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.

For aerosol sprays such as Lysol, are they essentially creating “dustlike” particles that float in the air?

Yes, except that the word “float” isn’t what you really mean. An aerosol is a suspension of fine solid or liquid particles in a gas. What holds those particles up against their downward weights isn’t the buoyant force—these particles are much more dense than the gas that surrounds them. Instead, it’s viscous drag. When the particles begin to fall downward through the gas, they experience such large upward viscous drag forces that they reach terminal velocity at only about 1 millimeter-per-second. The slightest breeze carries the particles with it so that they rarely have a chance to settle to the floor because of gravity. In an aerosol spray, the particles are carried forward by the gas emerging from the bottle and they hit the surfaces in front of the bottle.

How does a water aspirator pump work?

The water aspirator pump is essentially a pipe with a narrowing in it. As water flows through that narrowing, it speeds up and its pressure drops—it’s exchanging its pressure energy for kinetic energy. A tiny opening in the side of the narrowing allows water or air to enter the high-speed flow. Since the pressure in that high-speed flow is very low, atmospheric pressure pushes fluids through the tiny opening and into the flow. The flow pumps fluids through the opening and into the water stream. If you connect a hose to the tiny opening, you can suck chemicals up the hose and into the water stream.

How does an airbrush work? Can you briefly explain it again.

In an airbrush, slow-moving but high-pressure air from a hose is allowed to pass through a very narrow channel. As the air enters this channel, it speeds up and its pressure drops—it has exchanged its pressure potential energy for kinetic energy. The channel is so narrow and the air moves so quickly through it that the pressure inside the channel drops below atmospheric pressure! There is a tiny pipe that attaches to this channel at right angles and that dips into a bottle of paint. As the pressure inside the channel falls below atmospheric pressure, the atmospheric pressure in the paint bottle pushes the paint toward the channel. The paint begins flowing into the channel and it collides with the high-speed stream of air. The paint is ripped into tiny droplets and these droplets travels through the channel along with the air. As the air emerges from the narrow channel, its pressure rises and it slows down, but it still moves fast enough to carry the paint droplets to the object that’s being painted.

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.