Thursday, December 16, 2010

Newton's Laws part 2

I finished my related dream about a lesson plan for Newtonian physics with a question. If there is an equal but opposite force in every reaction and there's nothing to stop the Earth moving, why doesn't the Earth move down when you jump?

The answer is, of course, that it does, but our old friend F=ma comes into play. Rearranging the equation it becomes F/m=a the Force you apply when jumping isn't that great and the mass of the Earth so large that the resulting acceleration applied to the Earth is undetectable.

So now a second question. If I drop a water balloon from a great height it bursts when it hits the ground. If I drop it from the level of my feet it doesn't - why not?

Consider F=ma; if the mass of the two balloons are equal (say 1kg) and they are pulled to the ground only by gravity at an acceleration of 10m/s/s then in both cases the Force upon them is equal. Why therefore do they behave in different ways?

The answer lies in the point of impact - it's not the force that's moving them that causes them to burst or not, it's the force applied to them when they hit the ground. At this moment their speed is reduced to zero, and the only way this can happen is if a counter force is applied to them.

For the sake of argument let's say that it takes one-tenth of a second for the balloon's speed to drop to zero upon impact. If we take a balloon and let it fall under the influence of gravity for 1 second it is travelling at a speed of 10m/s (acceleration * time = speed) when it hits the ground it reduces its speed to zero in one-tenth of a second. to do so requires a negative acceleration (deceleration) of 100m/s/s (speed/time = acceleration). Plug that into F=ma and we see a force acting on the balloon of 100N.

Now take a balloon and let it fall for 10 seconds. It reaches a speed of 100m/s; to reduce its speed to zero in one-tenth of a second requires a deceleration of 1000m/s/s and therefore a force of 1000N acts upon it.

If the balloon can only withstand a force of 500N it will bounce in the first instance but burst in the second.

Of course this assumes the ground it impacts can also withstand such a force otherwise it may be that which breaks first.

My next 'lesson' will be about Energy in such systems.