Calculate the expectation value of momentum for the "free particle" system in the ground state (use n-1 wavefunction). explain the meaning of your result.

In an old-fashioned amusement park ride, passengers stand inside a 3.0-m-tall, 5.0-m-diameter hollow steel cylinder with their backs against the wall. the cylinder begins to rotate about a vertical axis. then the floor on which the passengers are standing suddenly drops away! if all goes well, the passengers will “stick” to the wall and not slide. clothing has a static coefficient of friction against steel in the range 0.60 to 1.0 and a kinetic coefficient in the range 0.40 to 0.70. part a what is the minimum rotational frequency, in rpm, for which the ride is safe? express your answer using two significant figures. f f = rpm

A10-kg piece of aluminum sits at the bottom of a lake, right next to a 10-kg piece of lead, which is much denser than aluminum. which one has the greater buoyant force on it? explain. b - the aluminum a) both have the same buoyant force. b) the aluminum c) the lead d) it cannot be determined without knowing their volumes.

What happens when the vapor pressure of a liquid is equal to the external pressure?