Describe the motion of a skydiver from the time he jumps to the time he lands safely on the ground
1 answer:
The skydiver accelerates at the beginning, while later he continues at constant velocity
Explanation:
There are two forces acting on the skydiver during its fall:
- The force of gravity, which is constant, of magnitude
, where m is the mass of the skydiver and
is the acceleration of gravity (
downward)
- The air resistance, whose magnitude is proportional to the speed of the skydiver:
, and which acts upward
At the beginning of its fall, the speed of the skydiver is small, therefore at the beginning the air resistance is negligible, and therefore the skydiver is accelerated downward with an acceleration of
However, as the skydiver falls, he gains speed; therefore, the magnitude of the air resistance increases. The net force acting on the skydiver is
As the air resistance increases, the net force decreases: therefore, the acceleration of the skydiver decreases. Eventually, he will reach a speed at which the air resistance becomes equal to the force of gravity:
when this occurs, the acceleration of the skydiver will become zero, so he will continue his fall at a constant velocity: this value of the velocity is called terminal velocity.
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Answer:
It increases proportionally
Explanation:
The gravitational force between the Earth and an object on its surface is given by
where
G is the gravitational constant
M is the Earth's mass
m is the mass of the object
R is the Earth's radius
In this problem, the Earth's mass is increased, while the diameter (and therefore, the radius) doesn't change. From the equation, we see that the gravitational force is directly proportional to the Earth's mass: therefore, if the mass is increased, the force will increase as well by the same proportion (for example, if the mass is doubled, the force will double as well)