Lab 5 Linear Momentum Nicole Caringal

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Phys 207 Lab CD4 Instructor: Luis A. Álvarez García Group: Rosemary Delgado Report 5: Linear Momentum Nicole Caringal Introduction (1pt) This lab helps to understand linear momentum through analysis of the change in a system’s momentum. Trials will be run in an experiment where a steel ball is rolled down a ramp that will collide into a wooden block, resulting in a change from the wooden block’s initial position. Procedure (1pt) Measure the ball’s velocity First, measure the height of the ball’s fall from the end of the ramp to the bottom of the box and record this value in meters. For ten trials, let the steel ball roll down the ramp from the highest height, and record the distance of its travel right when it hits the floor of the box. Use the markings made in the box to measure its distance. Standard Deviation Calculate the average of the distances from the ten trials. Next, calculate for the standard deviation of this value. Then, calculate for the ball’s time in the air and its velocity when it leaves the track. Finally, calculate for the standard deviation of the velocity value. Collide ‘em

With the slider placed on the slider guide, place the slider guide into the box. This will be used to measure the maximum change in distance of the wooden box when the steel ball collides. Set up the wooden block so that it its side are parallel to that of the wooden box below it. Ensure that the block is still and that the opening of for the steel ball is facing and aligned with the track. The block should have about a 1/8th inch gap from the end of the track. Measure and record the distance of the top of the system, where the block is hanging from, to the top of the block. Position the slider at a point where the block touches or barely touches it after impact with the steel ball. Conduct trial runs until a position is found for the slider where the wooden block barely or lightly makes contact with it. Record this position. Data and Calculations (3pts) Figure 1.b: Distance values of steel ball in flight Distance Values of Steel Ball in Flight Trial # Distance (in meters) 1 0.391 2 0.391 3 0.382 4 0.386 5 0.386 6 0.379 7 0.382 8 0.384 9 0.383 10 0.385 Figure 2: Trials for finding consistant distance of slider

Distances of Slider Trial # Distance of Slider (in meters) 1 0.182 2 0.285 3 0.273 4 0.322 5 0.353 6 0.359 7 0.365 8 0.366 9 0.380 10 0.381 Calculations Height of steel ball in flight: 0.130 m Measure of h: 0.416 m Mass of steel ball: 0.57kg Uncertainty in height of ball drop: 0.001/ / 2 = ±0.0005 Average/mean distance of ball drop: (0.391m + 0.391m + 0.382m + 0.386m + 0.386m+ 0.379m + 0.382m + 0.384m + 0.383m + 0.385m) / 10 = 0.385m

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Uncertainty in distance: 0.001 / 2 = ±0.0005 Standard deviation of the mean: [ (1/10) ∑(0.391m - 0385m)^2]^½ / [10^½] = 0.00122 Velocity: 0.385m [9.8 m/s^2 /(2 x 0.130m)]^½ = 2.36 m/s Uncertainty in Velocity using standard deviation: [(0.385m ± 0.00122) (9.8 m/s^2 /(2 x (0.130m ± 0.0005))^½] = ± 0.00589 Uncertainty in Velocity using uncertainty in distance: [(0.385m ± 0.0005) (9.8 m/s^2 /(2 x (0.130m ± 0.0005))^½] = ± 0.00295 Uncertainty in h: 0.001 / 2 = ±0.0005 Linear momentum before collision: 2.36m/s x 0.57 kg = 1.35 (kg * m)/s Calculate for y: 0.416m - [(0.416m^2) - (0.381m)^2]^½ = 0.249 m Linear momentum after collision: [0.0857 kg + 0.57 kg] * [2 x 9.8 m/s^2 x 0.249m]^½ = 1.45 (kg * m)/s

Questions (3pts) 1. Now we have two ways to calculate the uncertainty of an experimental measurement. The first simply looks at the average of the uncertainties over a repeated measurements, as you did in the first lab. The new method uses the standard deviation. How do multiple measurements of d change the uncertainty? Compare the uncertainties in the velocity of the ball using these two different methods. Taking multiple measurements helps to improve the accuracy of the data, which would change the uncertainty value to fit the resulting data recorded. The uncertainty using standard deviation is greater than the uncertainty using the average of the uncertainties to account for the gaps that are greater than 0.001 meter between varying values. 2. Within the limits of your experimental accuracy, is momentum conserved during the collision? Momentum is conserved during the collision according the limits of experimental accuracy. 3. Derive equation (1), starting from general physics principles. initial energy = final energy →initial kinetic energy + initial potential energy = final kinetic energy + final potential energy → 0 + mgh = 0.5mv^2 + 0 → v^2 = mgh / 0.5m → v^2 = 2gh → v = (2gh)^½

4. From your results, compute the fractional loss of kinetic energy of translation during impact. Disregard rotational energy of the sphere. Kinetic energy before impact: 0.5 * 0.57kg * (2.36 m/s)^2 = 1.59 kg * (m/s)^2 Kinetic energy after impact: 0.5 * (0.57kg + 0.0857kg) * [(2 x 9.8 m/s^2 x 0.249m)^½]^2 = 1.60 kg * (m/s)^2 (1.60 - 1.59) /0.159 = 0.06J 5. Derive an expression for the fractional loss of kinetic energy of translation in terms only of m and M, and compare with the value calculated in the preceding question. Consider the collision as a totally inelastic one. [mv^2] / [(m + M) v^2] * 100 [0.57kg * (2.36m/s)^2] / [(0.57kg + 0.0857kg) * ((2 * 9.8m/s^2 * 0.249)^½)^2)] * 100 = 99.2% of the energy was conserved. Hence, there was an 0.8% loss of kinetic energy of translation. Conclusion (2pts) The goal of this experiment was to understand the conservation of momentum when two systems collide. Considering the 99.2% of energy conserved, the results of this experiment supports the conservation of momentum. However, this also indicates that 0.8% of the energy had been lost from the system. This can be attributed to friction when the ball

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slides down the track, the wooden block acting against gravity as it swings, as well as a conversion of the energy into sound. As for inaccuracies in measurement, there is a lack of precision in measuring various lengths, which a digital form of measurement would be able to record more accurately. For instance, the ruler in use was curved, which could throw off the accuracy of a measurement. Hence, it would be better in the future to obtain a measuring tool that was not faulty. In addition, the slider was loose, furthering imprecise measurements. Generally, momentum is conserved but some energy will be lost from the system due to external forces such as friction, gravity, and sound from the collision.

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