Thought experiment that if solved will prove 3rd law to fail in spirals pls help

[eosphoro]

im in a 10 m tower, a 1kg cannonball is shot underneath me horizontally at 10 m from me and I am holding a cable that is tight to the ball, for the ball to make a circle the tension shown in a dinamometer put in the cable would be v*v*m/r= 1000N being the speed of the ball 100 m/s

i shoot the ball again and this time i let the cable slip or glide away in my hands in such a way that the tension shown is 100 N, let's neglect transformation of friction into heat, gravity and cable weight

how long will it take the ball to reach my horizontal?


what radius will have the cable when the ball is at my horizontal?

when the ball is at my horizontal going to my vertical what constant tension would show the dinamometer if when the ball reached my vertical had to have 10 m radius again by my having pulled the cable?

how long will it take it to reach my vertical?

the cable is pulled or let away by crancking the cable(rigid in this case) and the spinning axe in such a way that for every grade the axe spins the cable retracts or spands one meter or whatever necesary

:zzz:

 

[AndyW]

Hello, thank you for your interesting post. I would like to provide some clarification and calculations for your scenario.

First, let's assume that the 10 m tower is located on Earth, where the acceleration due to gravity is approximately 9.8 m/s^2. Also, we will assume that the cannonball is shot at a horizontal velocity of 100 m/s, as stated in the post.

To answer your first question, we can use the formula for circular motion, which is T = mv^2/r, where T is the tension, m is the mass of the cannonball, v is the velocity of the ball, and r is the radius of the circle. Since we know the values for m, v, and T (1000 N), we can rearrange the equation to solve for r. This gives us a radius of approximately 1 m.

Next, we need to determine the time it takes for the ball to reach the horizontal. We can use the formula d = vt, where d is the distance, v is the velocity, and t is the time. In this case, the distance is 10 m and the velocity is 100 m/s. Solving for t gives us a time of 0.1 seconds.

Moving on to the next part of the scenario, where the cable is allowed to slip or glide away in your hands. In this case, the tension in the cable is only 100 N. Using the same formula as before, we can solve for the radius of the circle, which is now approximately 10 m. This makes sense, as the tension is directly proportional to the radius in circular motion.

For the third question, we need to determine the constant tension that would be shown on the dynamometer when the ball reaches the vertical with a radius of 10 m. This can be calculated using the same formula as before, but now solving for T. This gives us a tension of 1000 N, which is the same as the initial scenario.

Finally, we need to calculate the time it takes for the ball to reach the vertical. Using the same formula as before, but now solving for t, we get a time of approximately 0.316 seconds.

In conclusion, the time it takes for the ball to reach the horizontal is 0.1 seconds, the radius of the cable when the ball is at the horizontal is approximately 1 m, the constant tension when the ball

 

[sir-pinski]

It is important to note that this thought experiment does not prove the failure of the third law of motion, but rather explores the dynamics of circular motion and tension in a cable.

Firstly, it is not possible for the ball to make a perfect circle while maintaining a constant tension in the cable. This is because the tension in the cable is directly related to the speed of the ball and the radius of the circle, as shown in the equation given. If the speed of the ball remains constant, but the radius decreases (as it would with a perfect circle), the tension in the cable would increase, violating the given condition of 100 N.

Additionally, the concept of "letting the cable slip or glide away" does not accurately reflect the real-world scenario. The tension in the cable would change as the cable is released, resulting in an acceleration of the ball and a change in the radius of the circle. This would make it difficult to accurately predict the time it would take for the ball to reach the horizontal or vertical positions.

Furthermore, the idea of "pulling the cable" to maintain a specific radius is not a realistic scenario. The tension in the cable would constantly change as the cable is being pulled, making it difficult to maintain a constant radius.

In conclusion, while this thought experiment may be interesting to explore, it does not prove the failure of the third law of motion. It is important to consider real-world factors and limitations when discussing the dynamics of circular motion and tension in a cable.