A bucket with a mass of one kilogram and a rope of negligible weight are used to draw water from a well that is 10 meters deep. The bucket is filled with 20 liters of water, and is pulled up at a rate of 0.5 meters per second. As the bucket is pulled up, water leaks out at a rate of 0.1 liters per second. (a) How long does it take to pull the bucket to the top of the well?
(b) What is the mass of the bucket (plus water) when it has been raised у meters?
(c) What is the weight force of the bucket (plus water) when it has been raised у meters? Hint: the density of water is one kilogram per liter
(d) Write an integral for the work done to raise the bucket to the top of the well.
(e) Evaluate the integral in part (d).

Describe the path of the electric current through a circuit?

Chapter 23, problem 075 the figure shows a geiger counter, a device used to detect ionizing radiation (radiation that causes ionization of atoms). the counter consists of a thin, positively charged central wire surrounded by a concentric, circular, conducting cylindrical shell with an equal negative charge. thus, a strong radial electric field is set up inside the shell. the shell contains a low-pressure inert gas. a particle of radiation entering the device through the shell wall ionizes a few of the gas atoms. the resulting free electrons (e) are drawn to the positive wire. however, the electric field is so intense that, between collisions with gas atoms, the free electrons gain energy sufficient to ionize these atoms also. more free electrons are thereby created, and the process is repeated until the electrons reach the wire. the resulting "avalanche" of electrons is collected by the wire, generating a signal that is used to record the passage of the original particle of radiation. suppose the radius of the central wire is 24 âµm, the inner radius of the shell 2.3 cm, and the length of the shell 14 cm. if the electric field at the shell's inner wall is 2.8 ă— 104 n/c, what is the total positive charge on the central wire?

Explain how the energy of rubber ball is tranforned as it roll down a ramp. give evidence that the energy of the og the ball remains the same at all points on the ramp