A block sliding down a ramp lab (with friction)

[stacope32]

Homework Statement

A block of 55 g is sliding down a ramp of 35 degrees of inclination.

The hypotenuse of the ramp is 63 cm and the height is 36 cm. vi = 0 as the block starts at rest.

Homework Equations

vf = vi + a(t)
d = vi*t + (a(t)^2)/2
kinetic energy = (mv^2)/2

The Attempt at a Solution

I did 3 trials of letting the block slide down the ramp and the time intervals I got each are:

1) 0.41 s

2) 0.44 s

3) 0.47 s

So then I used the d = vi*t + (a(t)^2)/2 formula to calculate the acceleration of the block and I got

1) 7.5 m/s^2

2) 6.5 m/s^2

3) 5.7 m/s^2

Then, I used the vf = vi + a(t) to find the velocity at the bottom of the ramp.

1) 3.1 m/s

2) 2.9 m/s

3) 2.7 m/s

And then I found the total energy at the top of the ramp , which would only be the potential energy as initial velocity is zero. So it's 0.19J that I calculated.

Then when I move to solve the total energy at the bottom of the ramp, there is a problem. Potential energy is zero and there's only kinetic energy, and also final energy should be smaller than initial energy because of friction, but I keep getting a greater value for all of them, as well as my change in mechanical energy, which should be negative and I keep getting a positive value. Please help.

initial energy 0.19 J

final energy (3 trials) calculated by (mv^2)/2

1) 0.26 J (it's greater that EI but should not be!)

2) 0.23 J

3) 0.2 J

*my teacher said that I should be getting a negative value for change of energy and she hasn't taught us how to do include experimental errors..she said the errors shouldn't affect the results like that so there must be something wrong with my process, but I can't figure out what it is?

 

[Dr. Courtney]

The way you are computing acceleration is very sensitive to any error you have in your time measurements.

 

[brainpushups]

There isn't anything wrong with your calculations.

How did you take your time measurements?

 

[Orodruin]

I did 3 trials of letting the block slide down the ramp and the time intervals I got each are:

1) 0.41 s

2) 0.44 s

3) 0.47 s

How did you measure these times? The accelerations which you have computed are far too large (although correct given the times) for an incline of 36 degrees. The absolute maximum should be 9.8*sin(36°) ≈ 5.8 m/s² in absence of friction. This should translate to t ≈ 0.48 s. Unless you really know that your precision in the time measurements is better than 0.1 s, you are simply dealing with measurement error.

Edit: The spread of your values alone suggests that you do not have the kind of precision needed to draw definite conclusions.

 

[stacope32]

I used the stop watch on iPad to time it. What confuses me is that all my classmates use stopwatch on their smartphones to measure the time and their results turned out fine. Does that mean my time should have been smaller or greater?

 

[haruspex]

The way you are computing acceleration is very sensitive to any error you have in your time measurements.

As I'm sure you realize, there's no need to go via acceleration at all. Just apply average speed for uniform acceleration: (v_i+v_f)/2=s/t. But this still produces speeds too great here, so I don't think the flaw is in the calculation.

The only time measurement that looks about right is the .47. With three times spanning .41 to .47, it is clear that there is considerable uncertainty in the value. A statistical analysis might reveal that the 90% error range is something like .38 to .5. That would easily explain the result.
The next most likely source of error is whether the base of the ramp has horizontal. Was this checked?

Edit: I see Orodruin beat me to the post (not unusual). I'll add that there's a useful lesson here. When you recorded the three times .41, .44, .47, you could have realized this implied the measurements were too inaccurate. You should have persevered until you got more consistency (or so many measurements that taking an average should be reasonably reliable).

 

[Orodruin]

I used the stop watch on iPad to time it. What confuses me is that all my classmates use stopwatch on their smartphones to measure the time and their results turned out fine. Does that mean my time should have been smaller or greater?

It is likely a systematic error in that you were generally pressing the stop button too soon (or the start button too late) in relation to your classmates. The iPhone timer really does not have the necessary precision for this measurement.

 

[brainpushups]

It is possible to make fairly accurate measurements of times this small using a stopwatch, but I think it requires some practice. As you can see there is only a difference between 0.06 seconds between your highest and lowest time (which doesn't seem like much), but that is greater than a 10% error in your average measurement! As Dr. Courtney pointed out, your calculation is particularly susceptible to this error.

Did you practice before taking measurements? This is something I always suggest that students do when using a stopwatch.

 

[Dr. Courtney]

We've used an acoustic technique to make accurate lab timing measurements in various situations where a clear sound can be associated with the needed start and stop times. The technique works well for everything from a falling ball (the linker paper) to potatoes shot from a cannon, to bullets in flight to using echoes to measure the speed of sound. Any digital sound recorder from which the data can be graphed and zoomed in on can be a much more accurate timer than a manually operated stopwatch.

http://arxiv.org/ftp/arxiv/papers/1102/1102.1635.pdf

When releasing objects to begin motion, one needs a bit of consideration how to accurately associate a sound with the moment of release. Putting something to hit (and make a sound) at the end of the motion is easier.

If one needs to resort to a manual release that is otherwise silent, the best way to do it is to practice with a countdown at a steady rhythm. Three, two, one, go ... and have someone tapping it out with the last tap on go as the acoustic signal to the start. It is still hard to do much better than 0.05 sec though.

 

[Orodruin]

We've used an acoustic technique to make accurate lab timing measurements in various situations where a clear sound can be associated with the needed start and stop times. The technique works well for everything from a falling ball (the linker paper) to potatoes shot from a cannon, to bullets in flight to using echoes to measure the speed of sound. Any digital sound recorder from which the data can be graphed and zoomed in on can be a much more accurate timer than a manually operated stopwatch.

Visual recordings also work wonders, although a bit more technically requiring than audio recordings. Having a software which can step one frame at a time is advisable (as well as knowing the frame rate of course). I still remember an experiment I did in high-school to disprove my math/physics teacher using a VCR recorder and measuring lengths on a TV-screen (a real one which gave that static feeling when you touched it, not like these new modern flat things). ;)

 

[Dr. Courtney]

Visual recordings also work wonders, although a bit more technically requiring than audio recordings. Having a software which can step one frame at a time is advisable (as well as knowing the frame rate of course). I still remember an experiment I did in high-school to disprove my math/physics teacher using a VCR recorder and measuring lengths on a TV-screen (a real one which gave that static feeling when you touched it, not like these new modern flat things). ;)

Good point. The time resolution of most common video equipment is 30 frames per second, which limits timing accuracy to 1/30 sec which is fine for some applications, but not near as precise as acoustic methods can be. Video also requires some care to ensure that everything is in the same plane perpendicular to the line of sight and also has some limitations imposed by the pixel resolution.

But if you can get it, high speed video allows doing some things that are much harder any other way.