A mass weighting 24 lbs stretches a spring 3 inches. The mass is in a medium that exerts a viscous resistance of 21 lbs when the mass has a velocity of 6 ft/sec. Suppose the object is displaced an additional 6 inches and released. Find an equation for the object's displacement, u(t), in feet after t seconds. u(t) =

A diver 50 m deep in 8°C fresh water exhales a 1.2 cm diameter bubble which rises to the surface of the water and has a diameter of 2.2 cm when it reaches the surface of the water. Assume the air bubble rises slow enough that it is always in thermal equilibrium with the surrounding water. Include units in all your numerical responses 1. Determine the pressure of the air inside the bubbles

Q1 A balloon is rising vertically above a level, straight road at a constant rate of 1 ft sec. Just when the balloon is 65 ft above the ground, a bicycle moving at a constant rate of 17 ft sec passes under it. How fast is the distance s(t) between the bicycle andoballoon increasing 3 sec later?

Suppose a body of mass (m) falls from a height (h) under gravity. It lands on a frictionless spring with spring constant (k). Which of the following expressions represents the spring compression (length change) at the time the falling body has come to rest? O (mgh)/(k) O (1/2)k1/2 ((mgh3)/(k))1/2 O (2mgh)/(k))1/2

7. Blood is flowing through point P (Figure 2.5), which is connected to a catheter tip manometer system. Blood enters the manometer and equilibrates the pressure of the various fluids within the system (as denoted in the figure). Calculate the pressure within the blood vessel. Blood density is 1050 kg/m³, atmospheric pressure is 760 mmHg 25 cm Blood Fluid 1, P₁ = 879 kg/m³ Ja 45 cm 2 1 10 cm ✓ Fluid 2. P2 = 1200 kg/m³ Atmospheric pressure Figure 2.5 Schematic of a catheter tip manometer to measure intravascular blood pressure

A 5-kg object is acted upon by a horizontal force P=18t [N], where t is time in seconds. The coefficient of kinetic friction is µk = 0.15. At t = 2 s, the object's velocity is 10 m/s. Determine the velocity at t = 4 s. Use the Impulse-Momentum method. Provide the free-body diagram and show all work. P

M T M H₂0 2 blocks in water The figure shows two blocks of wood (A and B) connected by a string in a tank of water. The masses are equal (M 0.5 kg). 75% of block A is under water. The volume of block B is 454 cm^3. (a) Determine the tension force of the string. (b) Determine the density of block A. =

Fluid mechanics problem Must draw a control volume for this problem

Sparky is on the university speed ice skating team. When crossing the finish line Sparky wants to show off and come across the finish line on one skate with a velocity of 35 ft/sec (V). Sparky weighs 150 lbf. Sparky’s weight is supported by a thin liquid film of water melted by the pressure of the skate blade. If the blade is 13 inches long and 0.125 inches wide estimate Sparky’s deceleration resulting from viscous shear in a water film of thickness of 0.0000575 inches (h). Neglect all end effects. Evaluate all properties at 32°F. Suggest creating a simple schematic of the problem using V, h, and the viscous shear stress (not required).

4. A pump is required to pump fresh water at a flow rate of 5000 m³/hour against a head of 8 mat a speed of 1500 rev/min. It is planned to test a scale model with a head of 2 m at a flowrate of 100 m³/hour under dynamically similar conditions (but neglecting changes in ReynoldsNumber). Determine: a) The speed at which the model must be run.b) The scale that must be used for the model.c) The mechanical power required to drive the model pump is found to be 680W at theoperating point. Calculate the power required to drive the full scale pump.d) After the full scale pump is fitted into the system it is found that the pump head risereally needs to be increased by 30%. At what speed should the full scale pump now berun at to achieve this head rise and what will be the new ideal flow rate and powerconsumption in order to match this operating condition?e) Briefly comment on the main advantages and limitations of testing a scale model toprove the performance of a larger prototype.