Simple accelerometer proof (a=tan(theta)) help

In summary, the conversation is about a ball attached to a string in a car, where the angle of the string is measured during acceleration. The proof for a=tan(theta) is discussed, with the understanding that tan(theta) is dimensionless and cannot be equal to acceleration. The need to find the ratio between weight and tension and how it relates to acceleration is also mentioned. The conversation ends with the clarification that a=g tan(theta) makes sense and the possibility that in some texts, acceleration is measured in units of "g".
  • #1
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The situation is there is a ball attached to a string in a car, and the angle that the string makes is measured when the car is accelerating. I'm having a bit of trouble with the proof that a=tan(theta)

so far I've gotten that
weight=mg=Tcos(theta)
a=ma=Tsin(theta)

But what I don't understand is why you need to find the ratio between them and how that shows acceleration.
a/g=sin(theta)/cos(theta)
a=gtan(theta)

another one of my questions is what happens to the g in the equation?

Help is much appreciated thanks!
 
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  • #2
DarkBlitz said:
The situation is there is a ball attached to a string in a car, and the angle that the string makes is measured when the car is accelerating. I'm having a bit of trouble with the proof that a=tan(theta)
It's normal to have trouble. This is not correct. Look at the units. Tan(theta) is dimensionless. How can be equal to the acceleration?

DarkBlitz said:
The situation is there is a ball attached to a string in a car, and
so far I've gotten that
weight=mg=Tcos(theta)
a=ma=Tsin(theta)

But what I don't understand is why you need to find the ratio between them and how that shows acceleration.
a/g=sin(theta)/cos(theta)
a=gtan(theta)

another one of my questions is what happens to the g in the equation?

Help is much appreciated thanks!

You have two equations with two unknowns (T and a). As you are interested in a, you can isolate T from the first equation, replace in the other one and solve for a.
a = g tan(theta) makes sense.

PS. It may be that you found the a=tan(theta) in a text where they measure acceleration in units of "g"?
Then what you have there is actually a/g=Tan(theta).
 
  • #3
AH, ok that makes sense. Thanks for the clarification!
 

What is a simple accelerometer proof?

A simple accelerometer proof is a demonstration or experiment that shows the relationship between the angle of an object and its acceleration. It is often used to illustrate the concept of acceleration and how it can be measured using an accelerometer.

How does a simple accelerometer proof work?

A simple accelerometer proof works by using the principles of trigonometry to calculate the acceleration of an object based on its angle. By measuring the angle and using the formula a = tan(theta), where a is the acceleration and theta is the angle, the acceleration can be determined.

What materials are needed to perform a simple accelerometer proof?

To perform a simple accelerometer proof, you will need a protractor, a string, a weight, and an accelerometer. The protractor is used to measure the angle, the string and weight are used to create the angle, and the accelerometer is used to measure the acceleration.

Can a simple accelerometer proof be done at home?

Yes, a simple accelerometer proof can be done at home with basic materials. This experiment is a great way to learn about acceleration and can be done as a fun and educational activity.

Why is a simple accelerometer proof important?

A simple accelerometer proof is important because it helps to illustrate the concept of acceleration and how it can be measured. This proof is also used in many real-world applications, such as in the design and testing of vehicles and electronic devices.

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