Yo-yo tension and force

A yo-yo of mass M has an axle of radius b and a spool of radius R. Its moment of inertia can be taken to be MR^2/2 and the thickness of the string can be neglected. The yo-yo is released from rest. a) What it the tension in the cord as the yo-yo descends and as it ascends? b)The center of the yo-yo descends distance h before the string is fully unwound. Assuming that it reverses direction with uniform spin velocity, find the average force on the string while the yo-yo turns around.

Pulley system

A disk of mass M and radius R unwinds from a tape wrapped around it. The tape passes over a frictionless pulley, and a mass m is suspended from the other end. Assume that the disk drops vertically. a) Relate the accelerations of m and the disk, a and A, respectively to the angular acceration of the disk. Ans clue- If A were to equal 2a, then angular acceleration would equal 3A/R b) Find a, A and angular acceleration

Calculating the beat frequency in organ pipes.

Two pipes, equal in length, are each open at one end. Each has a fundamental frequency of 479 Hz at 18 C. In one pipe the air temperature is increased to 21 C. If the two pipes are sounded together, what beat frequency results?

Working with underwater sound waves, intensity and distances.

A microphone in the ocean is sensitive to sounds emitted by porpoises. To produce a usable signal, sound waves striking the microphone must have an intensity of 10.7 dB. If porpoises emit sound waves with a power of 0.0491 W, how far can a porpoise be from the microphone and still be heard? Disregard absorption of sound waves by the water.

Calculating a planet's interior gravity field.

Assume a spherical, uniform planet with mass M and a radius R. a) Develop a relationship which will the give the gravity field of a planet at any point beneath its surface which is distance r from the center. b) Use the mass and radius of the earth to find the earth's field at a point halfway to the surface.