You throw a ball vertically upward. When you let go of the ball, it has a kinetic energy Ka (assume the ball has zero gravitational potential energy at the point where you let go). Without air drag, the ball reaches a maximum height h above the point where you let go. You throw the ball again, this time giving it a kinetic energy of Ko/2. What will be the maximum height of the ball (again without air drag)? (Note that the square root of 2 Is approximately 1.4.) 256*h 16h 4h O2 h 1.4 h /1.4 Oh/2 h/4 h/16 h/256

In some of Joule’s experiments (Figure 1), work was done on water held in an adiabatic calorimeter. The work was done by a rotating paddle, driven by falling weights. Assume the volume of the water remains constant during these experiments.a. In one experiment a 25-kg mass was allowed to fall 20 times through a height of 2 m; what was the maximum amount of work done? b. If a 25-kg mass were fired into the calorimeter and brought to a standstill, what should its initial velocity be to accomplish the same effect as in (a)? c. If the calorimeter held 1.2 kg of water and if process (a) caused the water temperature to rise from 288 to 290 K, what is the numerical value for the factor that connects temperature rise to work under these conditions?

HOMEWORK-2 Considering the steady-state laminar flow of a liquid with density p and viscosity p in a vertical tube of length L and radius R; a) Show the momentum flux and velocity profile in the figure. b) Determine the momentum flux distribution, the velocity distribution, the maximum velocity (Vzmax), and the average velocity (Vzaverage) expressions. PL L R ! Po 1111111 Flow in

Consider the steady, isothermal, irrotational flow of an incompressible frictionless fluid subject only to a body force characterized by a potential O, where F,=- V@ (in units of force/volume). Since the fluid is frictionless, the only surface force is due to pressure, F =-pn. By completing a momentum balance on a material volume of fluid subject to the constraints listed above, derive Bernouilli's law, P + ½pv² + O = constant along a fluid streamline.

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1. FA Newtonian fluid is flowing between two large parallel plates in the z direction. The top plate is moving in the positive z direction at a constant velocity Vo. The bottom plate is stationary. The velocity profile this flow is given by V(y) = V₁ (a) (b) (77) where 2H is the distance between the two plates. y is the vertical coordinate from the center plane, and is the velocity profile as a function of y. Draw a schematic of the flow system with the appropriate coordinate system. For plates with a total width W in the x-direction and length L in the z-direction, derive an expression for the volumetric flow rate Q through the plates.