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. L

    Two hanging masses and three strings

    Homework Statement Two masses m and M (where M = 2m) are attached with strings. One mass m is suspended from a single verticle string held by two strings each at 45 degrees to the horizontal. The suspending string to the left at 45 degrees is attached to a fixed point. The string on the right...
  2. P

    Question on velocity changes in free fall

    Homework Statement Assume a ping pong of mass 3g is falling, and it has fallen 1m and is now traveling at 5 m/s. If the air resistance force is half its weight, how far will it travel in the next 0.1 seconds. [Hint: you may want to sketch a velocity-time graph) Homework Equations Understanding...
  3. A

    Calculating Tension in a Hypothetical Moon-Earth System

    Homework Statement Suppose the moon were held in its orbit not by gravity but by a massless cable attached to the center of the earth. Find the tension in the cable. Homework Equations F=ma a=v^2/r v=2πr/T (since the pictures aren't working, I'm just going to post the url to the image)...
  4. Drew552

    Calculating Mass using F=ma and Friction

    Homework Statement Well i have the force which equals 500N and I don't have a given acceleration so should I be substituting 9.81 as the acceleration? or is their another way to find it given that I also have the friction which equals 125N. So which way is the right way of going? Homework...
  5. T

    Calculate Tension Between Car and Trailer

    Homework Statement Homework Equations I have no idea how to start this question, I looked at my notes from class and the textbook but just can't figure out how to start it! The Attempt at a Solution Any help would be greatly appreciated! Even if just to get started!Thanks Thomas
  6. Summer95

    Force Components, Friction, etc. Check my work?

    Could someone credible please check my work on this one? Homework Statement This problem is "pulling a sled up a slope" All relevant data is in the picture. I wanted to find FP (The force one has to pull to start the sled moving up with slope). mass = 26.0kg μs = 0.096 slope of hill = 12...
  7. P

    Pressing a Block against a Wall

    Homework Statement I have this homework question and was able to set up the free body diagrams for the two blocks but got stuck forming the equations in part a. Please help if you can and give explanations - I want to understand the concept for my test coming up. A block with mass M is pushed...
  8. T

    How to test f=ma using trolley and ticker timer?

    To test mass affects acceleration. is it correct to change the mass of plasticine attached to the trolley and measure the length of the ticker tape strip with the constant variable be the angle of the inclined plane?
  9. J

    Solve F=ma Zip Line Problem: Angles & Sag

    Question Info: A fun way to cross a chasm is to use a so-called Zip Line as shown in the figure. Assume that the width of the chasm you are crossing is, 21m . The rope must sag sufficiently so it won't break. Assume the rope can provide a tension force of up to 26kNbefore breaking, and use a...
  10. Q

    Deriving Coulomb's law and other fundamental equations from F=ma?

    I saw a joke crib sheet for a physics class that said "F=ma, derive the rest," but is it actually possible to derive at least electricity and magnetism questions from Newton's second law?
  11. A

    USAPhO 2014 F=ma exam #14, (rotational dynamics)

    PDF: http://www.aapt.org/physicsteam/2014/upload/exam1-2014-2-2-answers.pdf Homework Statement A disk of moment of inertia I, mass M, and radius R has a cord wrapped around it tightly as shown in the diagram. The disk is free to slide on its side as shown in the top down view. A constant...
  12. M

    F=ma with constant acceleration

    I'm new to physics, so I'm sure the explanation is very simple, but I cannot wrap my head around Newton's 2nd law F=ma. It is very easy to understand until I plug 0 into a. Wouldn't this make the force of the reaction disappear? For instance if a 100kg rock traveling east at constant velocity...
  13. A

    USAPhO 2014 F=ma exam #19, (tension, static equilibrium)

    Unfortunately there's no link to the test. This is from the test administered a month ago. Homework Statement A choppah is flying horizontally at constant speed. A perfectly flexible uniform cable is suspended beneath the choppah; air friction on the cable is NOT negligible. Which of...
  14. A

    USAPhO 2011 F=ma exam #12, (gravitational force, 3 body)

    http://www.aapt.org/physicsteam/2012/upload/exam1-2011-1-3-answers_1.pdf Homework Statement You are given a large collection of identical heavy balls and lightweight rods. When two balls are placed at the ends of one rod and interact through their mutual gravitational attraction (as is...
  15. A

    USAPhO 2009 F=mA exam #25, (torque, rotational energy)

    http://www.aapt.org/physicsteam/2010/upload/2009_F-maSolutions.pdf Homework Statement Two discs are mounted on thin, lightweight rods oriented through their centers and normal to the discs.These axles are constrained to be vertical at all times, and the discs can pivot frictionlessly on...
  16. A

    USAPhO 2009 F=MA exam #16, (angular frequency of a spring)

    http://www.aapt.org/physicsteam/2010/upload/2009_F-maSolutions.pdf Homework Statement Two identical objects of mass m are placed at either end of a spring of spring constant k and the whole system is placed on a horizontal frictionless surface. At what angular frequency ω does the system...
  17. L

    F=ma 2011 #24: Effects of Increasing Bearing Width & Radius

    Homework Statement A turntable is supported on a Teflon ring of inner radius R and outer radius R+δ (δ  R), as shown in the diagram. To rotate the turntable at a constant rate, power must be supplied to overcome friction. The manufacturer of the turntable wishes to reduce the power...
  18. A

    USAPhO 2008 F=ma exam #18, (gravitational potential)

    http://www.aapt.org/Programs/contest...08_fnet_ma.pdf Homework Statement A uniform circular ring of radius R is fixed in place. A particle is placed on the axis of the ring at a distance much greater than R and allowed to fall towards the ring under the influence of the ring’s gravity. The...
  19. A

    USAPhO 2009 F=MA exam #13, (spring SHM)

    Homework Statement Late correction, this is the 2008 F=ma exam: http://www.aapt.org/Programs/contests/upload/olympiad_2008_fnet_ma.pdf A mass is attached to the wall by a spring of constant k. When the spring is at its natural length, the mass is given a certain initial velocity, resulting in...
  20. A

    USAPhO F=ma 2010 exam # 17 (Gravitational potential energy)

    Homework Statement Four masses m are arranged at the vertices of a tetrahedron of side length a. What is the gravitational potential energy of this arrangement? Homework Equations U = -Gm2 / r The Attempt at a Solution The potential energy is the negative of the work done by gravity in...
  21. L

    2007 F=ma exam number 28 bicycle

    Homework Statement A simplified model of a bicycle of mass M has two tires that each comes into contact with the ground at a point. The wheelbase of this bicycle (the distance between the points of contact with the ground) is w, and the center of mass of the bicycle is located midway between...
  22. N

    Rethinking Newton's Equation: Re-writing F=MA with Reduced Mass

    I am the president of the Physics club at my high school. One of our members came up with a very interesting hypothetical. He asked each of us to re-write the famous Newtonian equation for motion, F=MA(force equals mass times acceleration). Here's the question we are all trying to answer, if...
  23. W

    Grouping all of the units at the end? I.E. F=ma = 2.3*424.3 [kg*m/s]

    In some papers I've read, I've seen the authors write down all of the units at the end. For example ##F=ma = 2.3*424.3 [kg*m/s^2]## In high school, I've never seen the teachers or textbooks write like this. How common is this is method? Assuming one keeps track of their units properly, I...
  24. O

    How do i prepare for the F=ma exam?

    Hello, How do i prepare for the F=ma exam? I have taken honors physics, but can only score about 5 on it :( i am taking AP Physics C this year however. Also, does anyone know where to find old practice tests, with FULL SOLUTIONS (not answer key--Solutions!)? THanks.
  25. V

    Skier down a hill- f=ma (is the QUESTION correct?)

    3rd time I'm posting in a day. Homework Statement A skier (68 kg) starts from rest but then begins to move downhill with a net force of 92 N for 8.2 s. The hill levels out for 3.5 s. On this part of the hill, the net force on the skier is 22 N [backwards]. T/I (a) Calculate the...
  26. V

    Maximum tension between train cars, F=ma

    Homework Statement A locomotive (6.4 × 10^5 kg) is used to pull two railway cars (Figure 11). Railway car 1 (5.0 × 10^5 kg) is attached to railway car 2 (3.6 × 10^ kg) by a locking mechanism. A railway engineer tests the mechanism and estimates that it can only withstand 2.0 × 10^5 N of...
  27. V

    Skater pulling another skater with a rope, F=ma

    Homework Statement Two people, each with a mass of 70 kg, are wearing inline skates and are holding opposite ends of a 15 m rope. One person pulls forward on the rope by moving hand over hand and gradually reeling in more of the rope. In doing so, he exerts a force of 35 N [backwards] on...
  28. I

    Is support force a true force ? it seems incompatibe with F=ma

    Is "support force" a "true force"? it seems incompatibe with F=ma For example if a box is sitting on a table, not moving, it is said that the table exerts a support force on the box. But the box and the table are both inertial right? so if F = ma (force = mass x acceleration) and...
  29. G

    Exploring the Relationship Between F=ma and e=mc^2: A Scientific Analysis

    Could this two equations be used together, since they have a common variable "m"? For example, you could deduce that the speed of light = sqrt(a*m), and since the speed of light is a constant, if acceleration goes up, then mass must go down. Is this true?
  30. J

    Distribution (Dirac&standard) formulations of f=ma how do they go again?

    Hi, I'm wondering how to formulate Newton's second law in terms of Dirac delta functions and standard mass density distributions. We define the Dirac delta function of a point mass with mass m located at point x0 as follows: \rho(x)=m\delta (x-x_0) If our point mass is represented by a...
  31. Astrum

    How Does Radio Wave Impact on Ionospheric Electron Integrate in Physics?

    This isn't a HM question, and I'm asking for an explanation. This is "The effect of a Radio Wave on an Ionospheric Electron" The integration is weird, I don't follow what is being done. a=\frac{-eE}{m} - reworking of F=ma \frac{-eE}{m}sin(\omega t only interested in the x axis...
  32. S

    2009 F=MA # 24 (A block tipping down an incline)

    Homework Statement #24 https://aapt.org/physicsteam/2010/upload/2009_F-maSolutions.pdf Homework Equations T = rfsinθ The Attempt at a Solution FBD: Axes: (along the incline is x), perpendicular to that is y: Down: mgcosθ Up: N Right: mgsinθ Left: Ff (friction) If the box is...
  33. S

    F=MA 2009 #23 (Power of a Spring)

    Homework Statement #23 https://aapt.org/physicsteam/2010/upload/2009_F-maSolutions.pdf Homework Equations P = Fv The Attempt at a Solution T = 2∏√(k/m) x = Asin(wt) v = Awcos(wt) a = -Aw2sin(wt) We are trying to maximize power, which is both dW/dt and Fv. Force is ma, given...
  34. S

    F=MA 2009 Exam # 18 (Pendulum, a small peg, and mass m)

    Homework Statement https://aapt.org/physicsteam/2010/upload/2009_F-maSolutions.pdf # 18 Homework Equations T = 2∏√(L/g) The Attempt at a Solution Honestly, I'm not sure how at all to do this question. All I know that the distance from the small peg to mass m is L/3 - so that should...
  35. S

    2009 F=MA Exam #6 (Conceptual Velocity Question)

    Homework Statement An object is thrown with a fixed initial speed v0 at various angles α relative to the horizon. At some constant height h above the launch point the speed v of the object is measured as a function of the initial angle α. Which of the following best describes the dependence of v...
  36. K

    Calculating Maximum Force Acting on 28kg Mass: F=ma

    The position of a mass m = 28.0 kg is given in by x(t) = 3.0sin ((15.0)t). Calculate the magnitude of the maximum force acting on the mass. F=ma. I tried deriving x(t) twice to get the acceleration equation so i could plug it into F=ma and then pick a random number for t. I chose t=1 but i...
  37. M

    Finding Acceleration of a Car with a Hanging Mass

    Homework Statement A point object of mass M hangs from the ceiling of a car from a massless string of length L. It is observed to make an angle θ from the vertical as the car accelerates uniformly from rest. Find the acceleration of the car in terms of θ, M, L, and g. Diagram...
  38. S

    F=MA 2012 Exam #19: Find Pipe Radius

    Homework Statement 19. A 1,500 Watt motor is used to pump water a vertical height of 2.0 meters out of a flooded basement through a cylindrical pipe. The water is ejected though the end of the pipe at a speed of 2.5 m/s. Ignoring friction and assuming that all of the energy of the motor goes...
  39. K

    Help Solve 2012 F=ma Problem 21

    Hi, I'm just training for the 2013 F=ma exam, and I took some old exams. I tried to do the 2012 exam, and could not figure out problem 21. Can anyone help me, please? Homework Statement A spring system is set up as follows: a platform with weight 10 N is on top of two springs, each with a...
  40. V

    How Does Friction Affect the Acceleration of Stacked Blocks?

    Homework Statement A block of mass m1 is on top of a block of mass m2. The lower block is on a horizontal surface, and a rope can pull horizontally on the lower block. The coefficient of kinetic friction for all surfaces is μ. What is the resulting acceleration of the lower block if a force F...
  41. K

    F=ma Confusion about answer given for F

    Hi, I'm reading a book and one of the questions asks: how much force is required to give an object weighing 3000lb an acceleration of 12ft/sec2? I calculated this as F=3000x12=36,000pdl. The answer given is "1125 force" (36,000/32). Why is this? Why isn't it just 36,000pdl?
  42. A

    Exploring the Meaning of Force: F=ma vs. F=mdx/dt

    I thought to myself yesterday: Is there really any way of measuring a force independent of F=ma? I don't see there is so you can more or less take F=ma as the definition of force and then use that to derive the expressions for the fundamental forces of nature. But then it occurred to me: Why did...
  43. R

    Solve F=ma Concept: Urgent Help Needed! Where Did I Go Wrong?

    Urgent help needed with F=ma concept! Where did I go wrong?? Help please Use the exact values you enter to make later calculations. A group of students performed the same "Newton's Second Law" experiment that you did in class. For this lab, assume g = 9.81 m/s2. They obtained the following...
  44. R

    Turning simple concept of F=ma into a nightmare

    2. A group of students performing Newton's Second Law experiment generated the graph shown below from their data. Which of the following statements is true regarding the trustworthiness of the data? (Select all that apply.) a) The graph should have a positive y-intercept because a certain...
  45. M

    Calculating Mass of an Astronaut in a Rocket with Two Accelerations

    Homework Statement An astronaut who is weighing himself inside of a rocket blasting off from the moon with an upward acceleration of 1.26m/s^2 records a scale reading of 188N . The acceleration due to gravity on the moon is 1.67m/s^2 . Find the mass of the astronaut Homework Equations...
  46. S

    I know f=ma but I need velocity

    While two forces act on it a particle is to move at the constant velocity v= (3m/s)I - (4m/s)j. One of the forces is F1=(2n)I +(-6n)j what is the other force? I want to say (1n)I + (2n)j but then I couldn't decided why that would be true. I guess I liked those numbers because if the mass...
  47. S

    What is the relationship between torque and F=ma in rotational motion?

    Hello, The concept of torque has always been confusing to me for a few reasons, but i guess it boils down to two things that really seem to bother me: 1.) We all posses an intuitive sense of the fact that pushing on a lever further away from the fulcrum makes the pushing easier. Most of the...
  48. V

    Can someone explain me why f=ma ?

    hey guys i had a doubt can someone please explain me why force=mass x acceleration?
  49. M

    ? Why does F=ma instead of F=mv ?

    I know this is probably a complete n00b question, but I have tried all over the www and couldn't find it explained. Correct any of these premises if they are wrong, maybe that's my problem, but... velocity is current speed and acceleration is change in speed. So, if something is moving...
  50. N

    Why can a motorcycle accelerate faster than a large truck?

    Homework Statement Use the concepts of momentum and Newton’s second law to explain why a motorcycle can accelerate at a greater rate than a large truck. Homework Equations The Attempt at a Solution The motorcycle will accelerate at a greater rate because the truck has a...
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