Areducing elbow in a horizontal pipe is used to deflect water flow by an angle θ = 125° from the flow direction while accelerating it. the elbow discharges water into the atmosphere. the cross-sectional area of the elbow is 150 cm2 at the inlet and 25 cm2 at the exit. the elevation difference between the centers of the exit and the inlet is 40 cm. the mass of the elbow and the water in it is 52 kg. determine the anchoring force needed to hold the elbow in place. take the momentum-flux correction factor to be 1.03 at both the inlet and the outlet. the density of water is 1000 kg/m3, and the flow rate of water is 30 kg/s.

The frequency of vibrations of a vibrating violin string is given by f = 1 2l t ρ where l is the length of the string, t is its tension, and ρ is its linear density.† (a) find the rate of change of the frequency with respect to the following. (i) the length (when t and ρ are constant) (ii) the tension (when l and ρ are constant) (iii) the linear density (when l and t are constant) (b) the pitch of a note (how high or low the note sounds) is determined by the frequency f. (the higher the frequency, the higher the pitch.) use the signs of the derivatives in part (a) to determine what happens to the pitch of a note for the following. (i) when the effective length of a string is decreased by placing a finger on the string so a shorter portion of the string vibrates df dl 0 and l is ⇒ f is ⇒ (ii) when the tension is increased by turning a tuning peg df dt 0 and t is ⇒ f is ⇒ (iii) when the linear density is increased by switching to another string df dρ 0 and ρ is ⇒ f is ⇒

Alarge box of mass m is pulled across a horizontal frictionless surface by a horizontal rope with tension t. a small box of mass m sits on top of the large box. the coefficients of static and

Find the dimensions and area of the largest rectangle that can be inscribed in the upper half of the ellipse. (give your answers in terms of a and b. enter the dimensions as a comma-separated list.)