To determine the relationship between the period of a pendulum and the amplitude, mass, and length of the pendulum system. Then once that is accomplished, recommend a length for a pendulum system which creates a period of 1.875 seconds.
Vernier photogate and
2 support stands and clamps
masses of 100, 200, and
300 g with hooks
- Place a support stand on the edge of a table and secure it to the table with a clamp or by placing a heavy mass on the base. Tie two strings of equal length to the 200 g mass. Attach the strings about 15 cm apart to a horizontal rod extended from the support stand. The pendulum should hang over the edge of the table, as shown on the previous page. This arrangement will let the mass swing only along a line, and will prevent the mass from striking the photogate. The length of the pendulum is the distance from the point on the rod halfway between the strings to the center of the mass. The pendulum length should be at least 1 m (you do not need an exact measurement now).
- Attach the photogate to a second support stand. Place the support stand on the floor and position the photogate so that the mass blocks the photogate while hanging straight down. Connect the photogate to the LabPro and turn it on.
- Observe the reading on the screen. Temporarily hold the mass out of the center of the photogate. Block the photogate with your hand; note that the photogate is shown as blocked. When you remove your hand, the display should change to unblocked. Now, set the time mode.
- Select PENDULUM from the TIMING MODES menu.
- Now you can perform a trial measurement of the period of your pendulum.
Hold the mass displaced about 10° from vertical and release. (For a pendulum that is 100 cm long, that corresponds to pulling the mass about 15 cm to the side.) After the mass has passed through the photogate, the average period begins to display on the calculator screen.
Part I Amplitude
- Measure the period for five different amplitudes. Choose a wide range of amplitudes, from just barely enough to unblock the photogate, to about 30°. For each trial, use the protractor to measure the amplitude before releasing the mass. Collect the data and record it in a data table like the one shown for Part I in the Data Tables section.
Part II Length
- Now you will measure the effect of changing pendulum length on the period. Use a constant mass and consistent amplitude of 10° for each trial. Vary the pendulum length in steps of 10 cm, from 100 cm down to 50 cm. Be sure to measure the pendulum length from the rod to the center of the mass. You may have to raise the photogate as the length changes. Record your data in a data table like the one shown for Part II in the Data Tables section.
Part III Mass
- Use three different masses to determine if the period is affected by changing the mass. Be sure to attach the masses so that the center of mass remains unchanged; otherwise, you are also affecting the length. For each mass trial, keep the length of the pendulum the same and use constant amplitude of 10°. Repeat step 8 for each trial. Record your data in a data table like the one shown for Part III in the Data Tables section.
Data Analysis: Using the Period vs Square Root graph to find a best fit line which my calculator solved to be .4.
To solve for a period of 1.875
to derive the equation above to get:
L = .87m
After looking at all of the graphs and data it can be concluded that mass and amplitude do no have an affect on the period of a pendulum in a system. So from the pivot point to the mass the distance is .87.
Purpose: Is to find and determine if energy within the pendulum system is conserved as it swings from left to right.
Equipment: Direct Measurement Video
The procedure was to open and look at the video. Then to gain data points by pausing and playing the video so that there was a sufficient amount of data to construct an equation. Then using these data points and kinematic equations, we deduced the velocity of the pendulum after each swing to see if there was a notable change in energy. Then finally we calculated the percent difference between the theoretical velocity that the pendulum should have and the calculated velocity.
Data & Data Analysis
Here is the video in which the data was derived:
Conclusion: In conclusion, using the data and examining the percent difference it is obvious that with each swing a slight yet palpable amount of energy was taken out of the pendulum system. This was interpreted because the first trial caused a 3.56% decrease from theoretical to measured velocity and this difference increased even more to 6.13% when the next trial occurred. So it can be concluded that energy is conserved as the pendulum swings, even though there is a percent difference of energy taken from the swing of the pendulum, this energy is most likely caused by the friction in the top of the rope and some slight air resistance.
The purpose of this lab was to use experimentation to verify that Newtons Second Law is correct and that impulse is equal to the change in momentum.
LabQuest Handheld Unit
Vernier Force Detector
Pascal Cart & Track
Mass Units (500g)
First we set the Pascal cart on the track. Then after we connected the LabQuest to the motion detector and the Vernier Force Sensor, we applied a force to the cart to make it move towards the motion sensor. And then collected the data onto the LabQuest unit and plugged it into the computer for data analysis.
Data & Data Analysis
Using the data above, it can be concluded that our experiment was successful in determining that momentum is equal to Impulse. It also proves that to no surprise Newton’s Second Law is true. Some points of error include, human error, motion detector calibration, and how level the track was. These errors may have caused some inconstancies within the data points but altogether they were within reason.
Purpose: The purpose of this lab was to understand and analyze the motion of a projectile in a 2d environment.
The procedure was to set up the meter stick, and the camera, and the we tossed the ball while the camera was recording to get our data. Then we analyzed the data using the program called Tracker to compile the data points into a graph that could be interpreted.
Conclusion: In conclusion, using the graphs to analyze velocity in the vertical and horizontal directions, I was able to determine that since there is no accelerating force in the vertical direction there is no change in velocity as the ball moves in that direction providing there is not air resistance. While in the horizontal direction, velocity increases as the force of gravity accelerates it downward.
In this lab we dropped a ball from a height and recorded the data as it fell. It was obvious from the curve of the graph that the velocity was not constant during the fall. I have concluded that the force of gravity caused the ball to accelerate, therefore it increased in speed and velocity.
In this measurement lab we measured the volume of a block of wood, a cylinder, and the classroom. We also determined the thickness of a piece of paper. We used a Vernier caliper to determine the length, width, and height of the block of wood and cylinder, and the thickness of the paper. Then we used a meter stick to measure the length, width, and height of the classroom. Once we calculated the volulme of the items using the LxWxH formula as well as the πr²h formula
Wood block: L:85.7 W:77.6 H:18.8
Cylinder: r:6mm h:105.4
Classroom: L:1077cm W:815cm H:382
Volume: 3,354,581,000 cm³
Tool: Meter Stick
Sources of error: The fact that all of the items measured are not 100% smooth and form fitting, makes our calculations slightly different than what a perfect block, cylinder, or classroom is.