Relationship between acceleration and slope

In summary, a high school student conducted an experiment to determine the quantitative relationship between an object's acceleration and the slope of the surface it is on, using only gravity as propulsion. The setup involved a track with one end lifted to various heights, a motion detector, and a cart. The student used linear regression on the collected data and obtained the formula a = 0.14h - 0.9, but was expecting to see a square root and an asymptote of 9.8 due to the limitations of gravity. They are still interested in finding the actual formula and are willing to learn more about the subject. They were provided with a helpful link and expressed a desire to learn more about the topic.
  • #1
leftyguitarjo
52
0

Homework Statement


Well, I did an experiment to find a quantitative relationship between an objects acceleration and the slope of the surface it is on. This involves no other propulsion other than gravity itself. It is a very simple setup: A track with one end lifted to various heights, a motion detector hooked up to a computer to log speed, acceleration and position, and a little cart to go down the track.


Homework Equations





The Attempt at a Solution


I used linear regression and the data collected, and got a=.14h-0.9
BUT
I was expecting a square root somewhere in there and an asymptote of about 9.8 because it obviously won't accelerate faster than gravity.

I already received credit for the work, but I want to know the actual formula (if any)
 
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  • #2
Figure it out. What's the component of gravity acting down the incline?
 
  • #3
I'm sorry, but I just don't know.

Remember, I'm only at a high school level. I've only gotten as far as kinematics, and through my electrical work, I know a bit about electrical theory.

But i will look into this subject further. I want to impress the teacher:rolleyes:
 
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  • #4
This might help: http://www.glenbrook.k12.il.us/gbssci/Phys/Class/vectors/u3l3e.html"
 
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  • #5
Thank you!

At this point in time, I'm a sponge, so I'll soak up anything you hurl at me!
 

What is the relationship between acceleration and slope?

Acceleration and slope are directly related to each other. In fact, acceleration can be calculated by finding the slope of a velocity-time graph.

How does slope affect acceleration?

The slope of a velocity-time graph indicates the rate at which an object's velocity is changing. Since acceleration is defined as the rate of change of velocity, the slope of the graph directly affects the acceleration of the object.

What does a positive slope indicate about acceleration?

A positive slope on a velocity-time graph indicates that the object is accelerating in the positive direction. This means that its velocity is increasing over time.

Can slope be negative in relation to acceleration?

Yes, slope can be negative on a velocity-time graph, indicating that the object is decelerating or slowing down. This means that its acceleration is negative, or in the opposite direction of its motion.

How can you find the acceleration from a position-time graph?

To find acceleration from a position-time graph, you can plot the points and draw a tangent line at any point on the graph. The slope of this tangent line represents the instantaneous acceleration at that point.

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