Planning The experiment is to determine the horizontal motion of a projectile when launched from a ‘ski slope at different speeds. It is thought that the rate at which the ball bearing is released from the slope will affect how far it travels in a horizontal direction. The height up the slope that the ball is released will be proportional to the distance that it travels. Therefore, if the height from which it is released is doubled it will travel twice as far. When the experiment is conducted, it must be insured that all of the apparatus is attached securely to ensure that nothing comes apart. General laboratory rules must be recognised to ensure safety throughout.
The apparatus that is required is: Curtain rail (ski slope) – reaching 0. 50 m in vertical height Ball bearing Metre ruler – 1 m long measuring in 0. 001 m intervals Carbon paper Banner of white paper – approx. 3 m long Clamps Retort Stands Set square – measuring 90 angles Horizontal bench – vertical height of between 0. 8 m and 1. 0 m is practical The variable that will be investigated is the range that the ball bearing is projected.
The independent variable is the height up the ski slope that the ball is released from. It is measured using a metre ruler. The dependant variable is the distance from the slope in the horizontal direction that the ball will travel. The method that will be undertaken is firstly to set up the apparatus as shown in the diagram. The height above the ground, H, should be measured using a metre ruler and this should be kept constant throughout the experiment. The angle at which the ski slope is at should also be kept constant and should be held in place by clamps, so that the edge of the slope is parallel with the edge of the table.
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The banner of paper should be placed on the floor running away from the table. Practice runs of placing the ball at differen heights should be done to find roughly the place where the carbon paper should be placed. For the experiment, the ball bearing should be held in place on the ramp at certain vertical heights above the table. It can then be released and as the ball strikes the carbon paper it should leave a mark on the paper below. The length / range can then be measured from the edge of the table to the centre of the mark left by the carbon paper. The experiment can then be repeated 3 times for each height to reduce the effect of anomalous results.
The experiment will be conducted using heights of release of the ball bearing from 0. 00 m to 0. 40 m in stages of 0. 05 m. This will hopefully obtain a good set of results.
In order to simplify this experiment, air resistance has been ignored as a factor in the range of the projectile. As it is a projectile that will be measured, the only other factor working on it are gravitational forces. The horizontal motion of the projectile is independent of the vertical motion, and that is why the falling motion of the ball bearing does not need to be considered. A ball bearing will be used, as it is a fairly dense object. This has benefits because although we are ignoring the effect of air resistance in the calculations, we should minimise the affect that it has.
A lighter object, or one that has a larger surface area (i. e. is less dense), would show more affect from air resistance. However, the smooth and relatively dense ball bearing should show little difference in trajectory due to the affects of air resistance whereas an object such as a polystyrene ball would be massively altered.
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This is known from the equation: F = ma Rearranged as: a = F m showing that acceleration is indirectly proportional to the mass if the force releasing the ball bearing remains constant. Therefore, if the mass is increased, the acceleration of the ball bearing will be decreased during its trajectory. Theory for horizontal motion: Loss of PE = Gain of PE mgh = mv 2 2 mgh = v 2 m v = (2 gh) It is range we are trying to find out: s = (u+v) t = ut = vt R = (2 gh) = (2 H/g) (from equation: ‘time of flight) R = (4 hH) R 2 = 4 hH From this derived equation a testable hypothesis can now be made. By comparing the derived formula with the formula for a straight line graph, which shows similar properties, it is thought that as height increases, range will also increase. R 2 = 4 x h x H R 2 = (4 x h) x H + 0 y = m x + c This comparison of equations shows that if Range 2 were plotted against height (h) then a straight line graph through the origin would be the result. It can therefore be said that Range 2 is directly proportional to height, considering that height (H) is constant.
The mass and size of the ball bearing must also be kept constant. To prove this, a graph of Range 2 on the y-axis and height (h) on the x-axis must be plotted and a straight line graph running through the origin must be produced from the data. This would show the theory and equations used to be correct. Implementing Height (h) mRange 1 mRange 2 mRange 3 m Average Range m (Average Range) 2 m 2 0. 0000.
0000. 0000. 0000. 0000. 000 0.
0500. 2720. 2750. 2730. 2730. 075 0.
1000. 4210. 4230. 4170. 4200. 176 0.
1500. 5170. 5180. 5160. 5170.
267 0. 2000. 6050. 6050. 6060. 6050.
366 0. 2500. 6780. 6770.
6770. 6770. 458 0. 3000. 7470. 7490.
7490. 7480. 560 0. 3500. 7990. 7950.
7950. 7960. 634 0. 4000. 8230. 8260.
8240. 8240. 679 Percentage Error (%) +/-0. 01+/-0. 001+/-0.
001+/-0. 001+/-0. 001+/-0. 001 % error of height 0.
400 m +/-0. 01 m 0. 01 x 100 = 2. 5% 0. 400 % error of range 0.
823 m +/-0. 001 m 0. 001 x 100 = 0. 1% 0. 823 There is a larger percentage error in the height than the range. Sources of error: There must have been some amount of friction during the movement of the ball bearing down the ski slope.
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There must also have been air resistance of the ball bearing during its trajectory. Both of these were ignored in the calculations. To minimise both types of friction, a dense and smooth ball bearing was used as this would lower the affect of both air resistance and resistance with the ski slope. The ski slope was also looked at to check that it was smooth and that there were no obstacles or blemishes on the surface to ensure a smooth run. The ruler was not set exactly vertical throughout the experiment, giving false readings. To try to minimise this, set squares were used to keep the ruler vertical, and clamps were used to try to hold it in place so that it was the same for every attempt.
The ball bearing was released in a way that tried to minimise the amount of spin in any direction apart from that of down the ski slope. Excessive spin or spin in an incorrect direction would alter the acceleration of the ball bearing down the slope. To try to avoid this the ball was released carefully using a piece of wood to hold it rather than a human hand releasing it, . This meant that it started to roll in the correct way from the start of its descent down the ski slope.
The carbon paper that was used to make an impression on the banner of paper may have moved slightly as the ball bearing struck it at an angle. It was either held in place, or sticky-tape was used to ensure that it did not move during impact. Also, to maintain accurate results, the reading was always taken from the centre of the circle impression made by the carbon paper.
