Average Velocity and Angle of Inclination of a Slope

In summary, the conversation discusses the relationship between a ball rolling down a slope (ramp) and its average velocity, using equations such as v^2 = ut + at/2 and F = mgsin(degree). The speaker also mentions conducting an experiment and plotting a graph to find the frictional force acting on the ball. The expert suggests comparing the ideal case with the actual data to compute the magnitude of the frictional force, and also mentions the possibility of using the point where the extrapolated graph crosses the x-axis to calculate the required rolling resistance. The speaker also asks for thoughts on a snapshot attached, which shows a different method for calculating the frictional force. The expert clarifies that the figure in the snapshot is for
  • #1
gonengg
5
0
What is the relationship between a ball rolling down a slope (ramp) and its average velocity.

I know we are supposed to use: v^2 = ut + at/2 and F = mgsin(degree). But assume initial velocity is zero.

Also if I do an experiment and I get results (make a graph between average velocity and cosine or sine of angle) how can I find the frictional force found within the slope? I'll know there is an error (friction) as the graph is linear but nor propotional.

Thanks!
 
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  • #2
gonengg said:
What is the relationship between a ball rolling down a slope (ramp) and its average velocity.

I know we are supposed to use: v^2 = ut + at/2 and F = mgsin(degree). But assume initial velocity is zero.

Also if I do an experiment and I get results (make a graph between average velocity and cosine or sine of angle) how can I find the frictional force found within the slope? I'll know there is an error (friction) as the graph is linear but nor propotional.

Thanks!

It seems that this is an ideal problem and thus friction would be zero by definition.
 
  • #3
jedishrfu said:
It seems that this is an ideal problem and thus friction would be zero by definition.

Sorry I should have clarified. I did an experiment with the aim of finding the relationship between average velocity and the angle of inclination. It turned out the average velocity squared was linear but not proportional (there was an y-inc).

Given my data, how do I find out the frictional force acting on the ball? What equations and how can I solve this?

Thanks
 
  • #4
gonengg said:
Sorry I should have clarified. I did an experiment with the aim of finding the relationship between average velocity and the angle of inclination. It turned out the average velocity squared was linear but not proportional (there was an y-inc).

Given my data, how do I find out the frictional force acting on the ball? What equations and how can I solve this?

Thanks

You could compare the ideal case with your actual data and from the difference compute the magnitude of the frictional force.
 
  • #5
Ahh good thinking... However someone, in another forum, suggested this (attached) in finding the frictional force. Thoughts?
 

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  • Screen Shot 2014-02-06 at 9.34.48 PM.png
    Screen Shot 2014-02-06 at 9.34.48 PM.png
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  • #6
gonengg said:
Sorry I should have clarified. I did an experiment with the aim of finding the relationship between average velocity and the angle of inclination. It turned out the average velocity squared was linear but not proportional (there was an y-inc).

Given my data, how do I find out the frictional force acting on the ball? What equations and how can I solve this?

So, as I understand this, you have raw data giving elapsed time versus angle for a ramp with a known length. From this you have computed average velocity (where the "average" is an average over time) and plotted average velocity squared versus (sine of?) angle. The theoretical expectation is that velocity squared will be proportional the sine of the angle. The graph approximately agrees with this. It is a straight-line graph. But extrapolating back to a zero angle yields a negative value for velocity squared.

One model for this would be to assume that the primary error contribution is from rolling resistance and look for the point where the extrapolated graph crosses the x axis. This is the point where rolling resistance would be equal to friction so that velocity would be constant and zero.

Given the angle where acceleration is zero, it is a simple high school physics exercise to compute the required rolling resistance.
 
  • #7
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  • #8
jbriggs444 said:
So, as I understand this, you have raw data giving elapsed time versus angle for a ramp with a known length. From this you have computed average velocity (where the "average" is an average over time) and plotted average velocity squared versus (sine of?) angle. The theoretical expectation is that velocity squared will be proportional the sine of the angle. The graph approximately agrees with this. It is a straight-line graph. But extrapolating back to a zero angle yields a negative value for velocity squared.

One model for this would be to assume that the primary error contribution is from rolling resistance and look for the point where the extrapolated graph crosses the x axis. This is the point where rolling resistance would be equal to friction so that velocity would be constant and zero.

Given the angle where acceleration is zero, it is a simple high school physics exercise to compute the required rolling resistance.

You are correct in your assumptions. Your suggestion is actually much easier than having to compare the expected vs actual hundreds of times in excel, I didn't think of that.

Alright, so let's say that the x-inc happens to be sin (0.2). I would just use that, and gravity on Earth (9.81ms^-2, to simply calculate the frictional force? Correct? If so, thanks!

What are your thoughts on the snapshot I attached above? It seems like an alternative to calculating the frictional force; although your method seems much easier.
 
  • #9
What are your thoughts on the snapshot I attached above? It seems like an alternative to calculating the frictional force; although your method seems much easier.

The figure I was calculating was rolling resistance. The figure that you seem to be intent on calculating in the middle of that snapshot as F is the force of static friction, i.e. the force that causes the ball to increase its rotation rate and retards its descent rate. Those are two completely different numbers -- apples and oranges.

The bottom portion of the snapshot seems to conclude that g is 13.6 m/sec2. But I think that ignores static friction/the moment of inertia of the ball.
 

1. What is average velocity?

Average velocity is the measure of an object's displacement over a certain amount of time. It is calculated by dividing the change in position by the change in time.

2. How do you calculate average velocity?

To calculate average velocity, you need to divide the change in position (displacement) by the change in time. This can be represented by the equation v = (xf - xi) / (tf - ti), where v is the average velocity, xf is the final position, xi is the initial position, tf is the final time, and ti is the initial time.

3. What is the relationship between velocity and angle of inclination?

The angle of inclination, also known as the slope, is the measure of how steep a surface is. The steeper the slope, the greater the angle of inclination. Velocity, on the other hand, is a measure of an object's speed and direction. The steeper the slope, the greater the velocity needed to maintain the same displacement over time.

4. How does the angle of inclination affect the average velocity?

The angle of inclination affects the average velocity in two ways. First, a steeper slope requires a greater velocity to maintain the same displacement over time. Second, if the angle of inclination is changing, the average velocity will also change as the object's speed and direction are adjusted to maintain the same displacement.

5. Can average velocity be negative?

Yes, average velocity can be negative. This means that the object is moving in the opposite direction of the positive direction defined by the coordinate system. For example, if an object is moving from a position of 10 meters to a position of 5 meters in 2 seconds, its average velocity would be -2.5 meters per second (since the displacement is negative).

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