Physics Lab Report 2 -Hooke’s Law and Simple Harmonic Motion Lab Report PDF

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Hooke’s Law and Simple Harmonic Motion Lab Report...

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Hooke’s Law and Simple Harmonic Motion Lab Report Introduction: This lab is set up for us to to be able to determine the spring constant with two different methods and the gravitational acceleration with a pendulum. The spring constant refers to how “stiff” a spring is. Springs are elastic meaning that once they are stretched or compressed they are able to return to their original state. Springs tend to have a higher spring constant, and once they are deformed they are a great example of Newton’s Third Law of Motion stating that for every force there is an equal opposite force. This elastic behavior of springs can be explained through Hooke’s Law and formula [1]. Objective: Within the experiment, in the first two parts we will determine the spring constant of a spring using two different methods. In the third part of the experiment we will determine acceleration due to gravity by using a simple pendulum. Hooke’s Law helps explain the first parts of this experiment. Hooke’s Law states that if a force (F), is applied to the opposite end of a material holded on, parallel to the length, then in general the material is either compressed or stretched by distance (x) .The relationship of this can be best explained through the equation: F = -kx [1] Where k is kept as a constant. In this experiment since the material used will be a spring then the constant k will be called a spring constant. In the third/last part of the lab, we are to determine acceleration due to gravity with a pendulum. Stated by theory the total time period of a pendulum can be calculated through the following equation T = 2π √ ℓ/g [2] Where g is the gravitational field of strength (9.8) and ℓ would be the length of the string attached to the pendulum. Where the mass of the bob does not affect in any way the pendulum's period. This equation can be algebraically be manipulated in order to be able to obtain the gravitational acceleration by itself. G = 4π2(ℓ/T) [3]

Procedure: Initial Setup ❏ Start the computer, and start the Data Studio program. ❏ Select Open Activity. From the mechanics folder, open the file “Hooke’s law”. ❏ Examine the apparatus. The top measurement device is the force sensor and will be connected into the A analog input of the Science Workshop interface. ❏ The bottom sensor is a motion sensor and will be connected into digital inputs 1 and 2, with the yellow plug connected into input 1.

❏ Suspend the spring from the hook on the force sensor. ❏ Suspend a mass hanger from the other end of the spring. Part 1: Determine Spring constant Calibrating Sensors First the Force Sensor ❏ On the side of the force sensor is a button labeled TARE. Press this button; this will zero the force sensor, thereby negating the force contributed by the spring and mass hanger. Now for the Motion Sensor ❏ Click the start button. ❏ Click the Keep button five times, then click the red box to stop the data run. ❏ Locate the Table Window at the bottom of the display. The mean value for the distance from the sensor to the bottom of the hanger is given. ❏ Locate the Data Panel in the upper left portion of the Experiment Window. Within this pane is a variable name pos. Double click on it to open a setup window. ❏ In the lower half of the setup window is a heading for Experimental Constants. Below this heading you will see the variable xstart, and a value box beneath it. Type the mean value given in the Table window in this box. ❏ Click the lower Accept button to change the previous value to the new one you just entered. ❏ Close the Setup window. ❏ From the upper menu bar, under the Experiment menu, click Delete Last Data Run Obtaining the First Data Set: Stretching the Spring ❏ Try to keep any oscillations of the mass to a minimum. A good technique to accomplish this is to support the bottom of the mass hanger with one hand as you add mass to the mass hanger. Then slowly lower the supporting hand to allow the mass hanger to descend gradually to its resting position. Then move your hand out of the way before taking a data point. Read through this entire step before performing it. ❏ Initially, with only the mass hanger suspended from the spring, click Start. Monitor the graph window and pay attention to the symbol that indicates where a data point is to be set . Currently, it should be bouncing around the origin of the graph. ❏ Click Keep, to acquire a data point. Do not click the red square to stop the data. ❏ Gently add a 100 gram mass to the mass hanger, allowing it to settle. Very small oscillations are expected and allowable. ❏ Check the display to see where the symbol is before clicking Keep, it should be on a path similar to that shown in Figure 7-5. Do not take a data point if the symbol is off track. If it is, clear the area around the sensor of the other possible targets. Again, do not click the red square to stop the data run. ❏ Continue collecting data, adding a 100 gram mass them Keep a data point, until ten 100 gram masses are on the hanger. ❏ Now, click the Red button. Part 2: Determine spring constant using Simple Harmonic Motion (SHM) approach. Initial Setup ❏ Suspend 0.55 kg of mass from the spring (mass hanger plus five 100 gram masses)

❏ From the File Menu, select Open Activity and open the file simple harmonic motion. [The files are located inside “My documents’, “Mechanics”] Calibrate the Sensor. ❏ In this part, only the motion sensor is acquiring data. The force sensor functions solely to provide a means to suspend the spring and mass. ❏ With the spring-mass system stationary, select Start. Data will be taken for 5 seconds, then stop automatically. The graph that is displayed in the Simple Harmonic Motion graph window should not have any large spikes. If it does, repeat until a spike-free graph is obtained. ❏ The Table window will display the mean value for the distance from the bottom of the weight hanger to the motion sensor. ❏ In the Data Panel, double-click on the pos=x-equilibrium icon. ❏ Enter the mean value into the box for the equilibrium value. ❏ Click the lower Accept button and verify that the value for equilibrium is equal to what was entered. ❏ Close the window. SHM ❏ Small amplitude oscillations work best. The best way to set the spring-mass combination into simple harmonic motion is to push the mass hanger straight up, no more than ½ in., so that the spring is no longer at equilibrium, and then release it. ❏ Click Start. After 5 seconds, it will automatically stop. The graph that is displayed in the Simple Harmonic Motion graph window should not have any large spikes. If it does, repeat until a spike-free graph is obtained. ❏ In the Simple Harmonic Motion graph window, click the first button on the left side of the ToolBar. It should be centered around zero. If not, use the mean value given in the Table window and enter it into the pos value described in Step 2. Save this data file. Click on “File”, “Export data”. “ Under “Pos”, select the run number you want to save. Then press OK. Save the file in desktop with appropriate name in txt format (default). . Part 3: Determine acceleration due to gravity by using a simple pendulum. ❏ Starting from 50 cm of length, increments of 10 cm for 5 different lengths. ❏ Tape protractors to force sensor ❏ Bring the force sensor to the edge of the bar to prevent bar from interfering with bob string pendulum hangs down 90° from the horizontal. ❏ Swing pendulum as you count 10 oscillations, using phone to time the completion of the oscillations ❏ Starting from 50 cm of length, increments of 10 cm for 5 different lengths. ❏ Use data to calculate the acceleration due gravity.

Tables Part 1:

Position (m)

Spring Force (N)

-2.840E-4

.023

6.000E-5

.984

1.092E-3

1.938

3.424E-3

2.956

.016

3.948

.024

4.913

.034

5.978

.043

6.985

.051

7.775

.059

8.950

.067

9.880

Part 2: Time (s)

Position (m)

.0192

-7.568E-3

.0356

-5.676E-3

.0520

-3.612E-3

.0685

-1.032E-3

.0849

1.376E-3

.1013

3.784E-3

.1177

6.020E-3

.1341

8.084E-3

.1505

9.632E-3

.1669

.011

.1833

.011

.1997

.011

.2161

.010

.2325

9.116E-3

.2489

7.568E-3

Part 3: Length (cm)

Total Time (sec)

T (total time/10) (sec)

T2

50

14.85

1.485

2.205225

60

15.81

1.581

2.499561

70

17.20

1.72

2.9584

80

18.02

1.802

3.247204

90

19.27

1.927

3.713329

Summary: For the first two parts of the lab, we were determine to find the spring constant in two different ways. In the first part we take into consideration the relationship between the spring force and the position, which represents the force displacement . Once we take the this gathered information and plot them in a graph, we are able to determine the spring constant through the slope. With the second part of the lab we were able to determine the spring constant through a different method, through the Simple Harmonic Motion approach. Once we graph it, our goal was to be able to determine the time period . Using the difference between two points time period of a simple pendulum oscillating in a vertical plane with a small amplitude [2] we were able to determine the time period being .21 seconds and the spring constant through calculating the slope. From my calculations from the two points I picked, the spring constant was 111.89 N, however since the line was not a perfect straight line, the slope will vary throughout the line. For the last part we were to determine the gravitational acceleration using the simple pendulum. Once plotting the gathered information, we were able to see the line showing the relationship between T2 and length. In the graph we notice that the straight line pases though the origin since in this trial there are two forces acting upon the mass; the gravitational force and the tension on the string and the direction of the force in this case points towards the origin. Nevertheless the tr in the graph is sinusoidal since the movement of the pendulum is a repetitive oscillation . The slope obtained from the graph helps us calculate the acceleration due to gravity . Using equation [3], we were able to successfully calculate the gravitational acceleration equalling 9.64 m/s2, which is relatively close to the actual gravitational acceleration of 9.8 m/s2.

Graphs

Part 1:

Part 2:

Part 3:

Works Cited

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Physics Lab Manual Mechanics and Sound Department of Physics University of Texas at

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Arlington Pendulum work out the value of acceleration due to gravity (g), by using the principle of kinematics of simple harmonic motion of a simple pendulum. - International Baccalaureate Physics - Marked by Teachers.com. (n.d.). Retrieved November 05, 2016, from http://www.markedbyteachers.com/international-baccalaureate/physics/pendulumwork-out-the-value-of-acceleration-due-to-gravity-g-by-using-the-principle-of-kinematicsof-simple-harmonic-motion-of-a-simple-pendulum.html Roberts, D. (n.d.). The Graphs of Sine and Cosine. Retrieved November 07, 2016, from http://regentsprep.org/Regents/math/algtrig/ATT7/sinusoidal.htm...