Two massive spheres of mass = 800 and = 2.5 are suspended by wires of negligible mass, which are attached to the ceiling as shown in the figure below. The smaller sphere is then raised from a height ℎ = 15 , in relation to its relaxing position, and released. When it reaches the lowest part of its trajectory, it collides with the largest sphere, which, in turn, is over a height . If the restitution coefficient of the system is = 0.65, determine the value of considering a central impact.

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

Along wire of diameter 1 mm is submerged in an oil bath of temperature ∞ 31°c. the wire has an electrical resistance per unit length of 0.01 ω/m. if a current of 103 a flows through the wire and the convection coefficient is 500 w/m2·k, what is the steady-state temperature of the wire? from the time the current is applied, how long does it take for the wire to reach a temperature that is within 1°c of the steady-state value? the properties of the wire are 8000 kg/m3, 500 j/kg·k, and 20 w/m·k.

Dc versus ac problem. suppose your dc power supply is set to 15 v and the vertical setting on the oscilloscope is at 5 v/div. how many divisions will the trace deflect if you connect the output of the power supply to the scope with the a input switch set on dc? how many divisions if the switch is on ac?