, I am not convinced that the proportion is really $$\frac{m_1}{m_1+m2}$$. If m2 << m1the proportion would be really big, right? But intuition tells me that it should be the opposite. Furthermore, if m2 >> m1, then one would expect the...
  4. physicsferret

    F=ma Prep and Resources for High School Students

    Hi all. This is the first time I am using this forum, so please forgive me if this has been said before already. I am a high-school sophomore and I took the AP Physics 1 course last year. I really enjoyed it because I had an amazing teacher and next year I will be taking AP Physics 2 and AP...
  5. T

    B F=ma Applied to a Billiards Cue

    Many years ago, I was asked if the weight of a billiards cue matters when breaking a rack of billiards balls. I.e. does a heavier cue apply more force to the cue ball. (typically the range of a break cue is 18-25 oz.) So, probably obviously, I used the formula F=MA as an explanation. RecentlyI...
  6. Ollz

    2 blocks and a spring, SUVAT and F=ma

    I have calculated the acceleration of truck B from v=u+at as 5ms/s. The force applied to truck B is therefore 5x10=50N. I am unsure whether this question is poorly worded, but I feel a reasonable assumption is that the force applied to truck A would be the same as truck B, without knowing its...
  7. mopit_011

    Question About an F=ma Problem with a small ball impacting a ramp

    (This is the diagram from the problem.) My professor assigned this as extra practice and I don’t understand why the answer is (C) instead of (B). Why would sharp bends be the correct answer? Isn’t the curved diagram more accurate for movement on a slope?
  8. mattlfang

    Stick leaning on the wall, find the acceleration from the initial position

    So the acceleration of point A was given by a force F exerted on cylinder that's along the direction of the stick, decomposed into the horizontal direction. so aA = F cos Θ The same force along the opposite direction is exerted on stick, and if we decompose that in vertical and horizontal...
  9. Hamiltonian

    A doubt in the rotational analogue of F=ma

    If we have a cylinder rolling on the ground ##\tau = I\alpha## can only be applied about the point in contact with the surface(Instantaneous axis of rotation) and its CoM I don't see why this should be the case. why can the equation ##\tau = I\alpha## only be applied about the axis passing...
  10. T

    B Understanding F=ma: Constant Speed & Acceleration

    I’ve been going back and reviewing my basic physics and I have a nagging question? F=ma aid acceleration in terms of units such as meters per seconds squared. for example, 20 meters per second per second. This indicates an increasing speed. so, let’s take an asteroid moving through space at...
  11. domingoleung

    Simple Mechanics Problem -- Block connected to a wall by a rope

    (So this is the system given) The following is my analysis: (i) (ii) Well, my problem is - I got a negative acceleration and its quite impossible to have block B moving to the left. So I am wondering if there are any mistakes I've made.
  12. C

    F=ma experiment: Trolley being pulled by a falling weight

    The weight accelerating/pulling the trolley is changed and corresponding acceleration recorded. What I don’t understand is why the weight added/removed to the hanging weight is removed/added to the trolley
  13. U

    Testing Preparing for the F=ma Exam: A Guide for High School Students

    I know there is quite a lot of similar posts like these but how do I prepare for this exam? I am a high schooler who has a decent amount of time. I am wondering what textbooks would prepare me. What I know is that the exam is focused on mechanics, more specifically, "A: The F=ma exam focuses on...
  14. Homgkung

    Can we find the frequency of a rod pendulum by just using F=ma?

    Summary: When I tried to find the angular frequency of a rod pendulum, I attempted to find its angular acceleration first, however, I realized that the results are different by using different approaches. i.e. (1) Newton's second law for a system of particles (2) Newton's second law for...
  15. A

    Newton’s Second Law applied: F=ma

    My attempt at solving this written out with random inputs Block A- F(100)=M(10)A(10) Block B- F(200)= M(15) A A=200/15 = 13.33 This was not in line with options.. which were 4x block A (1/4) block A Equal to block A (1/2) block A 2x block A Much appreciated some help as I am a beginner
  16. W

    I Variable mass F=ma versus Rocket F=ma

    In the book by Tipler & Mosca, the section on F=ma for variable mass derives the following equation: ##\mathbf{F}_{ext}+\frac{dM}{dt} \mathbf{v}_{rel}=M\frac{d\mathbf{v}}{dt}## where ##\mathbf{F}_ext## is the external force on the system as a whole (ie not just the variable mass sub-system...
  17. M

    Classical Which resources should I use to prepare for the F=ma contest and USAPhO?

    What textbook should I go through to be prepared for the F=MA contest and advance to USAPhO? Is Khan Academy AP Physics Enough? I have started HRK Physics but it seems to me to be quite boring, and out of ~50 practice problems at the end of each chapter I would say ~4-5 of them are interesting...
  18. C

    F=ma -- How did Newton find this?

    I did some googling but only found nothing to answer my question. How did Newton come up with this formula, literally/physically? Did he have chunks of stuff and moved them around, then logged various results. Then maybe he played around with various formulas and saw which fit the data?
  19. Z

    Energy to achieve constant acceleration - F=ma and 1/2mv^2

    I was in a discussion regarding the time it took to get to the speed of light with a constant acceleration of 1g, and the time was something close to a year. (ignoring all the other major factors ). Just from a Newtonian perspective, if you have a 100kg rocket putting out 900N of thrust, you...
  20. J

    Calculating Elevator Acceleration: Solve for F=ma

    Homework Statement A person stands on a bathroom scale in a motionless elevator. When the elevator begins to move, the scale briefly reads 1.05 times the persons regular weight. Calculate the magnitude and direction of the acceleration of the elevator. Homework Equations F=ma The Attempt at a...
  21. S

    What will stop me from going at the speed of light?

    Using Newton's 2nd law F=ma, If you provide a constant force of 1mil Newtons then an object will accelerate at 100m/s. Using V = U + AT I can say that (speed of light) 299,792,458 = 0 + 100T thus T = 2997924.58 seconds or I can achieve speed of light in 35 days or so. Why is this not...
  22. SaifTaher

    Why is F=ma? (Physics homework)

    I'm taking an AP physics course on the edx.org platform and I arrived today at the "Forces" Unit. One of the fundamental properties of force that it's equal to acceleration times mass, but I, as a curious stubborn nerd, always look for the "why's", so I thought to myself "why it's not equal to...
  23. Pranav

    B F=ma -- True or an Illusion....

    Imagine, There's a ball in deep space traveling with a constant velocity of 25m/s and is having mass 25kg. Now as I said, ball is traveling with a constant velocity that simply means acceleration=0 and now if we calculate the force with F=ma we will end up with 0. But if that ball collide with a...
  24. C

    Classical Chapters from Morin's book that help with F=ma exam prep?

    What chapters from Morin's Introduction to Classical Mechanics Textbook will help me prepare for the F=ma exam? I also have the Feynman Lectures and the Halliday Resnick textbook. Any help would be greatly appreciated! :)
  25. E

    Breaking Distance of a Car Traveling on an Inclined Plane

    Homework Statement Calculate the braking distance for a car traveling at a speed of 35.0m/s down a hill at an angle of 10.0 degrees relative to the horizontal. Homework Equations F=ma v=u + 2as[/B] The Attempt at a Solution The teacher briefly explained this in class saying that the total...
  26. J

    Calculating New Acceleration with F=ma: A Homework Problem

    Homework Statement If the acceleration of an object is 2.00 m/s2 and the force on it is divided by 3 and its mass is divided by 7, what is the new acceleration? Homework EquationsThe Attempt at a Solution so I know the equation we use is F=ma, and so i did (F/3)=(m/7) 2a i divided by (m/7) on...
  27. Kiwigami

    Finding Velocity: F=ma or KE = 0.5mv^2

    Here is a made up function of force changing with respect to displacement: F(x) = 2000 - 100x The force is applied onto an object, pushing it horizontally. Ignore friction and air resistance. The mass is constant. I'm trying to find Velocity with respect to displacement. Attempt 1: Knowing F =...
  28. R

    Determine the angular frequency of the system in SHM

    Homework Statement Determine the angular frequency of the system in the image. The cable is ideal but the pulley is not. I will present the same solution but with different coordinate axes. For some reason they arent the same and neither of them are correct. Given data: R is the radius of...
  29. J

    MHB Motion Problem Using F=Ma and s=ut+1/2xt^2

    Firstly, appologies if this is in the wrong place or wrote wrong, total noobie here. Ive been given some examples of math questions based on aviation, unfortunately this one didn't come with the correct answer or any example working and it seems a little more tricky than the others so I am...
  30. D

    How do you find acceleration with F=mg and F=ma?

    I know that you have to cancel out the masses and forces but still unsure how the equation goes
  31. K

    Statics of a particle, mechanics, F=ma

    Homework Statement A smooth bead B is threaded on a light inextensible string. The ends of the string are attached to two fixed points A and C on the same horizontal level. The bead is held in equilibrium by horizontal force of magnitude 2N acting parallel to CA. The section of the string make...
  32. Holden Kenne

    B Understanding Newton's Laws of Motion: Exploring Errors and Contradictions

    Hi, I'm a frehshman in High school writing a paper about Isaac Newton. One of my paragraphs is about the laws of motion. I came across a tidbit of information - there are instances in which Newton's laws are not correct. One example I found was that, at speeds approaching that of light, an...
  33. RoboNerd

    Force Systems Multiple Choice Thread

    Homework Statement http://gpschools.schoolwires.net/cms/lib05/MI01000971/Centricity/Domain/272/Chapter%205%20MC%2013.pdf It is problem 22 on page 7 of the document: A block of mass M1 on a horizontal table is connected to a hanging block of mass M2 by a string that passes over a pulley, as...
  34. S

    How Does Newton's Third Law Apply When a Truck Pulls a Car?

    Homework Statement A truck is pulling a car. is the magnitude of the force that the truck exerts on the car is the magnitude of the force that the car exerts on the truck Consider the following scenarios independently. 1. The truck is driving up a mountain with a constant velocity...
  35. RoboNerd

    Question on AP Physics C FRQ 2013. #3

    Homework Statement http://media.collegeboard.com/digitalServices/pdf/ap/apcentral/ap13_frq_physics_c_mechanics.pdf The problem is above. It is number 3. The solutions are below: http://media.collegeboard.com/digitalServices/pdf/ap/apcentral/ap13_physics_cm_scoring_guidelines.pdf Homework...
  36. Revolucien

    I Exploring F=MA: A Retired Electronics Tech's Questions

    I am not a student of Physics just a retired electronics tech who is interested so I am not sure what prefix this should be under. I have some questions about the F=MA equation... 1. If there are two bricks pushed against each other so an equal amount of pressure is applied, I have Mass in...
  37. A

    Understand Momentum, Force and Impulse

    Hi everyone! I've been getting confused with Momentum, Force and Impulse. From my understanding force when applied on object helps it gain momentum, the higher the force applied the higher the acceleration therefore more the momentum. And according to Sir Isaac Newton's first law of motion, the...
  38. RoboNerd

    Question on Rotational Motion and Torque Theory

    1. Homework Statement A cylinder of mass M and radius R rolls (without slipping) down an inclined plane whose incline angle with the horizontal is theta. Determine the acceleration of the cylinder's center of mass and the minimum coefficient of friction that will allow the cylinder to roll...
  39. B

    Forces on a Skydiver during the initial frefall phase of the jump

    Homework Statement A skydiver is jumping out of an airplane. During the first few seconds of one jump, the parachute is unopened, and the magnitude of the air resistance acting on the skydiver is 251N. The acceleration of the skydiver during this time is 5.96 m/s^2 [down]. Calculate the mass of...
  40. B

    How Does Friction Impact Bobsled Acceleration?

    Homework Statement In the men's four-man bobsled event in the winter olympics, the maximum mas of a bobsled with pilot, two riders, and a brakeman is 630 kg. During a practice run, the rear rider and the brakeman exert average forces of 1220N and 1200N [forward] respectively to accelerate a...
  41. B

    Net Force on 5.32 x 10^4 kg Airplane: Solve the Mystery

    Homework Statement An airplane with a mass of 5.32 x 10^4 Kg accelerates down the runway at 1.76 m/s^2 [forward]. Calculate the net force acting on the airplane. Homework Equations Fnet=ma The Attempt at a Solution I did this by multiplying the two given values, but my answer was 93632N...
  42. B

    How Can You Calculate Mass Using Force and Acceleration?

    Homework Statement This is not a specific problem, I was just wondering how you would calculate the mass of an object. If given the net force and acceleration, how would you calculate it if the net force is 0N or the acceleration is 0m/s^2? Isn't the equation just m=f/a? Homework EquationsThe...
  43. FruitNinja

    Time it takes for block to slide down an incline in elevator

    Homework Statement MECHANICS: Given Theta, L, M, and acceleration of elevator relative to ground. Find the time it takes for the block to reach the end of the incline. Here is a diagram: http://k-elahian.com/tmp/nip.PNG Homework Equations f=ma kinematics relative acceleration The Attempt...
  44. Prof. 27

    Pulley acceleration Problem

    Homework Statement The masses of blocks A and B in the figure (Figure 1) are 20.0 kg and 10.0 kg, respectively. The blocks are initially at rest on the floor and are connected by a massless string passing over a massless and frictionless pulley. An upward force F⃗ is applied to the pulley...
  45. S

    The relationship between F=ma and E=mc2

    I'm wondering about the relationship between F=ma and E=mc2. Is it simply that, at relativistic speeds, E=mc2 replaces F=ma? (much like D = v x t is replaced by the Lorentz Contraction at relativistic speeds)
  46. toboldlygo

    Finding Tension in a Massless String on an Inclined Plane

    Homework Statement In the figure below, the objects are attached to spring balances calibrated in Newtons. Give the readings of the balances in each case, assuming that the strings are massless and the incline is frictionless. I need help with (d). If the picture's too grainy to read off...
  47. L

    Work & Energy: Forces with Angles

    Homework Statement A student could either push or pull, at an angle of 30 degrees from the horizontal, a 40kg crate, where the coefficient of kinetic friction is .21. The crate is moved 18m. Calculate the minimum work for pushing and pulling. Homework Equations W=F•(change in)X•cos(angle in...
  48. P

    F=MA: Box Weights & Impact on Contents

    I suppose I make two boxes with cardboard, they have the same content : one weighs 10 kg of cardboard the second only 1 kg. I suppose the cardboard doesn't break when the boxes hit the ground : if I let fall the 10 kg box, will the content be more damaged when reaching the ground than in the 1...
  49. N

    Preparing for the F=MA (USAPHO) exam

    I realize that different variations of this question have been asked countless times on this forum, but my inquiries are bit more specific than the general "how do I prepare for it", so please bear with me. Some background: I am a rising high school junior, about to take AP Physics C. At the...
  50. Mellmann

    How to determine the "a" in f=ma or, a=f/m. If a 2200 lb car

    How to determine the "a" in f=ma or, a=f/m. If a 2200 lb car Is stationary and is struck by a 3300 lb vehicle and is propelled 27 feetfrom the impact? The 3300 lb vehicle had to be traveling how fast?
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