Simple Accelerometer Equations

[Helicase]

Greeting fellow science enthusiasts,

I just started learning physics so please excuse my primitive knowledge. I'm supposed to discuss a technology that applies concepts related to kinematics and I'd like to discuss accelerometers. Could you please explain the basic equations for motion in an accelerometer or direct me to a helpful resource?

Thanks

 

[Simon Bridge]

Welcome to PF;
All you need is the definition of acceleration. Helps if you know about graphs.

The accelerometer gives you a series of numbers which are the accelerations for each axis it keeps track of.
You graph them ... the area under the graph gives you the speed-time data, and the area under a graph of the speed-time data gives you the displacement-time data.

 

[Helicase]

That is quite helpful. Thank you!

 

[mpresic]

It is likely the most useful model for an accelerometer is a box with a mass suspended from the ceiling by a spring. When the box is not accelerating, the tension responsible for elongating (i.e. lengthening) the spring is equal to the force of gravity. A scale (ruler) along side the spring will record this (reference) length.
If the box accelerates (increases it's speed) upward, the mass moves downward, just like when you are in an elevator and it starts moving upward, you feel heavier. The downward motion of the mass indicates the force on the mass has increased. (A better way to say this is the spring has to provide a force that overcomes gravity and in addition it has to supply an additional force due to the acceleration of the elevator. Just like the scale would record your heavier weight when you ride in the elevator when it starts upward) The difference in length (current length - reference length) times the spring constant (k); divided my the mass is the acceleration of the box.

This describes the general idea for one-axis and this is oversimplified. If you need more detail I can provide it but this are the general idea.

To some extent, the other axes are simpler because gravity does not stretch the spring initially. The "reference" length is equal to the length of the un-stretched spring. I will check Resnick and Halliday Physics Vol 1. I think I remember learning this there.

 

[PJC01]

!

Hello there,

It's great to hear that you are interested in learning about accelerometers! These devices are commonly used in many technologies, such as smartphones, cars, and airplanes, to measure acceleration and movement.

The basic equations for motion in an accelerometer are derived from Newton's second law, which states that the net force acting on an object is equal to its mass multiplied by its acceleration. In an accelerometer, this net force is typically measured by a small mass suspended by springs or other materials that can detect changes in acceleration.

Some of the key equations used in accelerometers include F = ma (force equals mass times acceleration), a = Δv/Δt (acceleration equals change in velocity over change in time), and v = u + at (final velocity equals initial velocity plus acceleration multiplied by time). These equations can be used to calculate the acceleration of an object based on the force acting on it, or to calculate the velocity or position of an object over time.

I recommend checking out resources such as Khan Academy or Physics Classroom for more detailed explanations and examples of how these equations are used in accelerometers. Good luck with your studies!