Graphing acceleration versus theta to find gravity

[channel1]

Homework Statement

using the equation a = g*sin(theta) where theta is in degrees

how do i find g using the slope from a graph plotting acceleration versus theta? (i have acceleration on the y-axis versus theta on the x axis)

Homework Equations

a = g*sin(theta) where theta is in degrees

The Attempt at a Solution

i was able to set it up as slope = y/x = a / theta = [g*sin(theta)] / theta
but I am totally stumped on how to use it since theta is changing but the slope and g are constant...

 

[gneill]

What is the general equation for a line passing through the origin in the X-Y plane?

 

[channel1]

the question is to find g, i already HAVE the slope if that's what youre getting at. i need to use the value i have for the slope to find g

 

[gneill]

the question is to find g, i already HAVE the slope if that's what youre getting at. i need to use the value i have for the slope to find g

It's not quite what I'm getting at

What's the general form?

 

[channel1]

is standard form alright?

y = mx + b

 

[gneill]

is standard form alright?

y = mx + b

Okay, since the line will pass through the origin, b = 0 and you have just y = m*x. Now, let's identify each of the terms of your acceleration equation with the the standard form:

a --> y
m --> g {this is what you're trying to find}
x --> sin(θ)

So, if you were to plot a on the y-axis, and sin(θ) on the x-axis...

 

[channel1]

the line doesn't pass through the origin though it starts at a positive value for b right above the origin

 

[gneill]

the line doesn't pass through the origin though it starts at a positive value for b right above the origin

If you're plotting from collected experimental data, there's bound to be some offset due to human error, systematic error, or random error in the collection process. Some small amount of friction, for example, could bias the results.

How large is the offset compared to the range of data?

 

[channel1]

the data was given to us, its a exercise to help us learn how to use excel. by offset do you mean the R^2 value? its pretty close to 1. so do i just ignore the value for b and say the slope is the value for gravity? (thats why I am having such trouble i have no way to check my answer because they could be assigning the value for gravity to be anything as far as i know so I am not sure if I am supposed to manipulate formulas somehow to obtain 9.81 or if my value for "m" can be used for "g" even though i have a positive value for b)

 

[gneill]

the data was given to us, its a exercise to help us learn how to use excel. by offset do you mean the R^2 value? its pretty close to 1. so do i just ignore the value for b and say the slope is the value for gravity? (thats why I am having such trouble i have no way to check my answer because they could be assigning the value for gravity to be anything as far as i know so I am not sure if I am supposed to manipulate formulas somehow to obtain 9.81 or if my value for "m" can be used for "g" even though i have a positive value for b)

Since I haven't seen the data or a full description of the problem or experiment its supposed to represent, there's not much I can comment on with any certainty. It could be that if friction is involved a straight line fit to the data will be problematical. Friction will have the most effect at small incline angles when normal force is maximal.

 

[channel1]

neither have i really. we're given a table of data including theta and "a=gsin(theta)" and we're told to use excel to obtain the slope to find g