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I was pondering this hypothetical scenario earlier, and didn't know how to deal with the physics exactly (I think it has to do with momentum in collisions):

You and a block with mass $1kg$ are initially at rest on a frictionless surface. You start running while pushing the block on this frictionless surface. You are heavier than the block, let's say $80kg$. You put your hands out in front of you fully extended, walk towards the block to start pushing this block with a force of $5N$, therefore object will start to immediately accelerate at $5 m/s^2$. However, you are applying this constant force over a time of $2$ seconds. So won't I have to accelerate myself increasingly faster than the object in order for my hands to apply that constant force of $5N$? Or would it be the same? I don't completely understand how I can apply a constant force on this block if it's accelerating. If this situation is hard to visualize, I'm thinking of it like a parent pushing a child on a swing with a constant force over a period of time except without there being any resistance force.

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    $\begingroup$ Can you run on a frictionless surface? $\endgroup$
    – chandra
    Oct 16 '16 at 7:09
  • $\begingroup$ @chandra you're right and I was thinking of how to change that, but I mean hypothetical. So friction could be small but we would neglect it for this problem. $\endgroup$
    – rb612
    Oct 16 '16 at 8:38
  • $\begingroup$ You could put a fan/propeller on the block that provides a force of 5n. $\endgroup$
    – PaulD
    Oct 16 '16 at 9:20
  • $\begingroup$ You might want to edit the question itself to have an icy (frictionless) path adjacent to a sidewalk. Otherwise people are going to dismiss this question. $\endgroup$
    – garyp
    Oct 16 '16 at 12:57
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To provide a constant force of 5N you need to speed up with the block. Imagine pushing a car. Your 5N accelerates the car until it is moving at the same speed as you, so unless you speed up yourself, you can no longer apply the force. If you could, then eventually the car will be travelling faster than you and pulling away from you!

You should replace pushing the block and associated running on a friction less surface problems with a motor/fan/propeller on the block supplying the 5N force.

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