As you can see from the table above, my prediction of acceleration being 0. 30 m s-2 is relatively accurate. However, there are two anomalies, which give particularly high values for the ball bearing’s acceleration. The cause of this is most likely a measurement error, since a human-controlled stopwatch was used to measure the times. To time how long a ball bearing takes to move down the slope accurately is extremely difficult, especially when it takes only a fraction of a second. The use of light gates in place of the stopwatch is one method to overcome this problem. Theoretical acceleration of ball bearing
It is also possible to work out the acceleration using Newton’s Second Law of Motion, F = ma. Kinetic energy of the ball bearing Analysis Since the ball is moving down a slope, there must be a drop in gravitational potential energy. As the ball moves down, it also gains speed and kinetic energy though. According to the First Law of Thermodynamics, energy cannot neither be created nor destroyed but can be converted from one form to another. Thus, we can conclude that gravitational potential energy is converted into kinetic energy as the ball travels down the slope. G. p. e = mg? h K. e = 1/2mv2 G. p. e = K. e mg? h = 1/2mv2
So, although the above graph is one of distance against kinetic energy, the relationship for distance against gravitational potential energy lost would be exactly the same. However, there may be slight differences since some of the energy may be converted into heat. The graph displays a linear relationship, and shows that the ball bearing’s distance from bottom of slope is directly proportional to the kinetic energy. The general equation linking the two variables together will be y = kx – where k is an unknown constant. (0. 50, 4. 50) y = kx –> k = y / x k = (4. 50 i?? 10-3) / 0. 50 k = 9. 00 i?? 10-3 –> y = 0. 009x K.e = 0. 009s
By substituting in the coordinate (0. 50, 4. 50), we have found the constant. In doing so, we can deduce an equation which allows us to calculate the kinetic energy of the ball bearing providing we know the distance from the bottom of the slope. However, this equation would only work if the slope remains as 5i??. The constant in the equation is the same as the resultant force which we have calculated using Newton’s Second Law. This is due to the fact that the weight is a constant, and in this particular experiment, weight is the only force which controls the force at which the ball bearing moves down the slope.
Therefore, we can replace the constant in the equation with the resultant force to give K. e = Fs. This should enable us to calculate the kinetic energy of a ball bearing travelling down a slope no matter what the angle of the slope is. From this graph, we can see another anomaly, which is highlighted in red. This point is an anomalous result because it shows that the ball bearing has less kinetic energy when s = 0. 95 compared to when s = 0. 90. The cause of this anomaly would most likely have been due to some experimental error.
As explained before, the experiment appears to have been carried out by a human, so there will be quite a lot of systematic error. The person who carried out the experiment may have stopped the timer on the stopwatch to early or too late, leading to results which do not reflect my predictions. As you can see, this anomaly cannot be identified in any of the previous two graphs, so it was necessary to produce a distance against kinetic energy graph as well. Another reason as to why I produced this graph was to confirm my value for resultant force derived using Newton’s Second Law.