36. Example 5.7: You whirl a bucket of water around in a vertical circle of radius 1.22 m. What minimum speed at the top of the circle will keep the water in the bucket?
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- When a person sits erect, increasing the vertical position of their brain by 36.0 cm, the heart must continue to pump blood to the brain at the same rate. (a) What is the gain in gravitational potential energy for 100 mL of blood raised 36.0 cm? (b) What is the drop in pressure, neglecting any losses due to friction? (c) Discuss how the gain in gravitational potential energy and the decrease in pressure are related.You are part of a team in an engineering class that is working on a scale model of a new design for a life vest. You have been asked to find the mass of a piece of foam that will be used for flotation. Because the piece is too bulky to fit on your balance, you break it into two parts. You measure the mass of the first part as 128.3 0.3 g and the second part as 77.0 0.3 g. a. What are the maximum and minimum values for the total mass you might reasonably report? b. What is the best estimate for the total mass of the foam? Hint: Propagation of uncertainty is described in Appendix A.Suppose you are at the top of Mount Everest and you fill a water balloon. The air pressure at the top of Mount Everest is 58 kPa. a. What is the fractional change in the balloons volume V/Vi when you take it to sea level? b. If instead you take it 100 m below the surface of the ocean, what is the fractional change in its volume?
- Suppose you hit a steel nail with a 0.500-kg hammer, initially moving at 15.0 m/s and brought to rest in 2.80 mm. (a) What average force is exerted on the nail? (b) How much is the nail compressed if it is 2.50 mm in diameter and 6.00-cm long? (c) What pressure is created on the 1.00-mm-diameter tip of the nail?As it plows a parking lot, a snowplow pushes an ever-growing pile of snow in front of it. Suppose a car moving through the air is similarly modeled as a cylinder of area A pushing a growing disk of air in front of it. The originally stationary air is set into motion at the constant speed v of the cylinder as shown in Figure P8.32. In a time interval t, a new disk of air of mass m must be moved a distance v t and hence must be given a kinetic energy 12(m)v2. Using this model, show that the cars power loss owing to air resistance is 12Av3 and that the resistive force acting on the car is 12Av2, where is the density of air. Compare this result with the empirical expression 12DAv2 for the resistive force. Figure P8.32You are applying for a position with a sea rescue unit and are taking the qualifying exam. One question on the exam is about the use of a diving bell. The diving bell is in the shape of a cylinder with a vertical length of L = 2.50 m. It is closed at the upper circular end and open at the lower circular end. The hell is lowered from air into seawater ( = 1.025 g/cm3) and kept in its upright orientation as it is lowered. The air in the bell is initially at temperature Ti = 20.0C. The bell, with two humans inside, is lowered to a depth (measured to the bottom of the bell) of 27.0 fathoms, or h = 49.4 m. At this depth the water temperature is Tf = 4.0C, and the bell is in thermal equilibrium with the water. The exam question asks you to compare two situations: (i) No additional gas is added to the interior of the bell as it is submerged. Therefore, water enters the open bottom of the bell and the volume of the enclosed air decreases. (ii) The bell is fitted with pressurized air tanks, which deliver high-pressure air into the interior of the bell to keep the level of water at the bottom edge of the bell. This choice requires money and effort to attach the tanks. The exam question asks: Which scenario is better?
- Review. In a water pistol, a piston drives water through a large tube of area A1 into a smaller tube of area A2 as shown in Figure P14.46. The radius of the large tube is 1.00 cm and that of the small tube is 1.00 mm. The smaller tube is 3.00 cm above the larger tube. (a) If the pistol is fired horizontally at a height of 1.50 m, determine the time interval required for the water to travel from the nozzle to the ground. Neglect air resistance and assume atmospheric pressure is 1.00 atm. (b) If the desired range of the stream is 8.00 m, with what speed v2 must the stream leave the nozzle? (c) At what speed v1 must the plunger be moved to achieve the desired range? (d) What is the pressure at the nozzle? (e) Find the pressure needed in the larger tube. (f) Calculate the force that must be exerted on the trigger to achieve the desired range. (The force that must be exerted is due to pressure over and above atmospheric pressure.) Figure P14.46(a) What is the density of a woman who floats in freshwater with 4.00% of her volume above the surface? This could be measured by placing her in a tank with marks on the side to measure how much water she displaces when floating and when held under water (briefly). (b) What percent of her volume is above the surface when she floats in seawater?(a) Calculate the retarding force due to viscosity of the air layer between a cart and a level air track given the following information: air temperature is 20°C, the cart is moving at 0.400 m/s, surface area is 2.50102 m2, ad thickness of air layer is 6.00105 m. (b) What is the ration of this force to the weight of the 0.300-kg cart?
- To allow a car to slow down or stop, hydraulic brakes transmit forces from a master cylinder to the brake pads through a fluid. Imagine this system as a tube filled with an incompressible fluid and a piston on each end. A force of 95.0 N is applied to a piston 2.65 cm in diameter on one end of the tube. a. What is the magnitude of the force that is exerted on the piston 5.15 cm in diameter on the other side? b. If the 2.65-cm piston is displaced by 1.00 cm, by how much is the 5.15-cm piston displaced?An inflated spherical beach ball with a radius of 0.3573 m and average density of 10.65 kg/m3 is being held under water in a pool by Janelle. The density of the water in the pool is 1000.0 kg/m3. When Janelle releases the ball, it begins to rise to the surface. If the drag coefficient of the ball in the water is 0.470 and the constant upward force on the ball is 1875 N, what will be the terminal speed of the ball as it rises? Ignore the effects of gravity on the ball.The human brain and spinal cord are immersed in the cerebrospinal fluid. The fluid is normally continuous between the cranial and spinal cavities and exerts a pressure of 100 to 200 mm of H2O above the prevailing atmospheric pressure. In medical work, pressures are often measured in units of mm of H2O because body fluids, including the cerebrospinal fluid, typically have nearly the same density as water. The pressure of the cerebrospinal fluid can be measured by means of a spinal tap. A hollow tube is inserted into the spinal column, and the height lo which the fluid rises is observed, as shown in Figure P9.83. If the fluid ruses to a height of 160. mm, we write its gauge pressure as 160. mm H2O. (a) Express this pressure in pascals, in atmospheres, and in millimeters of mercury. (b) Sometimes it is necessary to determine whether an accident victim has suffered a crushed vertebra that is blocking the flow of cerebrospinal fluid in the spinal column. In other cases, a physician may suspect that a tumor or other growth is blocking the spinal column and inhibiting the flow of cerebrospinal fluid. Such conditions ran be investigated by means of the Queckensted test. In this procedure, the veins in the patients neck are compressed lo make the blood pressure rise in the brain. The increase in pressure in the blood vessels is transmitted to the cerebrospinal fluid. What should be the normal effect on the height of the fluid in the spinal tap? (c) Suppose compressing the veins had no effect on the level of the fluid. What might account for this phenomenon?
