The grooved pulley of mass m is acted on by a constant force F through a cable which is wrapped securely around the exterior of the pulley. The pulley supports a cylinder of mass M which is attached to the end of a cable which is wrapped securely around an inner hub. If the system is stationary when the force F is first applied, determine the upward velocity v of the supported mass after 4 seconds. Use the values m = 30 kg, M = 11 kg, ro = 345 mm, ri = 230 mm, kO = 250 mm, and F = 85 N. Assume no mechanical interference for the indicated time frame and neglect friction in the bearing at O. What is the time-averaged value of the force T in the cable which supports the 11-kg mass?

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.

Engineers find a new metal that is stronger than steel but much lighter. this material is also significantly cheaper than what is currently used for most aircraft, available in large quantities, and easy to manufacture. the engineers are excited because this new material will lower the costs of buying and operating airplanes for companies. what is probably the best step for the engineers to make next?

Arocket starts from rest and moves upward from the surface of the earth. for the first 10.0 s of its motion, the vertical acceleration of the rocket is given by ay = 12.80 m/s32t, where the +y-direction is upward. (a) what is the height of the rocket above the surface of the earth at t = 10.0 s? b) what is the speed of the rocket when it is 325 m above the surface of the earth?