physics question, direct proportionality

The term "Directly proportional" means that the relationship between force and acceleration can be represented in the form

. force = constant * acceleration + number

(The words "constant" and "number" refer to numbers. Force and Acceleration are your variables)

From your math class, hopefully you will remember the equation=

. y = m * x + b

This is a function for a straight line. Notice that these two equations look awfully similar.

I will leave the final bit for you. Tell me the punch line and I will tell you if you got it. (It would also help me to know what grade you are in. I am assuming you are a freshman in high school?)

Actually, A is directly proportional to B if A=K*B.

http://mathworld.wolfram.com/DirectlyProportional.html

Oops, markr is right.

You are really looking for the equation

. force = constant * acceleration

i'm not to sure what year a freshman is, as i'm from england, i will be in year 11 this year (if that helps at all), um, so does that mean that basically if you alter one, that will have a direct affect on the other? and this will result in a constant increase in A (acceleration) if you keep increasing B(force)? is this theory right or wrong? thanks for all your help.

If the relationshiop between force and acceleration is directly proportional, then yes, an increase in one will result in an increase in the other. Also, the size of the increase will be the same. Eg. If you double Force, then acceleration will also double. If one if tripled, then the other will triple as well. Good luck with your GCSEs?

Re: physics question, direct proportionality

You take a ruler and see if you can draw a straight line through your measurement points. If you can (allowing for some experimental error), they are proportional.

More generally, x is proportional to y if there exists a constant number c such that x= c*y.

Hope that helped

I think you are on the right track, but there is a very specific relationship. The best way to see it is just to try it. Let's assume that there is a direct relationship between force and acceleration. All we need to do is pick the constant.

In this case any constant will work. (You will soon learn that this constant is "mass". Each object will have a mass that you will use in this equation). Let's pick 8 (since it is a nice round number). So the equation will be:

. Force = 8 * Acceleration -- or I will rewrite this F = 8 * A

One good way to understand this function is to pick values of A and see what force you calculate.

When A = 1 -> F = 8
When A = 2 -> F = 16
When A = 3 -> F = 24
etc.

There are a couple of things you will notice about the pattern (if you check these things out, it will help you understand.)

1. If you add a specific value to A, F will increase by the same amount. For example if A = 1 and you add 2 to it (making A = 3) ... F will increase by 16 (from 8 to 24). If A = 25 and you add 2 to it (making it 27)... F will still increase by 16 (check it out). This will happen for any numbers you choose.

2. If you multiply A by a certain amount, F will be multplied by the same amount. For example if you double A ( i.e. changing it from 2 to 4) F will also be doubled (16 to 32).

3. If you graph this function, it will be a straight. If you don't have a straight line than there is no direct proportionality and the properties above will not be true.

Hopefully in you class, they will have you graph several examples of this type of function. If not, it is very interesting to try a few on your own.

Good luck.

Additionally, for a direct proportion, the line must pass through the origin (0,0).

that's hardly an additional condition considering that it will always be true given the definition you already supplied

You're absolutely correct. However, there have been subsequent posts that mention straight lines through the data points. I'm reminding them that not just any old straight line will do.

i dont really understand how the mass affects the results as the mass is kept constant, how does it affect the end results?

It doesn't. It's just the proportionality factor. Force = mass x acceleration, so if you double the force, the acceleration will double, since the mass stays the same. If you wanted to calculate the force on an object, you would have to multiply its mass times its acceleration.

The mass determines the slope of the line.