Copy of Hooke's Law Lab

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Stony Brook University *

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131

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Mechanical Engineering

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Jan 9, 2024

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pdf

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7

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PHY133 L69 Hooke’s Law And Springs Lab Report
Introduction: The relationship between the force of the spring and distance is written by the equation F s =-k x, here k is the spring constant of stiffness of the spring, and x is the distance stretched. When a spring is stretched,, there will be a force exerting a “restoring force” to return to equilibrium. Procedure: 1. Calibrate the device before the experiment begins 2. Attach the eye bolt onto the force sensor of the device 3. Make sure the device is positioned so that Y-axis is pointed to the surface 4. Press record and gently pick up the device for a couple of second 5. Stop recording 6. Solve for the mass of the device using F=ma 1. Attached long spring to the end of the eye bolt 2. Place the device face down and record 3. Pull on the device 4. Record for 10 seconds 5. Stop recording 6. Click on the parametric plot and highlight the section of the wave that corresponds to the experiment 7. Find the slope of the graph by selecting two points on the graph and solving for slope 8. Repeat steps 2-8 with the 2 other trials as well as with the shorter spring. 1. Use a flat surface like phone or wall 2. Attach shorter spring into the force sensor 3. Have the device face down on a surface 4. Start recording 5. Push the spring gently by pushing the device back and forth against the flat surface 6. Record for a couple seconds 7. Select parametric plot and highlight the section of the wave that corresponds to the experiment 8. Find the slope of the graph by selecting two points and solve for the slope with the equation m= Y2-Y1/X2-X1 1. Position the device face down 2. Face it so that the spring is in contact with a wall 3. Press record 4. Gently push device and stop recording when it rebound 5. Find the peak force, velocity before collision, velocity after collision.
6. Find displacement using Fs=-kx using the peak force and spring constant value of short spring 7. Use displacement to find spring potential energy 8. Find kinetic energy before and after collision using velocities before and after collision Results: Figure 1: Left: The Acceleration and force measured when iolab is suspended in air by an eye bolt. Acceleration of the device is -9.805m/s^2; Force due to gravity is -1.927N
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Figure 2: Position(m) vs Force (N) Trial 1: Left: Point Measures (-0.0130m, -0.6641N);Right: Point measures (0.0322m,-1.1238N) The beginning is unshaded for error Figure 3: Position(m) vs Force(N) Trial 2: Left: point of the graph (-0.0094m, -0.7802N); Right: point measures (0.0539m, -1.4153N) Figure 4: Position(m) vs Force(N) Trial 3: Left: Point measures (-0.0011m, -0.7155N); Right: point measures (0.0601m, -1.4245N)
Figure 5: Position(m) vs Force (N) of experiment 3, pushing the device with the spring attached onto a surface. Left: Point measures (-0.0172m, 3.1670N); Right: point measures (-0.0071m, 1.1107N) Table 1: Trials Left point (X1,Y1) Right point (X2,Y2) Slope (Y2-Y1/X2-X1) Spring Constant,k (N/m) 1 (-0.0130m, -0.6641N) (0.0322m, -1.1238N) -10.170 10.170 2 (-0.0094m, -0.7802N) (0.0539m, -1.4153N) -10.033 10.033 3 (-0.0011m, -0.7155N) (0.0601m, -1.4245N) -11.584 11.584 Short spring (-0.0172m, 3.1670N) (-0.0071m, 1.1107N) -203.594 203.594 Figure 6: Peak Force of the short spring Figure 7: Velocity of device before collision at -0.267m/s
Figure 8: Velocity of the device when colliding with a wall with spring attached. Velocity is 0.242m/s Calculations: Mass of Device ?𝑔 = ?𝑎 Slope of the 3 trials ? = ?2−?1 ?2−?1 Average of the 3 trials: : = ?𝑟𝑖𝑎? 1+2+3 3 −10.170𝑁/?+(−10.033𝑁/?)+(−11.584𝑁/?) 3 =− 10 /? Shorter spring slope: ? = 1.1107𝑁−3.1670𝑁 −0.0071?−(−0.0172) ? =− 203. 594 𝑜𝑟 203. 594 𝑁/? Displacement: Fs=-kx 1.237N=-203.594N/m(x) x=-0.00607 or 0.00607 m Kinetic energy before collision and after: 𝐾? = 1/2?𝑣 2 Spring Potential energy: ? = 1/2?(∆𝑥) 2 Error: Before collision ∆𝐾? 𝐾? = (σ?/?) 2 + (2 * σ𝑣/𝑣) 2 Discussions: For the error calculation, the error margin for kinetic energy before collision is 0.00745, which is greater than the initial kinetic energy of 0.00698 J and error margin for after the collision is 0.00580 J which is around the value of after the collision of 0.00573 J. There may be an error in calculation with the error which led to these values.
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