# Motion Down a Slope

There are a number of things that affect the acceleration of the marble:- Angle/Gradient of slope. Changing the angle of the slope would affect the acceleration of the squash ball as it changes the energy the marble starts with as steeper angles raise the slope start higher so the marble would have more potential energy.- Mass of marble. Changing the mass of the marble would affect the acceleration because it means it has more energy pulling it downwards and so would accelerate faster.- Surface. Changing the surface may change the amount of friction between the slope and the marble.

This would affect the amount of energy absorbed. If there was more friction then more energy is absorbed so the marble has less pushing it along and so accelerates slower.- Gravity. A change in the gravity would change the amount of energy pulling down the marble and so change the amount of energy pushing it along and so change the acceleration of the marble.- Aerodynamics.

A change in the aerodynamics would create a change in the air friction. This would change the amount of energy absorbed and so change the amount of energy left pushing it along changing the acceleration.I am going to investigate the angle of slope. The other variables must be kept the same. I will use the same marble so that the aerodynamics and mass of the marble stay the same. I will do the experiment in the same place every time and on the same slope so that the gravity and friction will remain relatively constant. This makes the investigation a fairer test.Measuring Acceleration:Acceleration cannot be measured directly.

It has to be derived from other measurements. The measurements required are starting speed, distance and time.I will use the formula: S=UT+0.5AT2S = Distance (m) S=0T+0.5AT2U = Initial speed=0 every time S=0.5AT2T = Time (sec) 2S=AT2A = Acceleration 2S/T2=AA=2S/T2Method:Set up the equipment as shown above. Place the marble at the top of the slope.

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Start the stopwatch at the same time as you release the marble and then stop the watch when it reaches the end. Do this 3 times and take the average speed to try to remove anomalous results. Repeat with the slope at: 10o, 20 o, 30 o, 40 o, 50 o, 60 o, 70 o, 80 o, and 90 o.Use the formula: Sin (Angle needed) x Lengthto find the height the slope must be to make it the required angle. This will make the angles more accurate.

Heights of top of slopes for required angles:10 o = Sin 10 x 150 = 26cm 20 o = Sin 20 x 150 = 51cm30 o = Sin 30 x 150 = 75cm 40 o = Sin 40 x 150 = 96cm50 o = Sin 50 x 150 = 115cm 60 o = Sin 60 x 150 = 130cm70 o = Sin 70 x 150 = 141cm 80 o = Sin 80 x 150 = 148cm90 o = Sin 90 x 150 = 150cmSafety Issues:There are no safety issues involved in this experiment.Prediction:I predict that the steeper the slope the faster the acceleration. This is because the steeper the angle the higher the marble starts and so the more potential energy it has.

More potential energy means that when it is released it will have more kinetic energy and so can accelerate quicker. Also the steeper the slope the less the marble is being pushed into the slope by gravity so there is less friction between the marble and slope.9.81 x Sin angle = Acceleration9.81 x Sin 90 = Acceleration9.

81 x 1 = 9.81m/sI also predict, using the formula above, that the marble will not accelerate faster than 9.81m/s. This is the maximum acceleration of the marble. This is due to the fact that this is the acceleration is if the marble was dropped 150cm at 90? without any frictional or rotational effects. As we are working with friction the marble should always be slower.

As the angles get nearer 90? the acceleration should begin to level off. This is because the later angles will not raise the height of the board and marble as much as the earlier angles so the marble will not be getting such a high increase in energy towards 90?. I predict that the formula 9.81 x Sin angle = Acceleration gives the exact acceleration of the marble.I predict my graph will look like this:This is because the marble’s acceleration is increasing as the slope angle rises and then it levels off before reaching 9.81m/s.

Results:Angle of SlopeHeight of Slope(cm)Time taken for marble to roll down slope (sec)(?)12345Average10261.481.501.491.

511.491.4920511.141.121.

111.101.161.

1330751.091.141.

121.110.971.0940960.620.

690.680.660.

630.66501150.610.670.680.690.630.

66601300.600.600.660.610.

610.61701410.510.540.

550.560.560.54801480.560.

570.580.560.580.57901500.550.560.

560.570.590.57Acceleration:To work out the acceleration use the formula:A=2S/T2Angle of SlopeAverage TimeAcceleration(m/s)(?)(sec)101.

491.35201.132.34301.092.52400.666.89500.

666.89600.618.06700.5410.28800.579.

23900.579.23Analysis:My prediction was correct with a few off measurements. The steeper the slope the faster the acceleration. So the angle of the slope is proportional to the acceleration, but it is not directly proportional. The graph had the same basic shape as my prediction, but again there were a few off points.

The graph has a curved, best-fit line, which proves the angle, and the acceleration are proportional.I had three main anomalous results. These angles were; 30?, 40? and 70?. I rectified these by repeating the angles.These were my new results:Angle of SlopeAcceleration(m/s)Time taken for marble to roll down slope (sec)(?)12345Average303.

001.011.030.961.060.931.00405.

060.750.790.

770.740.790.77708.920.590.610.

560.560.560.58I can now compare my set of results to the theoretical set of results, which I found using the formula: 9.81 x Sin angle = AccelerationThe calculated data is:10 o = 9.81 x Sin 10 = 1.70m/s 20 o = 9.

81 x Sin 20 = 3.55m/s30 o = 9.81 x Sin 30 = 4.91m/s 40 o = 9.81 x Sin 40 = 6.31m/s50 o = 9.81 x Sin 50 = 7.

51m/s 60 o = 9.81 x Sin 60 = 8.50m/s70 o = 9.81 x Sin 70 = 9.22m/s 80 o = 9.

81 x Sin 80 = 9.66m/s90 o = 9.81 x Sin 90 = 9.81m/sThe new graph is as I predicted and shows my data follows the same basic curve as the theoretical results. However all of my data is slower accelerating than the theoretical set. This is because the theoretical set ignores friction. As the marble is not perfectly spherical it often left contact with the table. This could have prevented the marble rolling in a straight line.

This means my results have also experienced rotational effects as they rolled whereas the theoretical results ignored this. The frictional and rotational effects would have absorbed energy from the marble causing it to be slowed down. This means the marble in my experiment could not have accelerated as quickly as the calculated results show.From this I can conclude that the steeper the slope the faster the acceleration. Also that the formula to find the theoretical data works and the theoretical data shows the acceleration of an object rolling down a slope with none of its energy lost.

Evaluation:The data I collected was quite good and follows the same basic pattern as the theoretical data. My original results were not very accurate, especially drop height 30?, 40? and 70?. However, these were redone and now are greatly improved. 30? is still slightly anomalous.

Despite this I feel my results are sufficiently reliable to support the conclusion that the theoretical data shows the acceleration down a slope where there is no energy lost from the object.I feel the reason for the inaccuracy could be because the marble was not perfectly round meaning it did not roll in a completely straight line and that it changed the friction. It could also be that the slope was not set at exactly the right height or angle.

Another more major reason could be that the time was not measured correctly or accurately. Measuring the time by hand and eye caused many problems. This meant the results could never be very accurate.

The clock could not be started exactly as the ball was released. Also the eye could not see exactly when the marble reached the end and the clock could not be stopped quick enough.To improve the experiment and the quality of the data you could get a computer to measure the time taken. There could be a clamp, meaning the ball is released exactly as the time is started.

Also using lasers could mean the timer was stopped exactly as the marble reaches the end. This would make it a lot more accurate. The computer could also set the angle of the slope perfectly. Also you could increase the number of times taken at each angle to get a better average and cut down anomalous results even more.

My results suggest that the theoretical data was correct, as mine where only slower due to friction, and they support the conclusion. Further investigation could be done to help support this. For example, using a perfectly round ball such as a metal ball bearing, and a smooth metal slope.

This would remove some of the friction and get closer results to the theoretical set. Also for further work the marble could be rolled down different texture slopes to investigate the effects of varying amounts of friction. This would provide additional information, which would help identify exactly how much friction does affect the results, compared to the theoretical set.To extend the investigation you could do the same experiment but keep the slope at the same angle and change the mass of the ball.

This would investigate how the mass effects the acceleration.

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