Two planets connected by a spring no gravity

In summary: Hello, the problem described involves two planets connected by a spring with a spring constant K. The lighter planet does circular motion around the heavier planet, with no gravity between the two objects. The question asks for the angular velocity (ω) of this motion. The equation for this problem is mv^2/R=kx, where the centripetal force is supplied by the spring. However, the TA clarified that in the equilibrium position, x=R. This allows us to simplify the equation to ω=(k/m)^(0.5).
  • #1
physicsishard
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hello I am confusing about a physics problem right now.
instead of gravity, two planets are connected by a spring with spring constant K. And since the mass of one planet is much bigger than that of the other. So, lighter planet does circular motion around the heavier planet. Then, it asks ω (angular velocity) of this circular motion (no gravity between these two objects). I know that the equation for this problem is that
mv^2/R=kx (centripetal force is supplied by the spring) but, my TA said that x=R in equilibrium position. And the ω=(k/m)^(0.5) I don't understand it !
Thank you very much if you can clarify this point !
 
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  • #2
physicsishard said:
hello I am confusing about a physics problem right now.
instead of gravity, two planets are connected by a spring with spring constant K. And since the mass of one planet is much bigger than that of the other. So, lighter planet does circular motion around the heavier planet. Then, it asks ω (angular velocity) of this circular motion (no gravity between these two objects). I know that the equation for this problem is that
mv^2/R=kx (centripetal force is supplied by the spring) but, my TA said that x=R in equilibrium position. And the ω=(k/m)^(0.5) I don't understand it !

It is not clear from the text, but the relaxed length of the spring is taken zero. So x, the change of length is equal to the distance of the smaller planet from the other one. You can write the equation for te centripetal force as mv^2/R=kR. As it is circular motion and the radius is R how is the linear speed v related to the angular speed ω ?

ehild
 

What is the concept of "Two planets connected by a spring with no gravity"?

The concept refers to a hypothetical scenario where two planets are connected by a spring, but there is no gravitational force acting between them. This scenario is often used in physics thought experiments to explore the behavior of objects in the absence of gravity.

What would happen to the two planets in this scenario?

In this scenario, the two planets would remain stationary in relation to each other, as there is no gravitational force pulling them towards or away from each other. However, the spring connecting them would still experience tension and compression forces, causing it to stretch and contract periodically.

How does the spring affect the motion of the planets?

The spring would act as the only force acting between the two planets, causing them to oscillate back and forth along the axis of the spring. This means that the planets would experience a constant change in their distance from each other, but their relative positions would remain the same.

What factors would affect the behavior of the spring in this scenario?

The behavior of the spring would be affected by its stiffness, length, and the masses of the two planets. A stiffer spring would experience greater tension and compression forces, causing the planets to oscillate at a higher frequency. A longer spring would result in a longer period of oscillation. Additionally, the masses of the planets would determine the magnitude of the tension and compression forces experienced by the spring.

How does this scenario relate to real-life situations?

Although this scenario may seem unrealistic, it can help us understand the principles of oscillation and the behavior of objects connected by a spring. It also allows us to explore the effects of gravity on the motion of objects without the complicating factor of other forces. In real life, springs are commonly used in various applications, such as in mechanical systems or in sports equipment, and their behavior is influenced by factors like stiffness and mass, similar to the scenario of two planets connected by a spring with no gravity.

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