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 52 kg, what is the value of a? Visualize the Earth as a perfectly solid object.
2 answers
why isnt acceleration = 9.81m/s^2 due to gravitational force?
That IS the acceleration due to gravity of the person, near the surface of the earth, if the person is free to fall.
It is a bit of a trick question. Actually, the person and the earth approach each other at different acceleration rates. They are reacting to equal and opposite force between them, but the earth "lurches upward" at a much lower rate,
a = g (m/M)
where M is the mass of the earth and m is the mass of the person.
a = 9.81 m/s^2*(52/5.97*10^24)
= 8.5*10^-28 m/s^2
It is a bit of a trick question. Actually, the person and the earth approach each other at different acceleration rates. They are reacting to equal and opposite force between them, but the earth "lurches upward" at a much lower rate,
a = g (m/M)
where M is the mass of the earth and m is the mass of the person.
a = 9.81 m/s^2*(52/5.97*10^24)
= 8.5*10^-28 m/s^2