Galileo’s law of falling bodies states that the rate of fall caused by gravity is the same for all objects, regardless of weight. This means that all objects have a free-falling acceleration of 9.8m/s2. However, a significant contradiction of this theory is the fact that a lump of lead will fall faster than objects such as feathers. According to Newton’s laws, an object will accelerate if the forces acting on it are unbalanced. Falling objects initially accelerate due to the fact that there is no force large enough to balance the downward force of gravity. Nonetheless, as an object gains speed, it encounters an increasing amount of upward air resistance force. In fact, objects will continue to accelerate until the air resistance force increases to a large enough value to balance the downward force of gravity. Overall, since the lump of lead has more mass, it weighs more and thus, experiences a greater downward force of gravity than the feather. Thus, the lump of lead will accelerate for a longer period of time before there is sufficient upward air resistance to balance the large downward force of gravity. Nonetheless, as the feather has more surface area when compared to its mass, it results in the proportionately higher surface area creating more air resistance for the feather. This means that the feather will have to accelerate for a shorter amount of time than the lead until there is enough air resistance to balance its lighter weight. However, in a vacuum – where there is no air resistance – the lump of lead would fall at the same rate as the feather under the force of gravity.
Is this correct?
Yes, your understanding of the difference in falling speeds between a lump of lead and a feather is correct. In the presence of air resistance, objects of different weights and shapes will fall at different rates. This is because, in addition to the downward force of gravity, there is also an upward force of air resistance acting on the falling object.
Initially, when an object starts to fall, there is no force large enough to balance the downward force of gravity. Therefore, the object accelerates and gains speed. However, as the object gains speed, it encounters an increasing amount of upward air resistance force. This air resistance force opposes the object's motion and tries to slow it down.
For objects with more mass, like the lump of lead, they have a greater downward force of gravity because gravity depends on mass. As a result, these objects will accelerate for a longer period of time before the upward air resistance force becomes large enough to balance the downward force of gravity. Hence, the lump of lead falls faster than lighter objects like feathers.
On the other hand, objects with a larger surface area compared to their mass, like feathers, experience a proportionately higher surface area for the air resistance to act upon. This creates more air resistance for the feather, causing it to decelerate faster than an object with less surface area, such as the lump of lead. Consequently, the feather has to accelerate for a shorter time before the upward air resistance force becomes large enough to balance its lighter weight.
However, in a vacuum environment where there is no air resistance, both the lead and the feather would fall at the same rate under the force of gravity alone, as Galileo's law of falling bodies states.