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 ...continues

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 e ...continues

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 ...continues

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.

Gravity Work required to move a mass radially outward from the c.m. of a planet

A uniform spherical planet has mass M= 8.5 E 25 kg and radius R= 7.5 E 6 m. A hole is drilled from the surface to mass m= 360 kg at an initial position r1= 2.5 E 6 m from the center. PART a. Find the initial gravity force F that the planet exerts on mass m. PART b. Find the work required to bring mass m to the surface at a ...continues

Satellite in circular orbit around Earth Find period, speed, height etc.

An observation satellite whose mass m= 4800 kg is to be put into a circular orbit around the earth at a height h= 322000 m above the surface in a precise north-south orbit. See attachment #1. PART a. In this orbit, find the force of gravity exerted by the earth on the satellite. PART b. Find the speed, v, and the period, T, of ...continues

A cube suspended in water by a cord. Buoyant force and equilibrium.

A cube of aluminum, whose volume is Va= .125 m^3, and whose density is Da= 2700 kg/m^3 is suspended from a cord which holds it stationary with the top surface horizontal and h= 2.2 m below the surface of fresh water. See attachment #1 showing known parameters. PART a. Find the mass of the aluminum. PART b. Find C, the fo ...continues

Archimedes' Principle for a block in two different liquids

A solid block of mass M= 21 kg floats with 80% if its volume submerged in carbon tetrachloride, whose density is Dc= 1600 kg/m^3. When this block is submerged in liquid X however, it requires an upward pull by a cord of F= 72 newtons to hold it stationary, completely submerged. a. Find Db, the density of the block. b. Find D ...continues

Friction problem

The asking problem: A block of weight W=60 lb rests on a rough plane as shown. Knowing that "alpha"= 20° and Us(coefficient of static friction) = 0.30, determine the magnitude and direction of the smallest force P required to start the block up the plane. The answer of this problem for verification:35.9 lb at 36.7° directe ...continues