What is the acceleration?
You stand on the seat of a chair and then hop off. During the time you are in flight down to the floor, the Earth is lurching up toward you with an acceleration a. If your mass is 84 kg, what is the value of a? Visualize the Earth as a perfectly solid object.
I have no clue what to do here--my only guess was negative gravity, but I was told that 9.8 m/s^2 differs significantly from the correct answer. What am I supposed to do?
As the third principle says if you have two objects, the action of the first object on the the second one, is equal to the reaction of the second object on the the first one. The action in the problem is, of course the gravitational attraction force with which the Earth is pulling the person downwards and making it to fall.
`F = G*m*M/R^2 =m*(G*M/R^2) =m*g`
Here `g` is the acceleration of the object in free fall and has the well known value of `9.81 m/s^2`
However, the same attraction force is exerted by the object on to the Earth, making the Earth to fall on its own toward the object. Thus we can write
`F = GMm/R^2 =M*(G*m/R^2) =M*a`
or equivalent `a= F/m = G*m/R^2 =6.67*10^-11*84/6371000^2 =1.38*10^-22 m/s^2`
Being so small in value (because Earth is such a massive body) this acceleration is usually overlooked when solving free falling problems.
Answer: The value of the acceleration of the Earth towards you is `a =1.38*10^-22 m/s^2`
Offcourse the answer is 9.8 m/s^2 irrespective of your mass.....Yes the value of 'g' depends upon mass, shape, and area facing the air...Even the type of fluid within which you are falling....But actually if in the question nothing about air is included it means the air is considered to be negligible....No air means no air resistance which means all bodies falls with the same acceleration irrespective of their masses shapes etc
we know f=ma
so a=f/m (keep this in mind)
now force acting on earth while a person jumps =GMm/r^2(force of gravitation)
and mass of earth is given as M
THEN BY THE EARLIER FORMULA a=GMm/r^2*M
say the peson weighs 50 kg then a=G50/r^2
after giving valuesof g&r a=very very very less than9.8m/sec62