Solution Found!
Solved: CP You are exploring a newly discovered planet.
Chapter 15, Problem 60P(choose chapter or problem)
Problem 60P
CP You are exploring a newly discovered planet. The radius of the planet is 7.20 X 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?
Questions & Answers
QUESTION:
Problem 60P
CP You are exploring a newly discovered planet. The radius of the planet is 7.20 X 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?
ANSWER:Solution 60P
The speed of a transverse wave in a string is given by , where T is the tension in the string and m is the mass per unit length of the string.
Given, length of the string
Mass of the string
Therefore, mass per unit length of the string
Time taken by the pulse to move from the lower to the upper end of the string
Therefore, speed of this pulse in the planet
Substituting these values in equation (1),
…..(2)
Now, the speed of the pulse on earth is