8. Place the solid sphere on the top of the wooden plate at a given height of 4 cm. and release it.
9. When the solid sphere is at the middle of the flat wooden plate (point "X" in diagram), measure and record the velocity of the solid sphere by using a motion sensor. Make sure to lift off the solid sphere when it is at the end tip of the wooden plate (point "Y" in diagram).
10. Do three trials per given height and the find the average velocity.
11. Find the average velocity squared "Average Velocity Squared=(Average Velocity)2"
12. Repeat steps 2-5 by changing the initial height with an increment of 2 cm. until reaching 20 cm.
16. Make sure the solid sphere is placed at the top of the wooden plate to obtain an accurate initial height
17. Make sure to measure the velocity when the solid sphere is at the middle of the flat wooden plate (point "X" in diagram).Data Collection and Analysis:<br />Table 1: The raw and processed data show the relationship of height (x) and velocity squared (y) of the solid sphere rolling down a wooden plate. The raw data shows the height and the velocity for three trials. The processed data shows both the average velocity and the average velocity squared with different uncertainties. Note the mass of the solid sphere is 400.000±0.001 g<br />HeightVelocity / ±0.005 ms-1 Average Uncertainty ofAverage Velocity Uncertainty of Velocity VelocitySquaredAverage Velocity Squared/ ±0.1 cm.Trial 1Trial 2Trial 3 / ms-1/ ms-1/ m2s-2/ m2s-24.00.4590.4480.479 0.4620.0150.2130.0146.00.6950.7190.726 0.7130.0160.5090.0228.00.9140.8820.895 0.8970.0160.8050.02910.01.0451.0641.033 1.0470.0151.0970.03212.01.1961.2091.171 1.1920.0191.4210.04514.01.2981.3201.281 1.3000.0191.6890.05016.01.3911.4081.442 1.4140.0251.9980.07118.01.5241.4811.530 1.5120.0242.2850.07420.01.5831.6321.602 1.6060.0252.5780.079<br />Sample Calculations:<br />Consider the data value:<br />HeightVelocity / ±0.005 ms-1 Average Uncertainty ofAverage Velocity Uncertainty of Velocity VelocitySquaredAverage Velocity Squared/ ±0.1 cm.Trial 1Trial 2Trial 3 / ms-1/ ms-1/ m2s-2/ m2s-24.00.4590.4480.479 0.4620.0150.2130.014<br />To find the average velocity for the three trials<br />Average Velocity=Velocity Trial 1+ Velocity Trial 2+Velocity Trial 33<br />=0.459+0.448+0.4793<br />=0.462 ms-1<br />To find the uncertainty of the average velocity<br /> ΔAverage Velocity=Maximun Velocity-Minimum Velocity2<br />=0.479-0.4482<br />=0.015 ms-1<br />Average Velocity=0.462 ±0.015 ms-1<br />To find the average velocity squared<br />Average Velocity Squared=(Average Velocity)2<br />=0.4622<br />=0.213 m2s-2<br />To find the uncertainty of average velocity squared<br />ΔAverage Velocity Squared=2×Average Velocity×ΔAverage Velocity<br />=2×0.462×0.015<br />=0.014 m2s-2<br />Average Velocity Squared=0.213 ± 0.014 m2s-2<br />Graph 1: This graph shows the relationship between the height (x) and the average velocity squared (y).<br />-608965137795<br />Equation with minimum slope: y=0.142x-0.3405<br />Equation with maximum slope: y=0.154x-0.415<br />Actual Equation: y=0.148x-0.377 (Equation determined by Microsoft Excel Program)<br />Conclusion:<br />The investigation indicates that there is a linear relationship between the height and the average velocity squared of the solid sphere.<br />(*)The relationship is indicated by the best fit line in Graph 1. Mathematically h∝v2 which support the equation.<br />v2=2gh1+25<br />The value of quot;
2g1+25quot;
is constant and is equal to the slope of the line. <br />The value of the slope in Graph 1 is 14.8 ms-2 . This compares with the slope of the equation (*) which is 14.0 ms-2. The percent error is 5.7%. Therefore, this shows that the experimental value fairly match with the equation (*) and supports that h is linearly proportional to v2.<br />The data plotted is fairly consistent with the trend line but show some random errors. From equation (*), Graph1 should be in the form of quot;
y=kxquot;
with the straight line passing through the origin. However, the equation of the line is quot;
y=0.148x-0.377quot;
which indicates a small y-intercept of-0.377 . This shows systematic error or an experiment uncertainty.<br />Evaluation:<br />A major limitation in this experiment is the friction between the solid sphere and the wooden plate. This causes the speed of the solid sphere to decrease compared to speed of a solid sphere on a frictionless inclined plane. Therefore, this affects the graph to shift-down and creates systematic error in which the line does not pass through the origin. This error can be eliminated by forming a new equation by considering work from friction. The new equation states that gravitational potential energy of the solid sphere is converted to translational and rotational kinetic energy and work from friction.<br />mgh=12mv2+12Iω2+W<br />where W is work from friction (J)<br />mgh=12mv2+1225mR2vR2+W<br />2gh=v2+25v2+2Wm<br />v2=2gh1+25-2Wm<br />The graph between h and v2 obtains a linear graph with a slope 2g1+25 and a y-intercept of -2Wm<br />The defect of the solid sphere affects the data and causes systematic error. This can be seen since there are lumps and roughness on the surface of the solid sphere. The defect in the solid sphere changes its volume and shape which affects its speed. A solution to this problem is using more samples of solid spheres in order to reduce errors from defect.<br />Another limitation is when the solid sphere is rolling down on the wooden plate; it does not always roll in a straight line. This causes the work from friction to increase which reduces the speed of the solid sphere and causes systematic error. This error can be eliminated by creating a gutter on the wooden plate to make the solid sphere roll down in a straight line.<br />A limitation in this experiment is not making enough measurements. The height in the data is insufficient. This makes it harder to create an accurate best fit line. One possible solution is conducting more number of heights in the experiment. <br />A random error is by the limited amount of trials in the experiment. The amount of trials at the velocity of the solid sphere is insufficient. This affects the precision of the slope on the best fit line of the graph. This error can be eliminated by conducting more trials in the experiment and use the average value to the data and the graph.<br />
![Investigative Question:<br />What is the effect of the velocity of the rolling solid sphere when it is released at a given height from an inclined plane?<br />Background Information:<br />When a solid sphere is released at a given height from a frictionless inclined plane, it rolls down. At the point of release, gravitational potential energy of the solid sphere is converted to translational and rotational kinetic energy.<br />mgh=12mv2+12Iω2<br />where m is mass of solid sphere (kg), v is linear velocity of solid spherems-1, I is the moment of inertia of the solid sphere (kgm2), ω is the angular velocity of the solid sphere (rads-1), g is the gravitational acceleration (ms-2), h is the height (m)<br />From the reference section in Eugene Hecht, 2003, the moment of inertia of a solid sphere is I=25mR2. Assuming that there is no slip-race, the angular velocity of the solid sphere is ω=vR<br />mgh=12mv2+1225mR2vR2<br />2gh=v2+25v2<br />v2=2gh1+25<br />Variables:<br />VariablesManipulated, Measured or Controlled by:IndependentVertical Height of Inclined PlaneUse a ruler to measure the heightDependentVelocity of the rolling solid sphereMeasure the velocity by using the motion sensorControlledSame wooden plateUse the same wooden plate Same rolling solid sphereSame motion sensorSurrounding TemperatureSurrounding Air pressureUse the same solid sphereUse the same motion sensorThermometer to monitor at the end of every trialBarometer to monitor at the end of every trial <br />-664210502920Experimental Setup:<br />Materials:<br />,[object Object]](https://image.slidesharecdn.com/irpsolidsphere-110516034313-phpapp01/85/energy-transformation-of-a-rolling-sphere-1-320.jpg)
