A baseball bat has a "sweet spot" where a ball can be hit with almost effortless transmission of energy. A careful analysis of baseball dynamics shows that this special spot is located at the point where an applied force would result in pure rotation of the bat about the handle grip.

Determine the location of the sweet spot of the bat shown in the figure (Figure 1) . The linear mass density of the bat is given roughly by (0.61+3.3x2)kg/m, where x is in meters measured from the end of the handle. The entire bat is 0.80 m long. The desired rotation point should be 5.0 cm from the end where the bat is held. [Hint: Where is the cm of the bat?]

find Xs.

An automobile of mass 2000 kg moving at 30 m/s is braked suddenly with a constant braking force of 10000 n. how far does the car travel before stopping?

An uplifted block of rock between two normal faults

As part of an industrial process, air as an ideal gas at 10 bar, 400k expands at steady state through a valve to a pressure of 4 bar. the mass flow rate of air is 0.5 kg/s. the air then passes through a heat exchanger where it is cooled to a temperature of 295k with negligible change in pressure. the valve can be modeled as a throttling process, and kinetic and potential energy effects can be neglected. (a) for a control volume enclosing the valve and heat exchanger and enough of the local surroundings that the heat transfer occurs at the ambient temperature of 295 k, determine the rate of entropy production, in kw/k. (b) if the expansion valve were replaced by an adiabatic turbine operating isentropically, what would be the entropy production? compare the results of parts (a) and (b) and discuss.