Tag: vacuum cleaners

Is terminal velocity the same for every object of the same mass or can the terminal velocity of two parachutists (same weight and height) be different? -CV

Terminal velocity is the result of a delicate balance between two forces—an object’s downward weight and the upward drag force that object experiences as it moves downward through the air. Terminal velocity is reached when those two forces exactly balance one another and the object experiences a net force of zero, stops accelerating, and simply coasts downward at a constant velocity. Since the upward drag force increases with downward speed, there is generally a velocity at which this balance occurs—the terminal velocity.

But while a parachutist can’t change her weight, she can change the relationship between her downward speed and the upward drag force she experiences. If she rolls herself into a compact ball, she weakens the drag force and ultimately increases her terminal velocity. On the other hand, if she spreads her arms and legs wide so as to catch more air, she strengthens the drag force and decreases her terminal velocity. Popping open her parachute strengthens the drag force so much that her terminal velocity diminishes almost to zero and she coasts slowly downward to a comfortable landing. So to answer your question—two twin parachutists will descend at very different terminal velocities if they adopt different profiles or if only one opens a parachute.

When an object is free falling, I understand that the earth’s gravity causes its velocity to increase at 10 meters/second² in the downward direction. Is there a point at which this object would reach a “terminal velocity” in the earth’s atmosphere and cease to accelerate? — CS, Sykesville, MD

Yes, most objects will reach a terminal velocity and stop accelerating downward. The faster an object drops, the more air resistance it experiences. This air resistance pushes the object upward and at least partially cancels the downward force of gravity—the object’s weight. When the object’s downward speed becomes high enough, the upward air resistance force exactly cancels the object’s downward weight. At that point, the object experiences zero net force and it no longer accelerates. Instead, it descends at a constant downward velocity—its terminal velocity. This terminal velocity is determined partly by the object’s density and size and partly by its aerodynamics. Large, dense, and aerodynamic objects tend to have very large terminal velocities while small, low-density, non-aerodynamic objects tend to have very small terminal velocities.

What is the approximate terminal velocity for a spent falling bullet that was fired into the air? Is this velocity sufficient to kill someone? – M

A bullet’s terminal velocity is the downward speed at which the upward force of air resistance acting on it balances its downward weight. Once the falling bullet reaches this speed, it coasts downward at a steady rate. Because air resistance depends largely on surface area while weight depends on volume, larger bullets will drop faster than smaller bullets (just as a piece of chalk drops faster than chalk dust). While I am not sure of the exact speed of a dropping bullet, I expect it to be several hundred miles per hour. As to whether or not it can kill someone, the answer is most definitely yes. In fact, a distant cousin of mine was killed several years ago during Mardi Gras when a falling spent bullet pierced her brain. Firing bullets into the air is an extraordinarily foolish and inconsiderate action. In cultures where it’s common to fire guns during celebrations, innocent people are frequently killed by these descending “party favors.” If you ever see people shooting guns into the air, you should immediately seek cover in a basement. Their bullets will return to earth in less than thirty seconds and will be just as deadly when they arrive as if they had been shot right at you.

Why do some parts of a house get dustier than others? — BC, North Reading, MA

Dust particles are tiny bits of rock, ash, and organic matter that have been ground into fine pieces by the wind and wear. Although these particles are denser than the air that surrounds them, they have trouble falling through the air because as soon as they move faster than about a snail’s pace, they experience considerable air resistance or drag forces. A dust particle has trouble falling through the air because the upward drag force it experiences while descending even a few millimeters per second is enough to balance its weight so that it stops accelerating downward. Because dust particles have so much trouble descending through air, they tend to be swept along with moving air. That’s why areas of your home that have large air currents tend to accumulate relatively little dust—the dust is swept along with the air currents and doesn’t have time to descend all the way to the floor or furniture. But in areas of your home with fairly still air, the dust can slowly settle out so that it coats all the surfaces.

In “Empire Strikes Back”, when Luke learns that Darth Vader is his father, he falls/jumps off a platform in Cloud City without his hand. Given the fact that objects reach terminal velocity, which would have a faster terminal velocity and which would hit the ground first if in the movie that fell from a height of 1000 meters?

Luke would probably reach the ground before his hand. An object reaches a terminal velocity as it fall because the upward force of air resistance becomes stronger as the object’s downward speed increases and this upward force eventually stops the object from accelerating downward. The object’s downward speed at the point when it stops accelerating is its terminal velocity. Since air resistance is what sets this terminal velocity, an object that experiences a great deal of air resistance relative to its weight will have a smaller terminal velocity than an object that experiences relatively little air resistance relative to its weight. Because Luke is much larger than his hand, he has lots of weight relative to his surface area. Since surface area largely determines air resistance, he experiences relatively little air resistance relative to his weight. His hand has less weight relative to its surface area and it experiences a lot of air resistance relative to its weight. So Luke’s terminal velocity is larger than that of his hand. He reaches the ground first. This tendency for large objects to descend faster than small objects explains why small animals, such as insects, can fall from incredible heights without injury. They reach their terminal velocities quickly and descend rather slowly to the ground.

How does the fan in a vacuum cleaner boost the pressure back up so that the air flowing through the vacuum cleaner the air will go back into the room?

The fan is a rotating assembly of ramps. As the ramps move, they sweep the air from one side of the fan to the other and do work on that air. The air either accelerates as the fan blades spin past, or its pressure builds up. Either way, its total energy increases. The fan can take low-pressure air from one side and whisk it over to the other side where the pressure is higher. It can push air against the natural direction of flow (from high pressure to low pressure). It’s essentially a pump for air.

Suppose that you fall out of a plane about 30 seconds after your parachute pack fell out. Is it really possible to catch up to your parachute pack and save yourself?

The answer depends on how high the plane was flying and just how much air resistance the pack experiences as it falls. After a few seconds of falling, an object reaches a terminal velocity—it stops accelerating downward. That’s because the upward force that air resistance exerts on it grows stronger as its downward velocity increases. Eventually, the upward force it experiences exactly balances its downward weight and it has no net force on it—it doesn’t accelerate. For a person, this terminal velocity ranges from about 100 mph to 200 mph, depending on the person’s shape. Curling into a compact ball should allow you to reach a relatively high terminal velocity of 200 mph. Since the parachute pack is relatively light but has substantial surface area for the wind to push against, it probably has a lower terminal velocity of say, 100 mph. This arrangement would allow you to approach the pack at a relative velocity of 100 mph. In order to actually overtake the pack, you’ll still need some time, so the higher the plane was when you started, the better your chances are. Since the pack has a 30 second head start and descends at 100 mph, it will be about 0.83 miles below you when you leave the plane. You’ll catch up to it 30 seconds later, during which time you will have dropped a total of 1.67 miles. Thus in principle, you could catch the pack so long as the plane’s altitude was more than about 1.67 miles. To allow time to put the pack on, for the parachute to open, and for your terminal velocity to then become low enough to avoid injury, you’d better have the plane at more than about 2.5 miles. Still, this doesn’t sound like a fun experiment.

What is drag force?

A drag force is a force that opposes an object’s motion through a fluid. Like sliding friction, drag always pushes the object in the direction opposite its motion though the fluid. Air resistance is really a drag force. You feel drag pushing you backward when you ride a bicycle fast. You also feel drag when you hold your hand out the window of a fast-moving car—it pushes your hand toward the back of the car and in the direction opposite your hand’s motion through the air. If you were to fall downward, you would feel a drag force upward, in the direction opposite your motion through the air. And leaves experience a drag force when wind blows on them—pushing them downwind and in the direction opposite their motion through the air (they are moving upwind through the air, so it pushes them downwind). Incidentally, the object pushes back on the fluid with drag force, too, and this force on the fluid pushes the fluid in the direction opposite its motion past the object. This force tends to stop moving fluids and to turn their kinetic energies into thermal energy.

When you suspended the Ping-Pong ball in the stream of air from the pipe, why did the ball spin? The same thing happened to the two flat pieces of plastic that were held together when air flowed out between them.

The Ping-Pong ball spun because the viscous drag forces it experienced weren’t equal on all sides. As we’ll see shortly, there are a variety of different drag forces and they can act at different locations on an object. In the case of viscous drag, it acts locally at each point where air slides across the surface of the object. Since the airflow from the pipe wasn’t perfectly uniform, the air swept past the ball faster in some places than it did in others. These differences in airspeed became most significant when the ball began to drift away from the airstream—the sudden increase in airspeed on the side of the ball nearest the center of the airstream is what created the low pressure that allowed the surrounding air to push the ball back toward the center of the airstream. But minor differences in airspeed also exerted unbalanced torques on the ball and caused it to spin. Similar flow imperfections between the two plates created differences in viscous drag and exerted torques on the two plates. That’s why they began to spin around slightly.

Why does dust settle on the moving blades of a fan?

As the air flows across the blades of a fan, the dust particles in it occasionally pierce through the airflow and hit the blades. The same sort of process occurs when a bug hits the windshield of a car; the bug would normally follow the airflow but its inertia prevents it from moving out of the way quickly enough and it hit. Once a dust particle hits the fan blades, there isn’t much to remove it. The air moves remarkably slowly right at the surface of the fan because that surface layer of air experiences lots of viscous drag. Even though the air is moving swiftly only a few millimeters away, the air right on the fan blade is almost stationary. Thus the dust can cling to the blade indefinitely.