Achild playing in a swimming pool realizes that it is easy to push a small inflated ball under the surface of the water whereas a large ball requires a lot of force. the child happens to have a styrofoam ball (the shape of the ball will not distort when it is forced under the surface), which he forces under the surface of the water. if the child needs to supply 5.00×102 n to totally submerge the ball, calculate the diameter d of the ball. the density of water is ? w=1.000×103 kg/m3, the density of styrofoam is ? foam=95.0 kg/m3, and the acceleration due to gravity is g=9.81 m/s2.

Next a skier is pulled by a tow rope up a frictionless ski slope that makes an angle of 15 with the horizontal. the rope moves parallel to the slope with a constant speed of 0.69 m/s. the force of the rope does 800 3 of work on the skier as the skier moves a distance of 8.4 m up the incline. (a) if the rope moved with a constant speed of 2.2 m/s how much work would the force of the rope do on the skier as the skler moved a distance of 8.4 m up the incline? at what rate is the force of the rope doing work on the skier when the rope moves with a speed of (b) 0.69 m/s and (c) 2.2 m/s?

Amichelson interferometer operating at a 600 nm wavelength has a 3.02-cm-long glass cell in one arm. to begin, the air is pumped out of the cell and mirror m2 is adjusted to produce a bright spot at the center of the interference pattern. then a valve is opened and air is slowly admitted into the cell. the index of refraction of air at 1.00 atm pressure is 1.00028.how many bright-dark-bright fringe shifts are observed as the cell fills with air?

Two identical stars with mass m orbit around their center of mass. each orbit is circular and has radius r, so that the two stars are always on opposite sides of the circle. (a) find the gravitational force of one star on the other. (b) find the orbital speed of each star and the period of the orbit. (c) how much energy would be required to separate the two stars to infinity?