A 6.00-kg crate is suspended from the end of a short vertical rope of negligible mass. An upward force F(t) is applied to the end of the rope, and the height of the crate above its initial position is given by y(t)=(2.80m/s)t+(0.610m/s^3)t^3. What is the magnitude of F when t = 4.00 s?

A0.750 kg aluminum pan is removed from the stove and plunged into a sink filled with 10.0 kg of water at 293 k. the water temperature quickly rises to 297 k. what was the initial temperature of the aluminum pan? the specific heat of aluminum is ca = 900 j/(kgk) and water is cw = 4190 j/(kgk)

6–43 a food department is kept at 2128c by a refrigerator in an environment at 308c. the total heat gain to the food department is estimated to be 3300 kj/h and the heat rejection in the condenser is 4800 kj/h. determine the power input to the compressor, in kw and the cop of the refrigerator.

Consider a double atwood machine constructed as follows: a mass 4m is suspended from a string that passes over a massless pulley on frictionless bearings. the other end of this string supports a second similar pulley, over which passes a second string supporting a mass of 3m at one end and m at the other. using two suitable generalized coordinates, set up the lagrangian and use the lagrange equations to find the acceleration of the mass 4m when the system is released. explain why the top pulley rotates even though it carries equal weights on each side.