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Newton's second law of motion

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Newton's second law of motion is F = ma, or force is equal to mass times acceleration. Learn how to use the formula to calculate acceleration. Created by Sal Khan.

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  • blobby green style avatar for user alsadeg123
    If we have a car with a mass of 500 kg and a constant velocity 50 mph and it hits some wall what force will be applied to the wall? As the velocity is constant the acceleration would be zero and substituting in the 2nd law F = 500 x 0 = 0. Which is impossible - please explain.

    Second question:
    If we throw a ball in the space where there are no forces at all ( gravity , friction ...etc ) and we applied a 500 N force on the ball which had a mass of 2 KG, then:
    500 = 2 x a
    a = 250 meter per second

    So in the first second the ball velocity would be 250 m /s and after 2 second the velocity would be 500 m /s and in the second n velocity would be 250n. The velocity will approach infinity which is impossible since nothing can go faster then the speed of light
    (275 votes)
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    • leafers sapling style avatar for user Peter Collingridge
      In the first question, the acceleration is not zero. It maybe zero before the car hits the wall, but when it hits the wall, the car's speed goes from 50 mph to 0 mph in a very short space of time. This is a large deceleration (i.e. acceleration in the opposite direction to its movement), hence it experiences a very large force in the opposite direction of movement. This is why having a large crumple zone at the front of the car is important as it allows the car to decelerate more slowly.

      In the second question, as soon as you let go of the ball, it is no longer accelerating (since there is no force acting on it). It will continue at the same speed that it had when it left your hand. Similarly, on Earth, when you throw a ball, it is travelling fastest at the instant it leaves you hand. It slows due to friction with the air and then the ground.
      (382 votes)
  • blobby green style avatar for user daewoongkim
    Why is it valuable to recognize scalar and vector values? I understand the difference between them, but I don't understand the practicality of it. Thanks.
    (43 votes)
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    • leaf red style avatar for user Jt wat?
      let's say your driving North at 50 mph for an hour (which is a vector because it has a magnitude, 50mph, and a direction, North), then you know you went 50 miles North, rather than just 50 miles in ay direction, and if you're like me then you might want to know which direction you're driving in.
      (66 votes)
  • piceratops sapling style avatar for user Unforgettable64
    what exactly is a vector force?
    (18 votes)
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  • piceratops ultimate style avatar for user Erik
    I understand the whole math part of the formula (it's pretty simple), but can anyone tell me what he means by 5 m/s^2? is it just saying that this object of mass is moving at a speed of 5 meters per second? Why is seconds squared?
    (10 votes)
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    • leafers seedling style avatar for user Samantha
      5 meters per second is a rate, but acceleration is a change in rate, so 5 meters per second per second. this would look like 5m/sec/sec. If you apply algebra to this, that would be the same as 5m/sec *1/sec, because dividing is the same as multiplying by the reciprocal. multiply it out and you get 5m/sec^2.
      (19 votes)
  • blobby green style avatar for user Jorge Garcia
    how do objects hit the floor at the same time
    (3 votes)
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    • duskpin ultimate style avatar for user [SKLZ] ▁ ▂ ▄ ▅ ▆ ▇ █ נк █ ▇ ▆ ▅ ▄ ▂ ▁
      HI Jorge Garcia,

      This only stands true when there is no air resistance present.

      Suppose that an bowling ball and a tennis ball are dropped off a cliff at the same time. To understand this we must use Newton's second law - the law of acceleration (acceleration = force/mass). Newton's second law states that the acceleration of an object is directly related to the net force and inversely related to its mass. Acceleration of an object depends on two things, force and mass. This shows that the bowling experiences a much greater force. But because of the big mass, it resists acceleration more. Even though a bowling ball may experience 100 times the force of a tennis ball, it has 100 times the mass. So, the force/mass ratio (from the equation acceleration = force/mass) is the same for each. Therefore, the acceleration is the same and they reach the ground at the same time.

      Hope that helps!
      - JK
      (11 votes)
  • blobby green style avatar for user prishabhugra
    hi there , I had a doubt in newtons laws of motion could you pls help me .....
    a person kicks a 1kg football to score a goal. When he kicks a 1kg brick , his foot gets hurt .give a reason for it. thank you
    (2 votes)
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    • male robot hal style avatar for user Charles LaCour
      What happens to the shape of the football and the brick when kicked? The football deforms and then elastically rebounds where as the brick is rigid and doesn't deform.

      The deformation of the football increases the amount of time that the force of the kick is spread out so to transfer the momentum from the foot to the football is done at a slower rate over a longer time requiring a lower force.

      The brick being rigid the momentum transfer has to occur quicker so there is more force on the foot and brick making it more painful and more likely to cause damage to the foot.
      (12 votes)
  • leaf green style avatar for user Assemble Academy
    I don't get one thing.
    In the 1d motion I learnt that 2 objects irrespective of their mass will fall with the same velocity. But, according to the 2nd law of motion i.e. F=ma, force on a body is directly proportional to it's mass. And more the force, the greater the velocity of the object.
    Please explain.
    (4 votes)
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  • blobby green style avatar for user austingae
    Am I correct?
    F ∝ M & F ∝ A & Multiplication represents proportionality, and therefore F = M * A.

    A better way to visualize everything is through A = F / M. Logically, doubling the force upon an object will double the acceleration of the object.

    The unit kg * m/s^2 cannot be comprehended as kg * m/s^2 because you have created a new unit out of two independent properties: mass & acceleration. Kg * m/s^2 is a new unit that represents force, right?
    (4 votes)
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    • leaf grey style avatar for user Alex
      You are correct. a = F / m is just an easier alternate form, because mass typically doesn't change in a lot of force problems. kg * m / s^2 is the unit of force called Newton. Just to slightly nitpick, it's usually better to write acceleration as lowercase a, to avoid confusion with area (A).
      (5 votes)
  • duskpin ultimate style avatar for user Triệu Quốc Anh
    why is force=massxacceleration
    (4 votes)
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  • piceratops ultimate style avatar for user Noah Thekkumpuram
    can we find what the mass of an object is if we know the force and the acceleration of that object just like how we found the acceleration because we knew the force and mass of that object?
    (2 votes)
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Video transcript

Newton's First Law tells us that an object at rest will stay at rest, and object with a constant velocity will keep having that constant velocity unless it's affected by some type of net force. Or you actually could say an object with constant velocity will stay having a constant velocity unless it's affected by net force. Because really, this takes into consideration the situation where an object is at rest. You could just have a situation where the constant velocity is zero. So Newton's First Law, you're going to have your constant velocity. It could be zero. It's going to stay being that constant velocity unless it's affected, unless there's some net force that acts on it. So that leads to the natural question, how does a net force affect the constant velocity? Or how does it affect of the state of an object? And that's what Newton's Second Law gives us. So Newton's Second Law of Motion. And this one is maybe the most famous. They're all kind of famous, actually. I won't pick favorites here. But this one gives us the famous formula force is equal to mass times acceleration. And acceleration is a vector quantity, and force is a vector quantity. And what it tells us-- because we're saying, OK, if you apply a force it might change that constant velocity. But how does it change that constant velocity? Well, let's say I have a brick right here, and it is floating in space. And it's pretty nice for us that the laws of the universe-- or at least in the classical sense, before Einstein showed up-- the laws of the universe actually dealt with pretty simple mathematics. What it tells us is if you apply a net force, let's say, on this side of the object-- and we talk about net force, because if you apply two forces that cancel out and that have zero net force, then the object won't change its constant velocity. But if you have a net force applied to one side of this object, then you're going to have a net acceleration going in the same direction. So you're going to have a net acceleration going in that same direction. And what Newton's Second Law of Motion tells us is that acceleration is proportional to the force applied, or the force applied is proportional to that acceleration. And the constant of proportionality, or to figure out what you have to multiply the acceleration by to get the force, or what you have to divide the force by to get the acceleration, is called mass. That is an object's mass. And I'll make a whole video on this. You should not confuse mass with weight. And I'll make a whole video on the difference between mass and weight. Mass is a measure of how much stuff there is. Now, that we'll see in the future. There are other things that we don't normally consider stuff that does start to have mass. But for our classical, or at least a first year physics course, you could really just imagine how much stuff there is. Weight, as we'll see in a future video, is how much that stuff is being pulled down by the force of gravity. So weight is a force. Mass is telling you how much stuff there is. And this is really neat that this formula is so simple, because maybe we could have lived in a universe where force is equal to mass squared times acceleration times the square root of acceleration, which would've made all of our math much more complicated. But it's nice. It's just this constant of proportionality right over here. It's just this nice simple expression. And just to get our feet wet a little bit with computations involving force, mass, and acceleration, let's say that I have a force. And the unit of force is appropriately called the newton. So let's say I have a force of 10 newtons. And just to be clear, a newton is the same thing as 10 kilogram meters per second squared. And that's good that a newton is the same thing as kilogram meters per second squared, because that's exactly what you get on this side of the formula. So let's say I have a force of 10 newtons, and it is acting on a mass. Let's say that the mass is 2 kilograms. And I want to know the acceleration. And once again, in this video, these are vector quantities. If I have a positive value here, we're going to make the assumption that it's going to the right. If I had a negative value, then it would be going to the left. So implicitly I'm giving you not only the magnitude of the force, but I'm also giving you the direction. I'm saying it is to the right, because it is positive. So what would be acceleration? Well we just use f equals ma. You have, on the left hand side, 10. I could write 10 newtons here, or I could write 10 kilogram meters per second squared. And that is going to be equal to the mass, which is 2 kilograms times the acceleration. And then to solve for the acceleration, you just divide both sides by 2 kilograms. So let's divide the left by 2 kilograms. Let me do it this way. Let's divide the right by 2 kilograms. That cancels out. The 10 and the 2, 10 divided by 2 is 5. And then you have kilograms canceling with kilograms. Your left hand side, you get 5 meters per second squared. And then that's equal to your acceleration. Now just for fun, what happens if I double that force? Well then I have 20 newtons. Well, I'll actually work it out. Then I have 20 kilogram meters per second squared is equal to-- I'll have to color code-- 2 kilograms times the acceleration. Divide both sides by 2 kilograms, and what do we get? Cancels out. 20 divided by 2 is 10. Kilograms cancel kilograms. And so we have the acceleration, in this situation, is equal to 10 meters per second squared is equal to the acceleration. So when we doubled the force-- we went from 10 newtons to 20 newtons-- the acceleration doubled. We went from 5 meters per second squared to 10 meters per second squared. So we see that they are directly proportional, and the mass is that how proportional they are. And so you could imagine what happens if we double the mass. If we double the mass in this situation with 20 newtons, then we won't be dividing by 2 kilograms anymore. We'll be dividing by 4 kilograms. And so then we'll have 20 divided by 4, which would be 5 and would be meters per second squared. So if you make the mass larger, if you double it, then your acceleration would be half as much. So the larger the mass you have, the more force you need to accelerate it. Or for a given force, the less that it will accelerate it, the harder it is to change its constant velocity.