Catapult

Name : Adam Okoe Mould Title : Internal Resistance of a Battery Criteria : DCP, CE Research Question : What is the relationship between the extension of an elastic band and the range of a ball using a catapult? Hypothesis: From the derived equation containing the variables extension and range, the square of the extension is directly proportional to the square of the range.

Apparatus Measuring tape Meter Rule Materials Catapult (includes the elastic band and hand grip) Powder Variables Independent Variable Extension of elastic band Dependant Variable Range of stone Controlled Variable The height of launch of ball –1 meter. This can be kept constant by placing a an upright meter rule so that the experimenter can put the catapult level with this fixed height and shoot the ball. The angle of launch of the ball – This can be kept constant by ensuring the catapult is upright and the elastic band is horizontally stretched. The same elastic band should be used – This is because different elastic bands have different elastic abilities

Raw Data Stated e.m.f of battery /V Measured e.m.f of battery /V ±0.01V Voltage /V ±0.01V 0.53 0.56 0.65 0.71 0.8 0.85 0.93

9.0

N.B In the analysis the measured e.m.f will be used since it is more accurate than the stated e.m.f on the battery

8.50 Current , I /A ±0.01 A 5.56 5.25 4.90 4.51 4.20 4.00 3.70

Analysis of e.m.f and internal resistance of battery

The formula for the e.m.f of a battery is as shown ; e.m.f = Potential difference across resistor + Potential difference of the internal resistance e.m.f = IR + Ir IR = e.m.f - Ir But IR = Voltage Voltage, V = e.m.f – Ir This equation is of the form y = mx + c Where y = Voltage, V m = -r , -internal resistance x = current , I

c = e.m.f Therefore a graph of voltage against current should be plotted in order to determine its internal resistance

Graph of Voltage against Current

8

y

7 6 5 4 oltage/ V

3 2 1

x -0.05

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1

Current / A

Comment on Graph and Processed Results • • •

The graph shows that as the voltage increases, the current in the circuit reduces. The results are fairly precise as the points are scattered fairly close to the line of best fit. There was only one random error which was in the first reading.

Determination of e.m.f and Internal resistance of battery

From the line of best fit the gradient is -4.23 VA-1 and the intercept is 7.60 Gradient = -4.227 But Gradient = -r Therefore -r = -4.23 r = 4.23 Ohms Hence, the internal resistance of the battery is 4.23 Ohms Intercept = 7.60 But Intercept = e.m.f Therefore e.m.f = 7.60 Therefore the e.m.f of the battery is 7.60 V Measured e.m.f - e.m.f derived from graph × 100 Measured e.m.f 8.5 - 7.6 × 100 = 8.5 = 10.6 % This percentage error of 10.6 % in the value of the e.m.f shows that the experiment was not very accurate but only fairly accurate. Percentage error of e.m.f =

Conclusion Based on the graph of voltage against current, the internal resistance of the battery is 4.23 Ohms and the e.m.f is 7.60 V. The experiment was fairly accurate as there was a percentage error of 10.6 % for the value of the e.m.f. Sources of Error 1. During the performance of the experiment, the batteries their energy drained out rapidly. This may have caused some errors in the experiment. 2. As the experiment progresses, the heat produced by the flow of current could have added further errors. Improvements to the Investigation 1. High quality batteries should be used so that the energy in the battery will last for the whole duration of the experiment. 2. To minimize the generation of heat in the wires uses thicker wires.