Two skydivers of different masses jump from a plane. Explain how their falls compare, including the effects of gravity, mass, and air resistance.
When two skydivers of different masses jump from a plane, their falls experience the same force due to gravity, air resistance, and mass. However, these forces affect each skydiver differently based on their mass.
1. Gravity: Both skydivers experience the same acceleration due to gravity, which is approximately 9.81 m/s² on Earth. This means that their velocities will increase by about 9.81 m/s for each second they are in free fall. However, since they have different masses, the force experienced due to gravity (F = m * a) will be different for both skydivers.
2. Mass: The skydiver with a larger mass will experience a larger gravitational force. As a result, they will have more inertia, which means they will be more resistant to changes in their motion (including the effects of air resistance). In a way, this makes the heavier skydiver better equipped for a terminal velocity free fall.
3. Air resistance: Air resistance acts against the motion of the skydivers, creating a drag force that opposes their downward motion. The drag force experienced by each skydiver depends on their size, shape, and velocity. At first, when both skydivers have just jumped out of the plane, their air resistance is low since they have relatively low velocities. As they fall and their velocities increase, the air resistance also increases. Eventually, the air resistance becomes large enough to counteract the gravitational force, reaching a constant velocity known as terminal velocity.
Since the heavier skydiver has a larger mass and more inertia, they are less affected by air resistance compared to the lighter skydiver. This means that the heavier skydiver will reach a higher terminal velocity than the lighter skydiver, taking a shorter amount of time to reach the ground. However, the difference in their terminal velocities and fall times will not be considerable, as air resistance still plays a significant role in slowing down both skydivers.
In summary, both skydivers experience the same gravitational acceleration and forces due to air resistance. However, their masses result in different forces experienced and levels of inertia. The heavier skydiver will be slightly less affected by air resistance and will reach a higher terminal velocity, taking a shorter time to reach the ground compared to the lighter skydiver. Nevertheless, the overall difference in their falls will not be very significant due to the considerable effect of air resistance on both skydivers.