Does Aristotle's Theory of Falling Objects Hold Up Against Galileo's Experiment?

[Destrio]

Correct me if my thinking is wrong:

Q: If m is a light stone and M is a heavy one, according to Aristotle M should fall faster than m. Galileo attempted to show that Aristotle's belief was logically inconsistent by the following aruement. tie m and M together to form a double stone. Then, in falling, m should retard M, because it tends to fall more slowly than M; but according to Aristotle the double body is heavier than M and hence should fall faster than M.

A: I believe Galileo's reasoning to be incorrect because there is no upward pull in the dropping of the stone, just the force of gravity pulling them to Earth as a constant rate (ignoring air resistance), the rocks m, M, and m+M, should fall all at the same rate.

Q: A block with mass m is supported by cord C from the veiling, and a similar cord D is attached to the bottom of the block. Explain this: if you give a sudden jerk to D, it will break, but if you pull on C steadily, C will break.

A: If you give a sudden jerk, there is high acceleration, and the force applied is greater than the tension force, causing D to break. If you pull on D steadily, that is to say, with arbitrarily low acceleration, the force from the block due to gravity in addition to the applied force will cause cord C to break.

Any comments/critique is much appreciated. Thanks

 

[Doc Al]

Correct me if my thinking is wrong:

Q: If m is a light stone and M is a heavy one, according to Aristotle M should fall faster than m. Galileo attempted to show that Aristotle's belief was logically inconsistent by the following aruement. tie m and M together to form a double stone. Then, in falling, m should retard M, because it tends to fall more slowly than M; but according to Aristotle the double body is heavier than M and hence should fall faster than M.

A: I believe Galileo's reasoning to be incorrect because there is no upward pull in the dropping of the stone, just the force of gravity pulling them to Earth as a constant rate (ignoring air resistance), the rocks m, M, and m+M, should fall all at the same rate.

Galileo was arguing against Aristotle's argument by taking it to its logical conclusion. You seem to be agreeing with Galileo's conclusion that all rocks fall at the same rate.

Q: A block with mass m is supported by cord C from the veiling, and a similar cord D is attached to the bottom of the block. Explain this: if you give a sudden jerk to D, it will break, but if you pull on C steadily, C will break.

A: If you give a sudden jerk, there is high acceleration, and the force applied is greater than the tension force, causing D to break. If you pull on D steadily, that is to say, with arbitrarily low acceleration, the force from the block due to gravity in addition to the applied force will cause cord C to break.

Not bad. A sudden jerk would require a large force to accelerate the mass, but such force exceeds the breaking strength of the lower string.

 

[charng]

!

A: Your thinking is correct. Galileo's reasoning is flawed because he assumes that the double body would experience a greater force of gravity due to its increased weight, which is not the case. Both the heavy stone and the double stone would experience the same force of gravity, resulting in them falling at the same rate.

For the second question, your explanation is accurate. A sudden jerk would result in a higher force being applied to cord D, causing it to break. However, when pulling on cord C steadily, the force applied is lower and thus the tension force in the cord can withstand it for a longer period of time before breaking. This is due to the concept of impulse, where a higher force over a shorter period of time results in a greater change in momentum and therefore a higher likelihood of breaking the cord.