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Free Fall

Free Fall is probably the example of motion with constant acceleration that is used most often. The constant acceleration is of course that of gravity. Gravity accelerates all objects regardless of how heavy they are at the same rate.

This is not really obvious and it took a genius like Galileo’s to figure this out. From experience you might think that heavier objects fall at a faster rate. Note that I don’t say “fall faster”. All objects when left falling will go faster and faster. So it is not correct to say the heavy object fall faster, even light objects will eventually fall fast. So, again, you might think that heavier objects fall at a faster rate, imagine a piece of paper and a rock. The piece of paper will probably hit the ground after the rock when dropped from the same height. The reason lies however, only in the resistance the air puts up against the downward motion. Ball up the same piece of paper and you will see that it now hits the ground sooner. The mass of the paper did not change but the acceleration did, therefore the acceleration cannot depend on the mass of object.

 

The acceleration due to gravity is 10 m/s/s or 10 m/s2.  The first way to write the units gives a little more insights into its meaning. Acceleration of 10 m/s/s or 10 (m/s)/s means that an object with this acceleration changes its speed by 10 m/s every second. That means that if you drop a rock down a deep well in one of those European castles on a hill by a river, this rock will reach a speed of 10m/s after one second. Its speed will be 20 m/s after the next second and 30 m/s after three seconds. That means that every second the speed increases by 10. This is gravity. Now how about figuring out how deep the well is. Let’s assume that you hear the rock it the bottom after three seconds. Therefore it will have a speed of 30 m/s just before it hits the ground. (When it hits the ground the speed is obviously zero and we can’t use it anymore.) How deep is the well? It is not 90 m as you might think since it is going 30 meters every second and hits the ground after 3 seconds. The rock is only going 30 m/s at the instant right before it hits the ground. You cannot use the equation v = d/t if you only have the instantaneous velocity of the rock right at the end. Instead if you want to figure out the distance the rock dropped you need to use the average velocity. If the rock is dropped from rest and the final speed is 30 m/s you find the average speed just like you would find the average of two other numbers (average of 12 and 6 is (12+6)/2 = 9). The average speed is therefore 15 m/s. The rock is going at this average speed for 3 seconds and covers a distance of 45 m (in each second the rock covers 15 m on average, that’s what 15 m/s means).

We first found the final speed of the rock, then the average speed and multiplied this speed by the time. This can all be done just by reasoning, using the meaning of the acceleration and then the meaning of speed. Both of these are rates or ratios are something that we worked with in the beginning of the year. It is always easier to reason your way to the final answer rather than using an equation, which can also be done in this case. If you want to find out how, please check out the power point. Using the equations however eliminates the reasoning, which might lead you to an answer that doesn’t make sense. Now, of course the equations will always give you the right answer if used correctly, however, I find that many of you use the equations in ways that don’t make any sense as many or most of you have never been taught how to make sense of equations. You think of equations mostly as shortcuts to find an answer. Since you math ability is in most cases lacking behind your reasoning capabilities, you will be less likely to find the right answer by using equations.

If you want more insight into solving motion problems check out this page on solving motion problems.

 

 

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