The figure shows a large uncovered container used to brew beer (p beer: 1015 Kg/M^3). The cross-sectional area of the container is 4m^2 . On one side of the container is a pipe used to take samples of the beer. Attached to the pipe is a pressure gauge. At a given instant of time when the beer level in the container is 2.00 m above the pressure gauge, the level of beer in the container is dropping at a rate of 1 m/Sand the speed of beer past the pressure gauge is 5 m/s .

(a) What is the flow rate in this beer brewing apparatus? M^3/s

(b) Beer flows out of the pipe into a keg of 0.13 m^3 volume . How long does it take to fill up the keg? s

c) What is the cross-sectional area of the pipe? m^2

(d) What is the absolute pressure at the position of the gauge in units of Pascals? Pa

To answer the following questions, refer to the figure shown here. Note that the initial position is .X= -2.25 m

(a) Suppose that the figure depicts the displacement of a mass in a horizontal mass-spring system as a function of time. Draw the mass-spring system at time t=0 s . Label the positions x=A, X= -A , in addition to x(t=0), where represents the amplitude. Draw an arrow to indicate which direction the mass is travelling.

(b) Simple harmonic motion can also be represented as the periodic motion of a point moving on the unit circle. Draw a unit circle, and indicate the point on the unit circle representing the system at time t=0 s

(c) If the simple harmonic motion of the mass is described by a wavey(t)=Acos (wt+ ), determine the amplitude A , angular frequency w , and phase constant , and write the function in terms of these values (give the angular frequency and phase constant to three significant digits). [Hint: When determining the phase constant, you may want to refer to your diagram in part (b)].

(i) The amplitude is the maximum positive displacement. A= ?m

(ii) The angular frequency w is related to the period by w=2 /T, where T is the period of one full cycle. ? S^-1

(iii) The initial phase 0 describes the particle's initial angular position. Express 0 as an angle between 0 and 2.0