Application of Aristotle with free fall

[Gear2d]

Homework Statement

Aristotle believed that the time it takes for an object to fall a given distance is inversely proportional to its weight. Given objects A,B,C and D with weights of 10,40,20 and 30 grams, which one would have the heights terminal velocity if dropped from the same height?

The Attempt at a Solution

I was done to object A (10g) and B (40g). The answer was object B.

My question is:

1)Terminal velocity is referred to when mg = Fdrag?

2) I see that time takes longer for object A than B, so how can I equate this to terminal velocity?

 

[PhanthomJay]

Homework Statement

Aristotle believed that the time it takes for an object to fall a given distance is inversely proportional to its weight. Given objects A,B,C and D with weights of 10,40,20 and 30 grams, which one would have the heights terminal velocity if dropped from the same height?

The Attempt at a Solution

I was done to object A (10g) and B (40g). The answer was object B.

My question is:

1)Terminal velocity is referred to when mg = Fdrag?

yes, but you don't really need this info in this problem.

2) I see that time takes longer for object A than B, so how can I equate this to terminal velocity?

Aristotle apparently presumed that the objects fall at some constant (uniform) speed, which the problem is referring to as 'terminal velocity'. You can use the basic kinematic equation that relates constant speed to distance and time to arrive at the 'Aristotlian' answer.

 

[baba89]

I would like to point out that Aristotle's theory on free fall has been disproven by modern physics. In reality, the time it takes for an object to fall a given distance depends on several factors, including air resistance, gravitational acceleration, and the shape and size of the object. Terminal velocity, which is the maximum speed an object can reach while falling, is also influenced by these factors and is not solely determined by the weight of the object.

To answer your first question, terminal velocity is indeed reached when the force of gravity (mg) is equal to the force of air resistance (Fdrag). This is because at this point, the net force on the object is zero and it can no longer accelerate.

To address your second question, the time it takes for an object to fall does not necessarily equate to its terminal velocity. While it is true that a heavier object will reach a higher terminal velocity than a lighter object due to the force of gravity being greater, the shape and size of the object also play a significant role. For example, a parachute will reach a lower terminal velocity than a small rock with the same weight, due to the larger surface area and increased air resistance of the parachute.

In summary, while Aristotle's theory may have seemed logical at the time, it has been disproven by modern physics. When considering free fall and terminal velocity, it is important to take into account all factors that influence these phenomena, rather than just the weight of the objects involved.