The mass of the bomb is entirely irrelevant, providing it is small compared with the mass of the Earth. Why? Because the gravitational pull of the Earth attracts all objects equally.
This result was established experimentally by Galileo in about ..... 1590? Reputedly in Pisa. He put a cannon ball and a feather in a vertical evacuated tube and dropped them. They hit the ground at the same time.
If you are going to take account of air resistance, then the
shape of the bomb is extremely important. It's internal structure is also vital, because it will affect the manner in which it falls. For example, imagine two bombs of identical mass and shape, but one has it's centre of mass near the tail and one has it's centre of mass near the middle. They will tumble in different ways, and consequently arrive at the surface of the Earth at different times.
The velocity of the aircraft will have a significant impact on where the bomb falls, but it will not in principle affect how long the fall takes. All we have discussed is the vertical component of the bomb's velocity: how long does it take to travel the vertical distance between the aircraft and the ground? Obviously the horizontal velocity may, in particular circumstances, have an effect on that: if the plane flies faster or slower the bomb may hit or miss the top of a mountain for example, but in general it is not relevant.
Think about it like this. A plane flying at 500 knots 5,000 feet drops a bomb. A chopper hovering at 5,000 simultaneously drops an identical bomb. Which hits the ground first?
Answer: they hit the ground at the same time.
And in case you were wondering, yes I do have a Physics degree.
To learn about the difference between mass (correctly measured in kilograms, pounds, etc.) and weight (correctly measured in newtons) try
this link. The mass of the bomb does not change during it's drop: however, it's weight does. As deaddog mentioned, the force of gravity is less at 50,000 feet above the surface of the Earth is less than it is at sea level, so the weight of the bomb will be less. Fortunatly, since weight is irrelvant to our calculation, that doesn't matter. ;D
Doolittle - if you test this (which is a fine idea) the actual time will be more than the 55 seconds odd mentioned above, because we have ignored lots of factors. In practice this time is a lower limit: the actual time will be more. Given that I have a vague recollection that some bombs do go supersonic during their fall, I suspect the true answer will not be all that higher: I would guess perhaps 70 or 80 seconds, something like that.
Topic: A Basic Physics question (Read 958 times)