Signature Assignment 1301 2325 2019

docx

School

San Jacinto Community College *

*We aren’t endorsed by this school

Course

2425

Subject

Mechanical Engineering

Date

Apr 3, 2024

Type

docx

Pages

Uploaded by scarleteverburn

Simple Harmonic Motion - Mass on a Spring (Force Sensor, Motion Sensor) Equipmen A spring that is hanging vertically from a support with no mass at the end of the spring has a length L (called its rest length). When a mass is added to the spring, its length increases by L. The equilibrium position of the mass is now a distance L + L from the spring’s support. What happens when the mass is pulled down a small distance from the equilibrium position? The spring exerts a restoring force, F = -kx , where x is the distance the spring is displaced from equilibrium and k is the force constant of the spring (also called the ‘spring constant’). The negative sign indicates that the force points opposite to the direction of the displacement of the mass. The restoring force causes the mass to oscillate up and down. The period of oscillation depends on the mass and the spring constant. As the mass oscillates, the energy continually interchanges between kinetic energy and some form of potential energy. If friction is ignored, the total energy of the system remains constant. Computer Setup-1: 1. Connect the 850 Universal interface to the computer, turn on the interface, and turn on the computer. 2. Connect the Force Sensor to Analog inputs. 3. Set the sensor to 5Hz. Equipment Setup-1: 1. Mount the C-clamp to the edge of the table, put the rod in the clamp, mount the Force Sensor vertically so its hook end is down. 2. Suspend the spring with hanger from the Force Sensor’s hook so that it hangs vertically. 3. Use the meter stick to measure the position of the bottom end of the spring (without any mass added to the hanger). For your reference, record this measurement as the spring’s equilibrium position in the Data Table-1 in the Lab Report section. t: Force Sensor 1 Hanger and Masses: 6-50 g; 2-100 g Motion Sensor 1 Support Rod Spring 1 Clamps: right angle; spring clamp; C-clamp

Procedure-1: Data Recordin g 1. Change the sensor sign 1.1. Click Hardware Setup In the Tools Palette 1.2. Click on the force sensor 1.3. Click Properties in the lower right corner of the Hardware Setup window. The Properties Window opens. 1.4. Click Change Sign 1.5. Click OK 2. Press the TARE button on the side of the force sensor to zero the Force Sensor. 3. For Entry #1, type in “0” (since the spring is not stretched yet). Record your value in the table 4. Generate the Force vs. Distance graph 4.1. Choose from the Quick Start templates 4.2. Click <select Measurement> in the first column 4.3. Select Create New > User-Entered Data 4.4. Optional: Rename the measurement as “distance” units (m). 4.5. Click in the cell of the User-Entered data column and enter your data. 5. Click on the triangle 5.1. Select to keep data points when commanded 5.2. Click on “Keep Mode” to record the data run. 6. Add 50 grams of mass to the end of the hanger. 7. Measure the new position of the end of the spring at equilibrium. Enter the difference between the new position and the equilibrium position as the ∆ x , in the table under distance column ‘Stretch’ (in meters) , and record the Force value for this Stretch value by clicking on keep s ample .

8. Add 50 grams to the hanger (for a total of 100 g additional mass). Measure the new position of the end of the spring, enter the ∆ x value in the table under distance column and click ‘Keep sample’ 9. Continue to add mass in 50 grams increments until you have added 300 grams. Each time you add mass, measure and7 enter the new displacement value from equilibrium. Click ‘Keep sample’ to record the force value. 10. End data recording. Analysis-1: 1. Click on the Selection tool ) drag and reshape the highlighted box on the best slop region. 2. Use the Curve Fit ) to determine the slope of the Force vs. Stretch (∆ x ) Graph. 3. Then click on the triangle in the Curve Fit tool and select “Linear” to determine the slop value then record it in the Data Table-1 at the Lab Report section. a. You may need to move the linear Curve Fit box to read the best slope Activity-2: Use the Motion Sensor and 850 Interface to record the motion of a mass on the end of the spring and determine the period of oscillation than compare the value to the theoretical period of oscillation. Computer Setup-2: 1. Unplug the Force Sensor’s plug from the interface. 2. Connect the Motion Sensor’s stereo phone plugs into Digital Channels 1 and 2 of the interface. Plug the yellow-banded (pulse) plug into Digital Channel 1 and the second plug (echo) into Digital Channel 2. Equipment Setup-2: • You do not need to calibrate the Motion Sensor. 1. Using a support rod and C-clamp, suspend the spring from the spring clamp so that it can move freely up-and-down. Attach it firmly to the outermost position. Put a mass hanger on the end of the spring. 2. Find the mass of the spring. Add 200 g to the hanger. 3. Record the mass of the hanger, the 200 g, and 1/3 the mass of the spring (in kg) in the Data section. Return the hanger and masses to the end of the spring. 4. Place the Motion Sensor on the floor directly beneath the mass hanger. 5. Adjust the position of the spring so that the minimum distance from the mass hanger to the Motion Sensor is greater than the Motion Sensor’s minimum distance (15 cm) at the maximum stretch of the spring.

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

Procedure-2: 1. Zero the position 1.1. Click Hardware Setup In the Tools Palette 1.2. Click on the motion sensor 1.3. Click Properties in the lower right corner of the Hardware Setup window. The Properties Window opens. 1.4. Select “Zero Sensor Now” and “zero the sensor.” 2. Pull the mass down to stretch the spring about 5 cm. Release the mass. Let it oscillate a few times so the mass hanger will move up-and-down without much side-to-side motion. 3. Begin recording data. 4. The plots of the position and velocity of the oscillating mass will be displayed. Continue recording for about 10 seconds. 5. End data recording. 5.1. The data will appear as ‘Run #1’. 5.2. The position curve should resemble the plot of a sine function. If it does not, check the alignment between the Motion Sensor and the bottom of the mass hanger at the end of the spring. You may need to increase the reflecting area of the mass hanger by attaching a circular paper disk (about 2” diameter) to the bottom of the mass hanger. 5.3. To delete a run of data, click on ) in the Controls Palette. Analysis 2: 1. Rescale the Graph axes to fit the data. 1.1. Click on the ) to adjust y-axis scale to fit data. 2. Find the average period of oscillation of the mass by taking the difference in time between any two peaks. Click the button ). 2.1. Move the Smart Tool to the first peak in the plot of position versus time and read the data coordinates. Record the value of time in the Data Table-2 in the Lab Report section. 2.2. Move the Smart Tool to each consecutive peak in the plot and record the value of time shown for each peak.

Record your results in the Lab Report section Lab Report - Activity P14: Simple Harmonic Motion - Mass on a Spring Data Table-1 Item Value Equilibrium Position 0.15 meters Spring Constant (slope) 6.78 N/m Data Table-2 Mass = 0.2078 kg Peak 1 2 3 4 5 6 7 Time (s) 0.250 1.25 2.25 3.20 4.25 5.25 Period (s) 1 1 0.95 1.05 1 Average period of oscillation = ___1_______ s Time (s)

Critical Thinking and Quantitative and Empirical Skills Assessment (Complete Individually) 1. Calculate the theoretical value for the period of oscillation based on the measured value of the spring constant of the spring and the mass on the end of the spring. T = 2 π √ m k => T = 2 π √ 0.2078 6.78 =1.099 s 2. How does your calculated value for oscillation compare to the measured value of the period of oscillation? What is the percent difference? | (1.099-1)/(1.099+1) |*200 = 9.4%. There is a 9.4% difference between the calculated and measured oscillation. 3. When the position of the mass is farthest from the equilibrium position, what is the velocity of the mass? The velocity of the mass is zero when the mass is farthest from equilibrium. 4. When the absolute value of the velocity of is greatest, where is the mass relative to the equilibrium position? The absolute value of velocity y is greatest when the mass is in the equilibrium position. 5. A mass of 225 g is suspended from a vertical spring. It is then pulled down 15 cm and released. The mass completes 10 oscillations in a time of 32 seconds. What is the force constant for the spring? T = 2 π √ m k => k =( 4 π 2 m )/ T 2 = 4 π 2 ( 0.225 ) 3.2 2 = 0.867n/m. The force constant is 0.867 n/m. 6. A block of unknown mass is attached to a spring with a force constant of 6.50 N/m and undergoes simple harmonic motion with an amplitude of 10.0 cm. When the block is halfway between its equilibrium position and the end point, its speed is measured to be 30 cm/s. Calculate a) the mass of the block, 1/2K(x)^2+1/2m(0)^2=1/2k(x/2)^2+1/2m(v)^2 => mv^2=(3*K*X^2)/4 => m= (3*6.5*(0.1^2))/(4*(0.3^2)) = 0.5416 kg. The mass is 0.54 kg. b) the period of the motion, and T = 2 π √ m k => T = 2 π √ 0.5416 6.5 = 1.8137. The period of motion is 1.814 seconds. c) the maximum acceleration of the block. f=ma =mg+Kx => a=g+(Kx)/m => 9.8+ ((6.5)(0.1))/0.5416 = 11.01. The maximum acceleration is 11.01 m/s^2.

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

Critical Thinking/Written Communication (Complete Individually) (Type at least a 1-page response.) 7. Purpose: State the purpose of the experiment. Explain exactly what the experiment investigates and what you are trying to determine. Be as explicit and thorough as possible. Explain the theory behind the experiment. Explain exactly what you measured and how it was used to fulfill the purpose of the lab. 8. Conclusion: Discuss the percent error and the uncertainties involved in the measurements and possible errors which made the experimental results different from the theoretical results. Suggest possible improvements in the experiment which could reduce these uncertainties.

The purpose of this experiment is to explore simple harmonic motion and the accompanying equations. This experiment investigates the conservation of energy in the simple harmonic system and the various things that could be determined from this, such as the spring constant, the time of the period, and the mass of the object in simple harmonic motion. The displacement over time was measured of a mass on a spring that is in simple harmonic motion. This allowed the simple harmonic motion of the system to be analyzed as the graph shows the period and the motion of the system. From this graph you can see that the energy is mostly conserved. Through knowing the mass and spring constant, the period of the spring was able to be determined from the equation T = 2 π √ m k . The calculated verses the measured period of the spring, which was only 9.4% different, was able to prove that T = 2 π √ m k is a good equation to use in terms of simple harmonic motion. It also proves that simple harmonic motion is consistent to have a working equation. Which also proves that energy is conserved through simple harmonic motion as the period is consistent. The percent difference between the calculated and measure period time was 9.4%. This means that the measured value was mostly constant to the calculated value. Some sources of error in this experiment include any wobble in the spring and the force of friction acting on the system. With any wobbles in the system, the simple harmonic motion would be changed and be slightly off as it would have other forces acting upon the system rather than just those that are accounted for. Friction would also cause variations in the data as it is not accounted for in the experiment or in the equation for the time. One way to improve this experiment is to have varying masses and to measure the simple harmonic motion of each

system and see if the equation consistently works for each system.

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version