Lab Report for Lab 11

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Feb 20, 2024

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Lab Report for LK-11: Energy Conservation (Using Smart Car) By: Erica Quintero-W212771048 Date: May 11, 2023

Introduction: The purpose of the lab is to determine if the magnitude of a force will affect the work done on the objects. Using the equations for Work-Kinetic Energy Theorem, Conservation of Mechanical Energy and Conservation of Energy. We can test this theory by using the tools below and determine whether the hypothesis is correct. Materials used:  Laptop with PASCO software installed.  Red cart  Weights  Thread  Friction block  Hanger to hold the masses.  Track and stop clamps.  Pulley Steps to set up : We first took the weight of the materials. The cart, the mass hanger and the mass. We did not take the mass of the thread since the thread was light enough to be negligible. We then took the mass of the friction block as well. We connected the cart to the laptop via Bluetooth and selected the sensor. We then input the conditions that allow to record the run at .05 m and stop recording at .5m. We did not need to measure the initial height of the hanging mass since the displacement is of the vertical height is the same as the displacement of the horizontal one. Table 1: We pushed the cart along the track 1 time before recording our results to test out the graph and the recording results. We then proceeded to run the track ready to be recorded and to keep the hanging mass constant. The 1 st run was the cart alone weighing at .250 kg traveling at a distance of .4116 m, with an initial speed of .332 m/s and final speed of .916 m/s. On the 2 nd run we added two bars totaling the whole mass of the cart and bars to .750 kg and traveling a distance of .4592 m with an initial speed of .193 m/s and a final speed .572 m/s. On the 3 rd run we removed one bar totaling the mass to .500 kg and traveled .3787 m with an initial speed of .354 m/s and a final speed of .889 m/s. To find out the change in kinetic energy, ∆ K , of each run we use the equation ∆ K = 1 2 M v b 2 − 1 2 M v a 2 . We then find out the Work done on the cart which is the area under the Force (y-axis) vs Position (x-axis) graph. Each run has a constant work of .16

Newtons. We then find the precent difference on each run using the equation % diff = ( W − ∆K ) | ( w + ∆K ) 2 | ∗ 100 Table 1: Work-Kinetic energy Theorem Mass of friction block: .1216 kg Run Number Mass of Cart + extra Weight M Hangin g Mass m Distance traveled by cart d=b-a d Initial cart speed v a Final speed of cart v b ∆ K of cart + masses ∆ K Work = Area under F v. X W % diff 1 .250 kg .025 kg .4116 m .332 m/s .916 m/s .91104 J .16 N 5.4% 2 .750 kg .025 kg .4392 m .193 m/s .572 m/s .109 J .16 N 37.91% 3 .500 kg .025 kg .3787 m .354 m/s .889 m/s .166 J .16 N 3.7% Table 2: For the second table we did not need to make additional runs because we can also calculate the potential energy (conservation of mechanical energy) of the cart. However now we take the hanging mass, m, into account when calculating for the change kinetic energy. We use the equation ∆ K = 1 2 ( M + m ) v b 2 − 1 2 ( M + m ) v a 2 for each run. We then calculate the potential energy for the hanging mass in each run using the equation U g = ( m ) ( g ) ( h ) . Remember that h is equal the horizontal distance travelled by the cart. We then proceed to calculate the percent difference between the change in Kinetic Energy and the Change in Potential Energy using the equation: % diff = ( ∆U − ∆K ) | ( ∆U + ∆ K ) 2 | ∗ 100 Table 2: Conservation of Mechanical Energy.

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Run Number Mass of Cart + extra Weight M Hangin g Mass m Distance traveled by cart d=b-a d Initial cart speed v a Final speed of cart v b ∆ K of cart + masses ∆ K ∆U g of hanging mass ¿ ∆U g ∨ ¿ % diff between ∆ K and ∆U g 1 .250 kg .025 kg .4116 m .332 m/s .916 m/s .1002 J .1008 J 5.9% 2 .750 kg .025 kg .4392 m .193 m/s .572 m/s .1123 J .1076 J 4.27% 3 .500 kg .025 kg .3787 m .354 m/s .889 m/s .1745 J .0927 J 61.22% Table 3: For table 3 we let the cart run again, but this time we put the friction block, defined as M 1 in front of the cart. We selected the same sensor graph and placed the same start and stop conditions. We also did not add any extra mass to the cart itself and instead put any extra weight on top of the friction block. Also, instead of the hanging mass weighing .025 kg, we increased the mass so that in now weighs .095 kg that way the cart was able to move. On the 1 st run we placed an extra mass of .100 kg on top of the friction block and the cart traveled .3648 m, with an initial velocity of .395 m/s and a final speed of .792 m/s. On the 2 nd run we increased the extra mass to .200 kg and the cart traveled .4126 m with an initial speed of .163 m/s and a final speed of .514 m/s. On the 3 rd run we increased the extra mass to .300 kg and the cart travelled .4479 m with an initial speed of .043 m/s and a final speed of .196 m/s. We then calculated the change in Kinetic Energy using the equation ∆ K = 1 2 ( M + M 1 + m ) ( v b 2 − v a 2 ) for each run. We then calculate the potential energy using the equation U g = ( m ) ( g ) ( h ) . Since friction is a constant, we will use μ = .18 N to find the friction work on the friction block using the equation | fd | = | μ k nd | = | μ k M 1 gd | for each run. We the find the change in mechanical Energy as defined by the equation ∆ E mech = ∆ K + ∆U . And finally, we calculate the precent difference between the mechanical energy and the friction work. Using the equation % diff = ¿¿ for each run. Table 3: Conservation of Energy (including friction):

Run Mass of smart Car M Mass of friction block + extra Mass M 1 Hangin g Mass m Distance travelled. d Initial Speed v a Final speed V b ∆ K ∆ K ∆U g ∆U g Friction work of friction block | fd ∨ ¿ ∆ K + ¿ ∆U g % diff 1 .25 kg .2216 kg .095 kg .3648 m .395 m/s .792 m/s .1335 J -.3396 J .1426 N -.206 J 36.42% 2 .25 kg .3216 kg .095 kg .4126 m .163 m/s .514 m/s .0789 J -.3841 J .2341 N -.305 J 26.41% 3 .25 kg .4216 kg .095 kg .4479 m .043 m/s .196 m/s .0140 J -.4169 J .3331 N -.403 J 18.36% Conclusion: In the first table work was a constant of .16 N, however the kinetic energy was different each time. We found the percent differences they were moderately small. However, we can account the percent difference for errors such as the hanging mass swinging as the cart moved forward, the friction of the track on to the cart or simply not pushing the cart or stopping with a constant force. We can determine that the work is dependent on the magnitude of the force, since the weight of the hanging mass was a constant. However, the Kinetic energy will be different depending in the mass of the object. For table 2 we used the same values however we used the hanging mass into the equation to calculate for the kinetic and potential energy of the hanging mass. We found that the Kinetic Energy is different than the Potential Energy however it nearly reached 0 as its result by a few decimals. But we can account the small percentage difference again by the distance traveled the, the hanging mass swinging and the velocity of the cart. So the equation of the sum of kinetic and potential energy is verifiable. And for table 3 friction, gravity, were all constants however, we had different results for each run since the mass was different each time. We saw that even though the friction force was constant, each increment of mass on the friction block made the cart travel slower. Resulting in different friction work and we got bigger precent differences, our team believed this was due to bigger masses and the addition of friction. We can say that the work done on the cart is dependent on the magnitude, direction and mass of a force.