A91.1 kg horizontal circular platform rotates freely with no friction about its center at an initial angular velocity of 1.73 rad/s . a monkey drops a 9.41 kg bunch of bananas vertically onto the platform. they hit the platform at 45 of its radius from the center, adhere to it there, and continue to rotate with it. then the monkey, with a mass of 21.1 kg , drops vertically to the edge of the platform, grasps it, and continues to rotate with the platform. find the angular velocity of the platform with its load. model the platform as a disk of radius 1.61 m .

Many machines- including inclined planes such as ramps- increase the strength of the force put into the machine but decrease the distance over which the force is applied. true or false

Na food processing facility, a spherical container of inner radius r1 5 40 cm, outer radius r2 5 41 cm, and ther- mal conductivity k 5 1.5 w/m · k is used to store hot water and to keep it at 100°c at all times. to accomplish this, the outer surface of the container is wrapped with a 800-w electric strip heater and then insulated. the temperature of the inner surface of the container is observed to be nearly 120°c at all times. as- suming 10 percent of the heat generated in the heater is lost through the insulation, (a) express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the container, (b) obtain a relation for the variation of temperature in the container material by solving the differential equation, and (c) evaluate the outer surface tempera- ture of the container. also determine how much water at 100°c this tank can supply steadily if the cold water enters at 20°c.

The electric field between square plates of a parallel-plate capacitor has magnitude e. the potential across the plates is maintained with constant voltage by a battery as they are pulled apart to twice their original separation, which is small compared to the dimensions of the plates. the magnitude of the electric field between the plates is now equal to a)e b)e/4 c)e/2 d)4e e)2e