Spring Energy Lab. Section I Kanishk Pandey Lab Partners: Hava Kantrowitz and Rahul Krishnan

Transcription

1 Spring Energy Lab Section I Kanishk Pandey Lab Partners: Hava Kantrowitz and Rahul Krishnan

2 Introduction Purpose: to design and perform an experiment which analyzes the conservation of energy in a spring-based system Researchable Question: Does the stretch distance of a slingshot rubber band affect the time it takes a race car to travel a fixed distance along a race track? Hypothesis (w/proportionality): The stretch distance of the slingshot is inversely proportional to the time it takes for the race car to travel a fixed distance along the track (Δx t)

3 Procedure Materials: Race car, track, pair of rubber bands, meter stick, table and a force sensor An experiment was conducted to determine the spring constant, k, of the rubber bands. A force sensor, connected to a laptop running the Logger Pro Application, was used to measure the value of the force (in N) when the rubber band was stretched for various distances. For each stretch distance, the force exerted on the rubber bands was recorded. Method: The mass of a car was measured. A pair of rubber bands was tied to the legs of a chair to create a slingshot. A track was placed underneath the chair, and a car was pushed backwards to stretch the rubber bands by different values (0.10 m, 0.15 m, 0.20 m, 0.27 m, and 0.30 m). After launching the car, the time it took the car to travel a distance of 1.8 m was recorded. Ten trials were repeated for each of the stretch distances of the rubber band.

4 Diagram Slingshot Track Race Car D Δx v f *See Appendix for pictures

5 Constants and Formulas Equations F(x)=55.32x x F(x) is the force on the slingshot (in N) when stretch Constants m car = kg Distance D traversed by race car = 1.80m µ = 0 distance = x (in m) W(X f )=Stored Energy = 0 x f F(x)dx = 18.44X f X f X f W(X f )= 1 2 mv i 2 ; v i = t theo = D vi = v f =v i (μ=0) 2W(Xf) m xf xf x TE i (car)=w(x f )= 1 2 mv i 2 TE f = 1 2 mv f 2

6 Summarized Data d t 1 t 2 t 3 t 4 t 5 t 6 t 7 t 8 t 9 t 10 t avg STDEV %RSD t T %err t avg 2 k TE i TE f %E Chang e (m) (s) (s) (s) (s) (s) (s) (s) (s) (s) (s) (s) (s) of t avg (s) of t (s 2 ) (N/m) (J) (J) (J) IV IV IV IV IV Avg 6.04 Avg 5.34

7 Rubber Band Stretch (m) Summarized Data 4.00 Slingshot Stretch vs Time y = x R² = y = x R² = Time (s)

8 Analysis The graph shows that there is an inverse relationship between the distance a sling shot is stretched and the time it takes for the projectile to travel a certain distance. However, there are a few exceptions. When the slingshot was stretched a distance of 0.27 m, the car took longer (t = 1.29 s) than when the slingshot was stretched a distance of 0.25 m (t = 1.25 s). This shows that the slingshot compression and the time trend may vary. The negative trend of the graph showed that as the distance of the slingshot increased, the time the car took to travel 1.8 m also decreased. The experimental values of the data were close to the theoretical values. No clear trend is found between the percent error and the percent RSD as the slingshot compression increased. The value of percent RSD was 6.04%, which shows moderate precision. The percent RSD mostly decreased as the rubber band was stretched at a greater distance. Furthermore, the percent error was 5.34%, which also showed moderate accuracy. Unlike percent RSD, the percent error did not have a clear trend as the rubber band compression increased. This experiment showed a strong mathematical model, since the R 2 -value was for the measured values, and for the theoretical values.

9 Conclusion The data and the graph supports the hypothesis. As the compression distance of the slingshot increases, the time decreases for the object to travel a certain distance, where t 1 d. Many sources of error occurred throughout the experiment. The k-value of the rubber band system was measured after the experiment, which means that it could have changed between the time intervals. The best fit quadratic line for the k-constant did not fit all the points on our graph perfectly, which may result in a slightly different k-value (see Appendix). Finally, friction and air resistance were both ignored in the experiment. Our values were higher than the theoretical values when the IVs were large, and they were lower than the theoretical values when the IVs were small. If friction had not been ignored, the measured time values would have increased. This means that our sources of error do not account for the slight variances between the theoretical values and our values. Although this is a unique lab, many follow-ups could be investigated in future labs, such as trying different rubber bands with different spring constants, launching the car at an angle on a ramp, or measuring the distance the car travels on the ramp after a specific time.

10 Appendix Spring Constant Δx F (m) (N) Trial Trial Trial Trial Trial Trial Trial Trial Trial Trial The spring constant was determined (after the experiment) by measuring the force required to pull the rubber band system a certain distance. The program used to measure the distance was LoggerPro.

11 Force (N) Appendix (Continued) The spring constant, k, was calculated by recording the force required to stretch the rubber band system at certain distances. After plotting the points on the graph, a best-fit power function was determined, which provided the k value to corresponding rubber band compression distances Spring Constant (k) y = 55.32x x R² = Rubber Band Compression (m)

12 Force (N) Appendix (Continued) While the power function was useful in order to calculate the theoretical time for each of the compression distances, a linear approximation of k values was used to calculate the initial energy of the car Spring Constant (k) Linear Approximation y = x R² = Rubber Band Compression (m)

13 Appendix (Continued)