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Homework Help: Speed dropping to zero when landing during a fall

  1. Jun 17, 2012 #1
    1. The problem statement, all variables and given/known data
    When a box falls in a vacuum, it accelerates at 10m/s^2 and if the mass is 10kg, then it has a net forfeit of 100N. As it falls for 10s, it has a final speed of 100m/s. At the moment of impact, there is a reaction force of 100N acted upon the box by the earth. But since the final speed where net force=0N is 100m/s, then why does the speed drop to 0? Since there is no other force to bring the speed down (decelerate) to 0m/s, so I'm unsure.

    2. Relevant equations

    Net F=ma

    3. The attempt at a solution
    I'm totally not sure what could bring the speed to zero since even if a body has 0 net force, it can have a high speed. And the only way to bring it to zero is if I have a external force to decelerate it to 0 speed first. Thanks for the help!
  2. jcsd
  3. Jun 17, 2012 #2
    Hi sgstudent!

    Not sure what you mean. There is an external force by the earth on the block as the impact takes place.
  4. Jun 17, 2012 #3
    But isn't the external force only the same magnitude as the weight of the object? So in that case won't the object continue at the same speed with no acceleration? Because in a car, if the car is moving at constant speed, that means that the car has no net force. So to stop it, the car must have another additional force to push it in the other direction deceleration it. But in the case of falling, it does not have another additional force to bring its speed down to zero. Thanks for the help Infinitum!
  5. Jun 17, 2012 #4
    The magnitude of force exerted by the earth due to impact is given as,

    [tex]F = \frac{\Delta mv}{\Delta t} = \frac{mv-0}{\Delta t}[/tex]

    And that is not always equal to mg.

    I also noticed something in the question

    This is not true always.
  6. Jun 17, 2012 #5
    Oh, so the normal upwards force acting on the object is initially greater than the object's weight to drop its speed to zero? Does it mean that that force is very large as it is almost instantaneous
  7. Jun 17, 2012 #6
    Yes. This is correct.

    If the earth were totally rigid, the box would have to deform, with the front end of the box coming to a stop first, followed by cross sections higher up. The details of the deformation would depend on whether the box behaves elastically or not. If the deformation were totally elastic, the box would bounce up after the compression wave passed from the bottom to the top, and then got reflected as a tensile wave back down to the bottom again.
    Last edited: Jun 17, 2012
  8. Jun 17, 2012 #7
    Yep! Chet nails it perfectly :smile:
  9. Jun 17, 2012 #8
    Oh, so we have to incorporate momentum to help us to answer the question? Because sometimes we are given similar questions like to describe a sky diver's falling. When the parachute opens there is a net upwards force in order to slow him down. Until the speed reaches zero which is at the ground. But in this case the ΔT is a lot larger and the upwards force is not constant? But they are also using the same principals? Lastly, what will the ΔT be in thus case? Cos have not learnt about momentum yet. Thanks for the help!
  10. Jun 17, 2012 #9
    That equation above is called the impulse equation, and is generally applicable to impulsive forces(collision). For the parachute problem, the force might be varying as frictional force usually varies proportional to the speed of the object, and so on. You cannot apply the impulse-force equation as this is not a collision situation. You should learn about it soon :smile:

    If you are still curious, read up in your text about this and also look at Khanacademy or MIT OCW for a good idea.
  11. Jun 17, 2012 #10
    Oh how interesting, looks like I only scratched the surface of forces since there's so much relation between momentum and force. Thanks for the help Infinitum!
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