# SHM: Planet Problem Homework Statement

• komarxian
In summary, the conversation discusses exploring a newly discovered planet with a radius of 7.20 * 107 m. A lead weight is suspended from a light string with a length of 4.00 m and mass of 0.0280 kg. The time it takes for a transverse pulse to travel the length of the string is measured to be 0.0685 s, compared to 0.0390 s on Earth. The weight of the string is negligible in comparison to the tension in the string. The question asks for the mass of the planet, assuming spherical symmetry in its mass distribution. The solution involves using the speed of transverse waves on a string and comparing it to the speed on Earth.
komarxian

## Homework Statement

You are exploring a newly discovered planet. The radius of the planet is 7.20 * 107 m. You suspend a lead weight from the lower end of a light string that is 4.00 m long and has mass 0.0280 kg. You measure that it takes 0.0685 s for a transverse pulse to travel from the lower end to the upper end of the string. On the earth, for the same string and lead weight, it takes 0.0390 s for a transverse pulse to travel the length of the string. The weight of the string is small enough that you ignore its effect on the tension in the string. Assuming that the mass of the planet is distributed with spherical symmetry, what is its mass?

## The Attempt at a Solution

I don't really know where to go with this? I was thinking something about comparing the radi of the planets, but I'm not sure??

What result/formula do you know for the speed of a transverse wave on a string? The speed of the wave is different in the new planet than at earth, because in the new planet the weight of the lead and hence the tension of the string (those two forces will be approximately equal during the experiment) is different.

komarxian said:
I don't really know where to go with this?
When you don't know where to start with a problem, try listing all the physics principles that you can recognize being involved in the problem statement. Then list any formulas involved with that physics. That should give you some clues as to how to move forward.

## 1. What is SHM and how does it relate to planets?

SHM stands for Simple Harmonic Motion, which is a type of periodic motion where a system oscillates back and forth around a central equilibrium point. This motion can be observed in planets as they orbit around the sun, where the gravitational force acts as the restoring force and keeps the planet in a stable orbit.

## 2. How is the SHM equation used to solve planet problems?

The SHM equation, which is given by x = A cos(ωt + φ), where x is the displacement from equilibrium, A is the amplitude, ω is the angular frequency, and φ is the phase angle, can be used to solve planet problems by representing the planet's motion as a sinusoidal function. This allows us to calculate various parameters such as the period, velocity, and acceleration of the planet.

## 3. What factors affect the SHM of planets?

The SHM of planets is affected by various factors such as the mass of the planet, the mass of the sun, the distance between the planet and the sun, and the gravitational constant. These factors determine the strength of the gravitational force and therefore, the amplitude and frequency of the planet's SHM.

## 4. How does the SHM of planets differ from other types of motion?

The SHM of planets differs from other types of motion in that it is a periodic motion with a restoring force that acts towards an equilibrium point. Other types of motion, such as linear motion, do not have a restoring force and do not exhibit periodic behavior. Additionally, the SHM of planets is influenced by the force of gravity, whereas other types of motion may be affected by other forces such as friction or air resistance.

## 5. Can the SHM equation be used to model the motion of all planets in the solar system?

The SHM equation can be used to model the motion of planets in the solar system, but it may not be an accurate representation for all planets. The SHM equation assumes that the planet's orbit is circular and that the gravitational force acting on the planet is constant. However, the orbits of some planets are not perfectly circular and the gravitational force may vary due to the presence of other celestial bodies. In these cases, more complex equations may be needed to accurately model the planet's motion.

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