PLEASE ANSWER ALL THE ANALYSIS QUESTIONS based on data! (Bottom Page)

2. The interface . Set the Motion Setup the equipment and place a single book or object under one end of the Dyna that it forms a small angle with the horizontal (see Figure 1). Adjust the points of two ends of the incline so that the distance, x, in Figure 1, is between 1 and 2 m 3. Place the Motion Detector at the top of the incline. Position it so the Dynamics closer than 0.15 m. 4. Open the file "04 Determining :" from the Physics with Vernier folder. 5. Record the mass of your cart in the data table. Make sure the spring plunger 6. Record the initial height the object is being released /. Click to start data collection; release the cart after the Motion Detector start hand out of the Motion Detector path quickly. 8. Find the velocity of the cart at the end of the track and record this value 9. Repeat Step 6-8 for three more times (3x) by raising the incline each measurement in the data table below. 10. Compute the measured kinetic energy of the cart from the measured velo and record in the data table 11. Using the conservation of energy, calculate what the kinetic energy of th of the track ad record this in Data Table #1 Table 1 Mass of Cart SIO. sg Height Speed at Potential Energy KE (J) (m) end of ramp (mgh) (1/2mv2) ( m/s) Measure O. 0 Gem 0. 7299 mls 2 0.083m. 0. 8771 mrs 3 0.0 92 m| 0. 9599 m/s 4 0. 118 m. 1.065 m/sPart B: Spring potential into Kinetic energy Ax rececellle Figure 2 1. Measure the spring constant of the spring that is given by your instructor. This is done by using Hook's law that Fx = k Ax Fry -Fx Hang a mass from one end of the spring and measure the distance (x) that spring stretches from its equilibrium position. Do this for few masses and find averaged value of k and record in data table #2 Mass (kg) Weight (N) Distance Ax (m) Spring constant, k 05 ky 0. 49 N 44. 55 . 100 Ky 0.98 N 6.029 m 33. 79 0. 200 Ky 010 67 m 29. 25 Average 35. 86 2. Create the setup in Figure 2. Make sure you place the Motion Detector at the end of the track to record the velocity of the cart. 3. With the spring attached to the cart and tether (holder), move the cart to a position by stretching the spring (this is effectively storing energy in the spring). 4. Record the Ax the spring is stretched from equilibrium in data table #2. 5. Click to start data collection; release the cart after the Motion Detector starts to click. Move your hand out of the Motion Detector path quickly. 6. Find the velocity of the cart when the spring reaches its equilibrium point (i.e. unstretched) and record this value 7. Repeat Step 6-8 for three more times (3x) by changing the amount the spring is stretched. You can also change the mass of the cart to vary your trials. Record your measurement in the data table #28. Compute the measured kinetic energy of the cart from the measured velocity and mass (1/2mv?) and record in the data table 9. Using the conservation of energy, calculate what the kinetic energy of the cart will be at the end of the track ad record this in Data Table #2 Mass of Cart 510. 5 9 % error Ax (m) Speed at Potential Energy | KE (J) KE (J) end of ramp spring (1/2kAx2) (1/2mv?) (1/2mv2) Measured Calculated ( m /s ) 1 0. 18 m. 0. 7433 2 0 123 | 0 . 8073 3 0: 28 m. 1.05 2 4 0. 33 m. 1. 327 Part C: Energy conversion from multiple sources In this part of the experiment, we will combine the knowledge from Parts A & B to assess conversion of energy from multiple sources of potential (Gravitational and Spring) into kinetic energy. Ax L SOH elececcle 121 121 Figure 3 1. Create the setup in Figure 3 by placing the dynamic track at an angle. You will be keeping this incline constant 2 . Record the angle 0 = _ Ry. 260 3. The starting position of your cart will be at the top of the track where the spring is at its equilibrium point (unstretched). 4. Click to start data collection; release the cart after the Motion Detector starts to click. Move your hand out of the Motion Detector path quickly. 5. From your measurements, find the velocity of the cart at approximately 30cm from your start position. Record this value 7 1/2 way point Velocity of the cart @ 30cm from start = _Q1 4sy( m /s 6. For the same trial, record the maximum distance the spring was stretched; Ax =_ 0_10 3 m midpoint v - 0.6541 mus Pe spring = 0, 5379 h: 12 cm ( initial ) stretched 30 con. 3 (0. 51 ) ( oncesul )Conversion and Conservation of Energy BACKGROUND Physical concepts of energy become very useful when describing the ability of a system to do work or extract meaningful work. Work, defined as application of constant force on an isolated system over a distance, d is thus transfer of energy from one system to the other. Wnet = Fnet * d * cos (0) We, have seen that energy exists in many forms, be it chemical, radiant, nuclear, or thermal energy. As a law of nature, all energy is conserved and only gets converted from one form to another. Even in instances when we think energy is lost, it is only converted to thermal energy as form of heat. The work-energy principle state that unbalanced transfer of energy through work results in an object changing its kinetic energy or storing that energy in the form of potential energy. However, conversion between kinetic energy and potential energy is always constant. In the equation form, AKE + APE = 0 KEi + PEi = KEf + PEf Kinetic energy of an object is described as KE = = mv While the potential energy exists in many otherforms, some of the common ones we have considered: PEgravity = mgh (h is the height of the object relative to a reference) PEspring = =kx2 (x is the distance spring is moved from point of equilibrium) Thus, according to conservation of energy, the equation that would take into account kinetic and potential energy 5mu ? +mghit - kx ? = = mvp + might , kx ; In this lab, we will consider the conversion of gravitational and spring potential energy into kinetic energy as well complex systems where combination of energy forms and conversions take place.Analysis Part A: 1. How does you calculated KE at the end of the track compares to the measured KE? 2. Does your data show that PE gravitational gets completely converted to kinetic energy at the end of the track? 3. How can you explain the % error in your data? 4. From each track, calculate the work done by kinetic friction. How does your value compare if we assume the dynamic carts have a coefficient of kinetic friction of 0.004 Part B: 1. How does your calculated KE compared to measured KE from your data table #2 2. Is the potential energy from the spring completely converted to kinetic energy? 3. How does your efficiency of conversion compare between Part A and Part B? What can you say this difference is attributed to (if any)? Part C: 1. Using the equation of energy conservation, calculate the velocity of the cart at 30cm away from it's starting point. Please show all your work below. 2. How does this value compare to the measured value of the velocity from step 5 in part C? 3. When the cart is at its lowest point before returning back up, calculate the energy of the system. Account for all the energy (both kinetic and potential) at this point. 4. Why does the cart stop and return back up?Table 1 Trial 1 timara Outa Analyze Insert Options Par DC- Page 1 Determining g 1.0 0.8 Position (m) 0.6 0.4- 0.2 3 Time (s) 0.8 0.6 0.4- Velocity (m/s 0.2 0.0 102- Time ( s ) Part 2 plan b wining golf File Edit Experiment Data Analyze Insert Options Page H DGAG Page 1 - HAQQ YN yz/ / XOM Collect 0.8 Determining g 0.7 0.6- Position (m 05 0.4- 3 (1.613, 0.660) (At:0.04 4x:0,000) Time (S) 0.5 0.0 Velocity (m/s -0.5 min: 0.7433 at 1.900 max 0.7433 at 1.900 ed. Gov. 0 samples: 14 0 Time (s) (41:0.04 Av:0.021)