A cylindrical object can roll down an incline, as shown in Figure 1. The incline is slightly less
than one meter in length. A group of students wants to determine the acceleration of the object
while it is rolling down the incline. The students have access to the following equipment.
• A stopwatch, which can measure time intervals up to 999 s with a precision of 0.01 s
• A clock, which can measure time intervals up to 12 hours with a precision of 1 min ute (60 s)
• A meterstick, which can measure lengths up to 1 m with a precision of 1 mm
• A pair of calipers, which can measure lengths up to 10 cm with a precision of 0.05 mm
(a) Assume the object moves with a constant acceleration as it rolls down the incline. Write an
equation that includes acceleration and quantities that can be measured or obtained from
measurements by using the available equipment in the list.

Two horizontal plates with infinite length and width are separated by a distance h in the z direction. the bottom plate is moving at a velocity u. the incompressible fluid trapped between the plates is moving in the positive x-direction with the bottom plate. align gravity with positive z. assume that the flow is fully-developed and laminar. if the systems operates at steady state and the pressure gradient in x-direction can be ignored, do the following: 1. sketch your system 2. identify the coordinate system to be used. 3. show your coordinates and origin point on the sketch. list all your assumptions. 5. apply the continuity equation to your system. nts of navier stokes equations of choice to your system 7. solve the resulting differential equation to obtain the velocity profile within the system make sure to list your boundary conditions. check units of velocity 8. describe the velocity profile you obtain using engineering terminology. sketch that on the same sketch you provided in (1). 9. obtain the equation that describes the volumetric flow rate in the system. check the units.

1. a net force of 100 newton’s is applied to a wagon for 5 seconds. this causes the wagon to undergo a change in momentum of

J. j. thomson’s experiment disproved the theory that an atom