explain why a flat sheet of paper and a sheet of paper crumpled into a ball which are dropped from a height of 2 meters will not accelerate at the same rate?

Air friction depends on the area of a an object

When a flat sheet of paper and a crumpled sheet of paper are dropped from a height of 2 meters, they will not accelerate at the same rate due to the differences in air resistance acting on them.

Initially, both objects experience the force of gravity, pulling them towards the ground. According to Newton's second law of motion, the force experienced by an object is equal to its mass multiplied by its acceleration. Therefore, if the objects have the same mass, the force of gravity acting on them should be the same.

However, the shape of the objects affects the amount of air resistance they experience. Air resistance is the frictional force exerted by the air on a moving object. The flat sheet of paper has a larger surface area exposed to the air, leading to more air molecules colliding with it and creating greater resistance. On the other hand, the crumpled sheet of paper has a smaller surface area, resulting in fewer air molecules colliding with it and comparatively less resistance.

Due to this difference in air resistance, the flat sheet of paper will experience more resistance and therefore a lower acceleration compared to the crumpled sheet of paper. The crumpled sheet, with less air resistance, will experience a smaller opposing force from the air and therefore a higher acceleration.

To verify this, you can perform an experiment. Drop both the flat sheet of paper and the crumpled sheet of paper from the same height simultaneously and observe their descent. You will notice that the crumpled sheet of paper will reach the ground faster than the flat one, demonstrating the difference in acceleration caused by air resistance.