Take the mass of the Earth to be 5.98 * 10^24 kg. If the Earth's gravitational force causes a falling 63 kg student to accelerate downward at 9.8m/s^2, determine the upward acceleration of the Earth during the student's fall.
2007-02-04 15:25:32 · 6 answers · asked by krstilyzed 1 in Science & Mathematics ➔ Physics
The Earth exerts a force of gravity on the student equal to the student's weight (which is the force of gravity).
Weight = mass * gravity
Where “gravity” is the gravitational acceleration the student experiences (9.81 m/s^2).
Weight = (63 kg) * (9.81 m/s^2) = 618.03 Newtons
Likewise, just like the Earth exerts a force of gravity on the student, the student exerts an equal force right back on the Earth.
So the Earth’s “weight” due to the student is also 618.03 Newtons.
This weight is a force and will cause the Earth to accelerate toward the student.
But the Earth’s mass is HUGE compared to that of the student.
Force = mass * acceleration
An equal force with a much larger mass will cause a much smaller acceleration.
Acceleration = Force / mass
Where now the force is the Earth’s “weight” and the mass is the mass of the Earth.
To find the Earth’s acceleration just plug in the values we know.
Acceleration of the Earth = (618.03 Newtons) / (5.98 E24 kg)
Acceleration = 1.033 E-22 m/s^2
This is an incredibly small acceleration and in most cases it is totally negligible; this question is just asking for trivia basically.
2007-02-04 15:50:58 · answer #1 · answered by mrjeffy321 7 · 1⤊ 0⤋
Force acting on student by earth = 63*9.8 N
By Newton's third law, force on earth by student = 63*9.8N
Acceleration of earth = F/5.98*10^24 m/s^2
2007-02-04 23:47:35 · answer #2 · answered by priya 2 · 0⤊ 0⤋
Whatever answer you get will only be an approximation, since the acceleration increases as they close, but f=ma, and f is = and opposite, so 63* 9.8 divided by 5.98*10^24 is ??? You do the math!
2007-02-04 23:42:46 · answer #3 · answered by CLICKHEREx 5 · 0⤊ 0⤋
Due to the earth, the upward acceleration is 0.
Because the only force due to the earth is pulling down.
Air is another matter.
2007-02-04 23:35:42 · answer #4 · answered by Anonymous · 0⤊ 1⤋
The gravitational attraction between 2 objects is given by
F=GMm/r^2
where G is the gravitational constant M is the Mass of object 1 and m is the mass of object 2 and r is the distance between them.
2007-02-04 23:49:43 · answer #5 · answered by SWH 6 · 0⤊ 0⤋
0 there is no acceleration the earth is stationary in regards to the falling student
2007-02-04 23:30:35 · answer #6 · answered by Wills 2 · 0⤊ 1⤋