Cases – Chapter 6
1.A glider is a propulsionless airplane that is completely dependent on external energy to remain airborne. It must be pulled forward to obtain the lift it needs to start flying. Once aloft, it can use the air rising off hot spots on the ground to remain in the air almost indefinitely. But for the moment, let’s suppose that the air is completely motionless.
a.One way to launch a glider is to pull it with a car, using a rope that can be detached from the glider when it’s in the air. Just after the glider’s wheels leave the runway, what four forces are acting on the glider?
b.When the glider releases the rope, one of the four forces disappears. With only three forces left, what happens to the glider’s forward component of velocity?
c.If the glider begins to descend gradually, the air no longer approaches it horizontally. From the glider’s perspective, the air is now blowing upward toward it at a shallow angle. How does this new wind direction affect the directions of the three forces on the glider, as viewed from the ground?
d.It’s possible for the descending glider to maintain a constant forward component of velocity. Explain.
e.Now suppose that the air is rising quickly, perhaps heated by contact with a hot spot on the ground. In that case, the glider doesn’t have to descend in order to maintain a constant forward component of velocity; it can glide straight and level forever. Why?
2.A helicopter suspends itself from a spinning rotor. Each blade in the rotor is actually a wing, with an airfoil shape that creates lift as it slices through the air. To hover, the helicopter’s rotor creates just enough upward lift to exactly balance the helicopter’s downward weight.
a.The rotor keeps turning at a constant rate. To control the rotor’s lift, the helicopter adjusts the angles of attack of the blades as they turn. If a hovering helicopter increases the angles of attack of all of its blades simultaneously, what will happen to the forces on the helicopter and how will it move?
b.The helicopter can also adjust the angle of attack of a single blade. If it increases the angle of attack of whatever blade is currently on the pilot’s right, the helicopter will experience a torque about its center of mass. Which way will the helicopter begin to tilt?
c.If the helicopter is tilted nose down and tail high, the helicopter will begin to accelerate forward. Why?
d.To turn the helicopter so that it faces a different direction, something must exert a torque on it about a vertical axis. That’s one reason why the helicopter has a small rotor at the end of its tail boom. This rotor pushes air to the right or left, depending on the angles of attack of its blades. Which way should the tail rotor push the air to turn the helicopter to the right?
e.The main rotor blades are actually flexible, but they extend almost straight outward when the rotor is spinning. Why?
3.A parachute slows your descent after you jump out of a plane. In the parachute’s frame of reference, wind is blowing upward toward it and its large surface area creates a great deal of upward drag force. This drag opposes your weight and slows your fall.
a.As air rushes past the parachute, the pressures above and below the cloth become different. Why is the pressure below the parachute higher than atmospheric pressure?
b.Why is the pressure above the parachute roughly equal to atmospheric pressure?
c.How does air exert an upward force on the parachute?
d.Why does the amount of upward force exerted on the parachute depend on how fast you’re falling?
e.If you open your parachute while you’re falling very rapidly, the parachute slows your descent. Which way is the net force on you pointing, and which way do you accelerate?
f.A few seconds after your parachute opens, you reach terminal velocity. You are no longer accelerating. How does the parachute’s drag force compare to your weight?
g.How heavy do you feel when you first jump out of the plane? when your opening parachute first begins to slow your descent? when you are descending at terminal velocity?
4.The sail of a sailboat acts like a wing, creating both lift and drag. Because it deflects the wind horizontally, the lift is horizontal, too, and pulls the boat through the water.
a.Wind blows around both sides of the sail. It bends inward, toward the sail, as it travels around the outside. How does the pressure on that side of the sail compare with atmospheric pressure?
b.Air passing across the inside surface of the sail bends outward, away from the sail. How does the pressure on that side of the sail compare with atmospheric pressure?
c.What is the direction of the overall force exerted on the sail by the wind?
d.A sailboat has a flat keel that projects into the water and prevents the boat from tilting or drifting sideways. The keel effectively produces a straight track through the water along which the boat can move. If the wind is blowing toward the boat from north to south and the boat’s sail is experiencing an eastward lift force, show that the keel can be turned so that the net force on the boat is toward the northeast. (This is how sailboats manage to sail upwind!)
e.Without a keel, the only horizontal forces pushing the boat through the water come from the wind. These wind forces always push the boat at least partly downwind. Why can’t forces from the wind push the boat partly upwind?
f.The wind and keel together can push the boat in an upwind direction. But the boat doesn’t accelerate forever; it eventually reaches a maximum forward velocity. What other force acts on the boat to reduce the net force on the boat to zero so that it maintains a constant velocity?
g.As the boat moves forward, it’s steered by its rudder. With the rudder turned so that it deflects water to one side as the boat travels forward, the boat begins to rotate. How do the water and rudder exert a torque on the sailboat?
5.Umbrellas are subject to many forces on a windy day.
a.When you hold the umbrella upright, its curved surface is above you like a dome. When the wind blows horizontally, why does the umbrella feel lighter than normal?
b.If you are walking into the wind and tip the umbrella forward so that it’s in front of your face, why doesn’t your face feel much wind anymore?
c.If you hold your hand just beyond the edge of the umbrella while it’s still tipped into the wind, you’ll feel that the airspeed there is even higher than that of the wind. Explain.
d.If you accidentally tip the umbrella backward, so that the inner surface of its dome is exposed to the wind, the wind will push the umbrella backward hard. Why is this force stronger than when the umbrella is tipped forward?
e.When the inner surface of the umbrella is exposed to a strong wind, the umbrella may turn inside out. Explain this effect in terms of a pressure imbalance.
6.You’re watching a downhill ski race. In this race, the skiers are trying to descend a mountain as quickly as possible without crashing. The veteran skier standing nearby makes a number of observations about the racers that can actually be explained scientifically.
a.The veteran points out that one of the skiers is skidding around corners and that such skids slow her down. During a skid, the skis slip sideways across the snow rather than sliding straight forward through it. Why will skidding always slow the skier down?
b.The veteran notes that skiers slow down and lose time whenever they remain airborne too long after passing over a jump. Why should a skier regain contact with the slope as soon as possible after a jump?
c.A skier loses control and skis off the course into a net. The veteran remarks that it’s much better to hit a net than a tree. In terms of force and momentum, why is it safer for the skier to crash into a net rather than into a tree?
d.The veteran is impressed by one skier’s consistent compact form, a tight tucked shape. Why doesn’t the skier want to push on the air during the descent?
e.The veteran remarks about the high air pressure that skiers feel in front of them as they travel swiftly downhill. What causes this high pressure?
7.A ballpoint pen uses a tiny ball to apply ink to paper. As you draw the pen across the paper, the ball rotates and transfers very viscous ink from a supply tube to the paper.
a.What force exerts the torque that makes the ball rotate?
b.What force carries ink around with the turning ball?
c.A ballpoint pen won’t write upside down for long—the ink descends a small distance in the supply tube and the ball can’t transfer any to the paper. But the ball prevents air from entering the supply tube, so the ink stops descending and won’t leak from the pen. Why does the ink stop descending?
d.Occasionally air does get in between the ball and the ink and the pen stops working. How does shaking the pen drive the air past the ball so that the pen works again?
8.You and your best friend live on the 58th floors of two adjacent high-rise apartment buildings. You have windows that face one another across an open courtyard. One day, the city turns off all the water to your friend’s building. You decide to help your friend obtain water. You immediately buy 500m of garden hose, enough to reach from either apartment to the ground at least two times.
a.Your first thought is to run water from the gardener’s faucet, which is at street level in the courtyard, up to your friend’s apartment. Although water runs briefly into the hose, it never reaches your friend’s apartment. Why not?
b.You decide to obtain water from a faucet in your apartment. You run the hose out your window, down to the courtyard, and up to your friend’s apartment. To your surprise, the hose bursts in the courtyard when you turn on the water. Why does the hose burst?
c.You patch the hose and decide not to let it droop down to the courtyard. With the hose running almost directly across the gap between windows, you turn on the faucet. What happens this time?
d.Water is flowing rapidly through all 500m of hose as your friend fills a bathtub. To stop the flow, your friend suddenly makes a kink in the end of the hose. The pressure in the hose increases and the hose bursts. What produced this pressure surge?
e.As water flows out of the narrow split in the hose, it accelerates to a very high speed. What happens to its pressure as its speed increases?
9.A kite is an airfoil that uses the wind to produce lift. Held in place by a string, a kite can remain aloft indefinitely. The diamond kite is a particularly simple kite.
a.As the wind passes under the lower surface of the diamond kite, it bends away from the surface and slows down. How does the air pressure there compare to atmospheric pressure?
b.As the wind passes over the upper surface of the diamond kite, it separates from the kite and creates a turbulent air pocket. How does the air pressure there compare to atmospheric pressure?
c.In what direction is the overall force that the air exerts on the kite?
d.If the upper surface of the kite were bowed outward so that the air didn’t separate from it, the kite would experience more upward lift. Why?
e.Both the diamond kite’s center of mass and center of aerodynamic pressure are roughly at its geometrical center. By itself, the kite is unstable. Why does the kite tend to turn around or flip upside down?
f.To make it stable, the diamond kite has a fabric tail attached to the bottom of the diamond. How does the tail’s extra weight help to keep the kite from flipping upside-down?
g.How does the tail’s extra drag help to keep the kite from flipping back to front?
10.Centrifugal pumps are commonly used to move water through pipes. The pumping mechanism is a spinning rotor, usually turned by an electric motor. Water enters the rotor near its center and leaves from its outer edge. The rotor has vanes that help to push the water around in a circle. The pump has no valves or narrow passages, so it can be used to pump almost anything, even sewage.
a.If the outlet of the pump is sealed, the water will travel around in a circle with the rotor. Which way is the water accelerating as it turns?
b.For the water to accelerate in this direction, how must the pressures at the center and edge of the rotor compare to one another?
c.How do the energies of the water at the center and edge of the rotor compare to one another?
d.If the outlet of the pump is opened, water will begin to flow out of the pump. Why will additional water flow outward from the center of the rotor to replace it?
e.If the outlet of the centrifugal pump is opened to the air through a narrow nozzle, the water will leave it at high speed. Why must the water pass through a narrow nozzle before it can speed up?
f.How could a centrifugal pump be used to propel a boat?
11.To measure its airspeed, an airplane uses a device called a pitot tube. This rod-shaped instrument points forward into the onrushing airstream. It has two holes, each of which is connected to its own pressure gauge: one hole in its front to catch the onrushing air and one hole on its side to examine the moving air as it passes the tube.
a.When air enters the front hole of the pitot tube, it slows down. How is the pressure of the slowed air inside this hole related to the plane’s airspeed?
b.When air passes by the side hole of the pitot tube, its speed doesn’t change. The hole permits the pitot tube to measure the pressure of this passing air. Is that pressure related to the plane’s airspeed? If so, what’s the relationship?
c.How can the plane use pressure measurements made at these two holes to determine how fast the plane is moving?
d.An airplane’s pitot tube is carefully suspended away from the plane’s surface. Why shouldn’t the tube be mounted right along the surface where it would be less vulnerable to damage?
e.The pitot tube is mounted in a region of the plane that isn’t involved in lift. Why shouldn’t the pitot tube be mounted on a lifting surface, such as the top of a wing?
12.You are washing a car in front of your apartment. You have a garden hose attached to a water faucet and a bucket with a sponge in it.
a.When the water faucet is on, water flows through the hose and out the nozzle. What causes water to accelerate to high speed as it leaves the nozzle?
b.As it arcs through the air, the stream of water is at atmospheric pressure. But when you accidentally hit the bucket with the stream of water, the bucket accelerates away from you and falls off the car. Evidently, the water pressure increases when it touches the bucket. Why does the water pressure increase?
c.You decide that perhaps the water would clean more effectively if it were moving faster, so you let the water spray upward and fall back down on the car. But the falling water is traveling no faster than it was when it first left the nozzle. Why not?
d.The sponge sinks to the bottom of the bucket of water. What can you say about the sponge’s average density?
13.A professional house washer uses a powerful pump to create the very high-pressure water needed to remove dirt and grime from a house’s surface.
a.The same amount of water leaves the pump through the sprayer hose as enters it from a water faucet. In what way is the water’s energy different in the sprayer hose than it was in the garden hose that delivered the water to the pump?
b.As the water flows out of the sprayer nozzle, what happens to its energy?
c.As the water flies through the air toward the house, it’s at atmospheric pressure. Why then does the water pressure in the sprayer hose affect the water’s ability to clean the house’s surface?
d.Some gadget stores sell special “pressure-boosting” nozzles that are supposed to clean better than normal garden hose nozzles. These devices claim to increase the water pressure and are supposedly powered by the water itself. Why is this claim impossible?
14.When a patient receives an injection, fluid passes from a cylinder with a plunger in it, through a narrow, hollow needle, and into the patient’s arm.