Falling objects: remedial education desperately needed

In summary, the conversation discusses a question about the behavior of two falling objects of different masses, and the use of Galileo's thought experiment and algebra to try to prove their movement. The conversation also mentions the use of the correct formula and understanding its application. Ultimately, the conversation concludes with a link to a helpful resource on the topic.
  • #1
usererror
3
0
I apologize many times in advance for asking what I suspect to be that which is the most repeated question on this site. Last night over dinner with friends, somebody whose judgment was impaired dared me to prove that two falling objects released simultaneously (the usual suspects like friction etc. ignored) of mass m and mass 2m would move side by side. My friend played a two year old asking ”why, why why?” no matter what I said. Not a problem: I was a philosophy student, so I was – am - one of those kids. Anyway, I knew from Middle School the classical laws of motion and the law of gravity, so I dived in. First, I used Galileo’s (I think he said this) thought experiment of two falling masses chained together. But, that seemed to beg the question and so I had to buy another round. Then, I resorted to deriving (via algebra) from f = ma that the acceleration for 2m is 1/2 that for 1m, thus showing that the acceleration of m is twice of 2m. But so what? I needed to prove, but I failed to prove, that, at each instant, m and 2m are side by side. In fact, my showing of the differences in acceleration seemed to falsify my point. I had managed to confuse myself. I had to buy another round. There was laughter. I don’t speak Calculus. Is there an algebraic manipulation of Galileo’s laws that gives the answer? Better yet, is there a thought experiment that does this without begging the question? thank you, physics folk.
 
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  • #3
usererror said:
First, I used Galileo’s (I think he said this) thought experiment of two falling masses chained together. But, that seemed to beg the question and so I had to buy another round.
Galileo's clever argument should have been all you needed.

Then, I resorted to deriving (via algebra) from f = ma that the acceleration for 2m is 1/2 that for 1m, thus showing that the acceleration of m is twice of 2m.
The problem here is that you assumed that the force is constant, but it's not. The force of gravity is proportional to the mass. Twice the mass then twice the gravitational force. Just right to keep the acceleration constant.
 
  • #4
Thanks to both responders. Now I get it. I am proud to have demonstrated that using the correct formula is not the same thing as understanding that formula. Thanks for the help.
 
  • #5
"both" should be "all". (Is there anything else that I can screw up?)
 

FAQ: Falling objects: remedial education desperately needed

1. What is the definition of a falling object?

A falling object is any object that is accelerating towards the ground due to the force of gravity. This can include objects that are dropped from a height, as well as objects that are thrown or propelled upwards and then fall back down.

2. How does the mass of an object affect its rate of fall?

The mass of an object does not affect its rate of fall. All objects, regardless of their mass, will fall at the same rate in a vacuum. This is known as the principle of equivalence, first demonstrated by Galileo in the 16th century.

3. What factors can affect the speed of a falling object?

The speed of a falling object is affected by the object's mass, the force of gravity, and air resistance. Objects with larger masses will experience a greater force of gravity, causing them to fall faster. Air resistance, or the friction between the object and the air, can also slow down the speed of a falling object.

4. What is the formula for calculating the speed of a falling object?

The formula for calculating the speed of a falling object is v = gt, where v is the speed in meters per second, g is the acceleration due to gravity (9.8 m/s²), and t is the time in seconds.

5. Why is remedial education needed for understanding falling objects?

Remedial education is needed for understanding falling objects because it is a fundamental concept in physics and can have practical applications in fields such as engineering and construction. Without a clear understanding of the principles and factors involved in falling objects, it can be difficult to accurately predict and analyze their behavior. This can lead to potentially dangerous situations and compromised structural integrity.

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