Lab #5 Hooke’s Law

Running Header: HOOKE’S LAW Lab #5: Hooke’s Law September 30th, 2020 HOOKE’S LAW Purpose: The purpose of this experiment is to understand Hooke’s law regarding the elasticity of the springs and how adding extra weight would affect the restoration force. According to Hooke’s law, a restoring force of a spring or other elastic material is considered to be directly proportional to the distance that the spring is stretched or compressed. This could be measured using the restoring force equation: F sp=−k∆x . During this experiment specifically, we measured the displacements of several springs, each with varying spring constants, and added different increments of weights in order to see the effect on the elasticity. Therefore, we were determining whether our experiment results, such as the graphs and collected measurements, were in obedience of Hooke’s law. Results: Red Spring Mₒ = 250g Uncertainty: ±0.5cm Yₒ = 53.5cm Red spring constant value: 25N/m ±10% Mass (g) 0 20 40 120 140 200 240 Height (cm) 0 4.5 5.5 8.5 9.5 12.0 13.5 F sp (N) 0 1.125 1.375 2.125 2.375 3.00 3.375 HOOKE’S LAW Yellow Spring Mₒ = 250g Uncertainty: ±0.5cm Yₒ = 48.0cm Yellow spring constant value: 35N/m ±10% Mass (g) 0 20 40 120 140 200 240 Height (cm) 0 0.5 1.0 3.3 4.0 5.5 6.7 F sp Height (cm) 0 0.2 0.8 2.5 2.7 4.0 4.6 F sp (N) 0 0.175 0.350 1.155 1.400 1.925 2.345 Green Spring Mₒ = 250g Uncertainty: ±0.5cm Yₒ = 48.5cm Green spring constant: 50N/m ±10% Mass (g) 0 20 40 120 140 200 240 (N) 0 0.1 0.4 1.25 1.35 2.0 2.3 HOOKE’S LAW Hutton 4 Calculations: Red Spring: Yellow Spring: Green Spring HOOKE’S LAW Questions: 1. Hooke’s law is based upon elasticity properties of materials, which in this case would be the spring. Elasticity is an object or material’s willingness to return to its original position or dimension. This is demonstrated by a restoring force in which the spring or material is returned to its original equilibrium state. The negative in Hooke’s law indicates the direction of this restoring force. The spring constant (k) regards the stiffness of the spring, meaning that the larger the k value, the larger the force needed to stretch it and vice versa. 2. When there was weight added, our springs appear to follow Hooke’s law as they stretch with the weight. The additional weight acts as an extra downward force that acts upon the spring, resulting in it stretching. Each spring did return to its original position, which establishes its elastic properties. On the other hand, our graph for the green spring indicates that it did not follow Hooke’s law entirely or that there was human error. Since it was close to creating a linear result, the skewed data is most likely due to human error, which means that it was still closely following Hooke’s law as the spring did not overextend beyond its limit. 3. Since a majority of our data resulted in linear graphs, we can assume that none of our springs were stretched beyond their normal range. If our graphs had resulted in slightly curved lines, the springs may have been stretched beyond their normal range. However, it appears that ours were not stretched outside of their normal range to lose their shape and enter the plastics region. The way to check our assumptions would be to check the equation of our graphs, which should be linear if the spring is within Hooke’s law, and indeed it is. 4. For this graph, the constant y is equal to the force being exerted on the spring and for our graphs, we did have to invert our y-values or else we would have ended up with a negative graph. Therefore, the constant m represents the spring constant and the b represents the change in the length of the spring as weight is added. For the red spring in the first trial, the spring constant for the red spring is approximately 0.25N/m. The spring constant for the yellow spring is 0.35N/m, and the spring constant for the green spring is 0.49N/m. These values were taken from the slope of each graph for its corresponding spring that was calculated using excel. Using these values, if we were to multiply each of them by 100, this would be exactly what the spring constants are. 5. To calculate the percent error of our data, we took the estimated value, which was the slope multiplied by 100 and subtracted it from the accepted value and then divided it by the accepted value and multiplied it by 100. This gave us the percent error in our data. An example calculation of the red spring can be seen below: HOOKE’S LAW | ( 0.25N / m )( 100 )−25N /m | ×100=0% error 25N /m The values obtained for the yellow and green springs, using the same method as above, were Yellow: 0%, Green: 0.02% 6. Most of the errors that may have been made during this lab were likely result of human error, but there were still some extra errors that may have been made. I am not entirely sure why our slope needed to be multiplied by 100 in order to match the spring constant, but this may have to do with needing to invert our y-values in order to get a positive slope. This may have also factored in to getting nearly perfect results according to our percent error analysis. These were mainly errors in the calculation, but it still does ultimately provide some room for error. Conclusions: Overall, it would appear that each of our spring trials did follow Hooke’s law very closely. Each of our graphs has a linear trend, with the slight exception of the green spring due to human error. These linear results would indicate that the springs do have elastic properties and that they have restoring forces, which is what we were able to graph and plot based upon our gathered measurements. The human error that occurred with the green spring may have been that the spring was stretched beyond normal, but not overstretched to the point of the coil losing elasticity and its restoring force. Considering how slightly the potential error affected our data, our experiment was fairly successful in creating three linear graphs in order to prove Hooke’s law of elasticity and restoring forces.