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Galileo's Rolling Ball experiment

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Introduction

Galileo’s Rolling Ball experiment

Aim:

Galileo in his rolling ball experiment investigated the acceleration of a ball rolling down an inclined plane, using a similar setup I will investigate how the time taken to roll down the inclined plane varies with the vertical height change.

Theory:

When two similar objects are thrown vertically downwards, they are in a state of free-fall. Both objects will hit the ground simultaneously; the force which causes these objects to fall down is the pull of gravity which is also the acceleration of these objects.

As the object falls down, its speed increases hence its acceleration increases.

Using the equation of motion;

S= u t + ½ a t2

Since u = o, we can ignore initial velocity so:

S = ½ a t2

Straight line equation: y = m x + c  

The variables in this experiment are: S and t2

When compared with the straight line equation:

S = ½ a  t2

y = m     x

  a sinimage09.png

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Middle

 t2                image12.png   g = 2

Prediction:

I think that as the ball will run down the slope its acceleration will increase and the time for the ball to roll down will decrease. Also if the vertical height (h) is increased, the time for the ball to roll down will decrease, i.e. it will travel faster due to increase in the force of gravity.

Diagram:image01.png

image13.pngimage08.pngimage06.pngimage06.pngimage07.pngimage04.pngimage05.pngimage02.pngimage03.png

Method:

  • First setup the apparatus as shown in the diagram above by:
  • Placing a 2m ramp on a horizontal surface.
  • Having the ramp at an angle so it makes a slope for the ball to run down from, the ramp will be supported on a clamp-stand.
  • Put a mark on the ramp for where the ball will be released and where it will stop.
  • Then measure the vertical height of the inclined slope and record it.
  • Place a cup at the end of the ramp where the mark is, so when the ball bearing reaches the end it will make a sound which will make it easy to stop the stopwatch.
  • Place a ball bearing at the highest point of the slope where the mark is.
  • Release the ball and simultaneously start the stopwatch.
  • When the ball bearing reaches to the bottom of the slope where the mark is, then stop the stopwatch upon hearing the sound made by the ball on contact with the cup.
  • Repeat the experiment several times and get an average for all repeats to get a more accurate result.

Safety:

  • When carrying out the experiment make sure the ramp is securely held on the clamp.
  • Handle the ramp carefully when carrying it around. Do not swing it around.
  • When changing the height, first remove the ramp then adjust the height before returning the ramp to its place.
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Conclusion

Max        % error  (with 3 readings)        = image15.png = 6.7%

Max        % error  (with 6 readings)        = image16.png = 3.3%

From the above calculation it can be clearly seen that increasing the number of readings significantly reduces the % error by 3.4% or by half.

Another way of increasing the accuracy of the timing would be to use a motion sensor to record the time.

The maximum percentage error in the height measurement is:

image17.png= 10%

This error could be reduced by measuring the height of the clamp accurately using a ruler with a mm scale.

The percentage error in the experiment was:

Error in height + (2x error in time) = 10 + 6.7 = 16.7%

From looking at the graph the points are scattered further away from the line of best fit as the height was increased. This is expected because the percentage error is greatest at these values.

        Page         

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