Marked Report 1
When a pointed object is dropped onto a lump of plasticine it makes a dent in the surface, the depth of this hole depends on the height from which the mass was dropped.
What is the relationship between the depth of hole and the height of drop.
Independent variable: Height of drop.
Dependent variable: Depth of dent.
Mass and dimensions of dropped object
Angle of attack of dropped object
Temperature of plasticine
Thickness of plasticine
When the pointed object hits the plasticine its KE is converted to heat as it does work to squash the plasticine, the amount of work done equals the Force x distance so if the force was constant the amount of work done would be proportional to the distance travelled. The amount of work done in bringing the object to rest equals its original KE which is in turn equal to its original PE (mgh). The work done is therefore proportional to the height of drop, so the depth of the dent should also be proportional to the height. The situation is however not quite so simple since the force will increase as the point goes deeper, this is because the object will have to push aside more plasticine as it goes deeper. This will lead to a non linear relationship similar to that shown in the graph below. Once all the point is below the surface of the plasticine I expect the graph to become linear.
Measurement of Height
It is important that the object lands vertically on the surface of the plasticine, to make this happen I Arranged a tube made out of a rolled up piece of clear plastic (an OHP transparency) vertically above the plasticine sample. The object was held by a string in the tube and the height of the point from the plasticine surface was measured with a ruler. This was made vertical by holding a plumbline next to it. Since the tube was transparent I could measure the position with the object in situ.
Measurement of depth of dent
After dropping the object it was held vertically in the tube, to measure the depth of the dent made the height of the top of the object from the table was measured. To calculate the depth of dent the length of the object + thickness of plasticine was measured
Control of variables
After each drop the plasticine was reformed using a small plastic box so that the thickness remained constant. Care was taken not to work the plasticine too much so that the temperature remained about the same. The same object was used each time and always dropped vertically through the tube.
Range of independent variable
The maximum height of the drop was limited by the length of the tube (60cm), by making the tube longer this could have been extended but it became difficult to make it straight, the minimum height was taken as 10cm, below this the dent was quite small so the percentage error would be large. I decided to split this range into steps of 5cm. After each reading I had to reform and reposition the plasticine, this meant I did not have time to repeat each run several times. To find the uncertainty I repeated one run (40cm) 5 times.
The uncertainty in height was estimated as ±0.1cm as the error in each end was approximately 0.05cm (1/2 the smallest division)
The uncertainty in the Depth was estimated to be 0.05cm by repeating the measurement for 40cm. This gave a range from 0.85cm to 0.95cm. The uncertainty was then found from half of this range.
The shape of the graph is roughly as predicted from the hypothesis however the end part does not seem to be linear. The best fit curve is a quadratic but without a mathematical model I have no idea of the physical significance of the coefficients.
Looking at the spread of data from the smooth curve it appears that my estimation of errors was about right. According to my hypothesis the graph should have become linear the reason it didn't could be due to the fact that the pointed object did not go deep enough. The pointed part was about 1cm long. The biggest uncertainty was in the depth measurement, this was not due to the way I measured it but due to the method not giving the same result each time. One reason for this could be that the plasticine was being heated by contact with my hands during reformation. Another possibility is that contact with the guide tube caused energy to be lost so that the KE was a bit less than the PE.
If the variations were caused by temperature variations in the plasticine then it would be a good idea to insert a temp probe into it to monitor the temperature. The plasticine could then be allowed to rest between runs so that the temperature to return to room temp. To solve the problem with the tube it could be removed, this however might make it difficult to keep the object vertical.