|
shareAcceleration
Discussion
definition
When the velocity of an object changes it is said to be accelerating or more formally acceleration is the rate of change of velocity with time.
In everyday English, the word acceleration is often used to describe a state of increasing speed. For many Americans, their only experience with acceleration comes from car ads. When a commercial shouts "zero to sixty in six point seven seconds" what they're saying here is that this particular car takes 6.7 s to reach a speed of 60 mph starting from a complete stop. This example illustrates acceleration as it is commonly understood, but acceleration in physics is much more than just increasing speed.
Any change in the velocity of an object results in an acceleration: increasing speed (what people usually mean when they say acceleration), decreasing speed (also called deceleration or retardation), or changing direction. Yes, that's right, a change in the direction of motion results in an acceleration even if the speed didn't change. That's because acceleration depends on the change in velocity and velocity is a vector quantity — one with both magnitude and direction. Thus, a falling apple accelerates, a car stopping at a traffic light accelerates, and an orbiting planet accelerates. Acceleration occurs anytime an object's speed increases, decreases, or changes direction.
Much like velocity, there are two kinds of acceleration: average and instantaneous. Average acceleration is measured over a "long" (that means measurable) time interval while instantaneous acceleration is measured over a "very small" (unbelievably short or infinitesimal) time interval. For each kind of acceleration, there's an equation …
|
average acceleration |
|
instantaneous acceleration |
For those of you familiar with calculus, check out the second equation, which states that acceleration is the first derivative of velocity with respect to time and the second derivative of displacement with respect to time. Or if you prefer, acceleration is the rate of change in velocity and also (since velocity is a change in displacement) the rate of change of the rate of change of displacement.
units
Calculating acceleration involves dividing velocity by time — or in terms of units, dividing meters per second [m/s] by second [s]. Dividing distance by time twice is the same as dividing distance by the square of time. Thus the SI unit of acceleration is the meter per second squared.
| ⎡ ⎣ |
m | = | m/s | = | m | 1 | ⎤ ⎦ |
|
| s2 | s | s | s |
Another frequently used unit is the acceleration due to gravity — g. Since we are all familiar with the effects of gravity on ourselves and the objects around us it makes for a convenient standard for comparing accelerations. Everything feels normal at 1 g, twice as heavy at 2 g, and weightless at 0 g. This unit has a very precise definition (g = 9.80665 m/s2) but for everyday use 9.8 m/s2 is sufficient.
The unit called acceleration due to gravity (represented by a roman g) is not the same as the natural phenomena called acceleration due to gravity (represented by an italic g). The former has a defined value whereas the latter has to be measured. (More on this later.)
Although the term "g force" is often used, the g is a measure of acceleration, not force. (More on this later.) Of particular concern to humans are the physiological effects of acceleration. To put things in perspective, all values are stated in g.
- In roller coaster design, speed is of the essence. Or, is it? If speed was all there was to designing a thrill ride, then the freeway would be pretty exciting. Most roller coaster rarely exceed 30 m/s (60 mph). Contrary to popular belief, it is the acceleration that makes the ride interesting. A well designed roller coaster will subject the rider to maximum accelerations of 3 to 4 g for brief periods. This is what gives the ride its dangerous feel.
- Despite the immense power of its engines, the acceleration of the Space Shuttle is kept below 3 g. Anything greater would put unnecessary stress on the astronauts, the payload, and the ship itself. Once in orbit, the whole system enters into an extended period of free fall, which provides the sensation of weightlessness. Such a "zero g" environment can also be simulated inside a specially piloted aircraft or a free fall drop tower.
- Fighter pilots can experience accelerations of up to 8 g for brief periods during tactical maneuvers. If sustained for more than a few seconds, 4 to 6 g is sufficient to induce blackout. To prevent "g-force loss of consciousness" (G-LOC), fighter pilots wear special pressure suits that squeeze the legs and abdomen, forcing blood to remain in the head.
- Pilots and astronauts may also train in human centrifuges capable of up to 15 g. Exposure to such intense accelerations is kept very brief for safety reasons. Humans are rarely subjected to anything higher than 8 g for longer than a few seconds.
- Acceleration is related to injury. This is why the most common sensor in a crash test dummy is the accelerometer. Extreme acceleration can lead to death. The acceleration during the crash that killed Diana, Princess of Wales, in 1997 was estimated to have been on the order of 70 to 100 g, which was intense enough to tear the pulmonary artery from her heart — an injury that is nearly impossible to survive. Had she been wearing a seat belt, the acceleration would have been something more like 30 or 35 g — enough to break a rib or two, but not nearly enough to kill most people.
Here are some sample accelerations to end this section.
| Acceleration of Selected Events | |
| a (m/s2) | event |
|---|---|
| 1012 | free fall acceleration on a neutron star |
| 106 | free fall acceleration on a white dwarf star |
| 106 | bullet |
| 104–106 | medical centrifuge |
| 600 | airbags automatically deploy |
| 270 | free fall acceleration on the sun |
| 100-200 | ejection seat |
| 0–150 | human training centrifuge |
| 80 | limit of sustained human tolerance |
| 20–50 | roller coaster |
| 24.8 | free fall acceleration on jupiter |
| 20 | space shuttle, peak |
| 10–40 | manned rocket at launch |
| 9.8 | free fall acceleration on earth |
| 3.7 | free fall acceleration on mars |
| 8.8 | International Space Station |
| 1.6 | free fall acceleration on the moon |
| 1 | elevator, cable |
| 0.6 | free fall acceleration on pluto |
| 0.5 | elevator, hydraulic |
| 9 × 10−10 | anomalous acceleration of pioneer spacecraft |
| 1 × 10−10 | dark matter contribution to galactic acceleration |
| 5 × 10−14 | smallest acceleration in a scientific experiment |
| Automotive Acceleration (g) | ||||
| event | typical car | sports car | F-1 race car | large truck |
|---|---|---|---|---|
| starting | 0.3–0.5 | 0.5–0.9 | 1.7 | < 0.2 |
| braking | 0.8–1.0 | 1.0–1.3 | 2 | ~ 0.6 |
| cornering | 0.7–0.9 | 0.9–1.0 | 3 | ?? |
| Acceleration and the Human Body | |
| a (g) | event |
|---|---|
| 2.9 | sneeze |
| 3.5 | cough |
| 3.6 | crowd jostle |
| 4.1 | slap on back |
| 8.1 | hop off step |
| 10.1 | plop down in chair |
| 60 | chest acceleration limit during car crash at 48 km/h with airbag |
| 70–100 | crash that killed Diana, Princess of Wales, 1997 |
| 150–200 | head acceleration limit during bicycle crash with helmet |