How does the fan in a vacuum cleaner boost the pressure back up so that the air …

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 …

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?

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.