AP Physics Lab 10

Ryan Partain, Trey Seabrooke, Tyler Kolby, Daniel Hanna

Mechanical Wave Model Lab

Objective: to determine the graphical and mathematical relationship between velocity and amplitude, velocity and length of the pulse, velocity and distance, and velocity and force.

Picture of Apparatus:

Materials:

• Distance measurement device
• Spring of length greater than ~1 meter
• Timer
• Force measuring device

Procedure:

To begin, obtain all materials listed above. Lay the spring flat on the ground. Straighten the spring but do not stretch the spring, and record the length of the spring in a straight line.

First record data for the relationship of velocity vs. amplitude. Position the spring at a slightly stretched position and record the length. Two group members are holding the stretched spring at their fixed positions. One group member places his or her foot next to the spring ~1 foot from their end of the spring. The portion of the spring in between the group members foot and the fixed end will now be used to create the amplitude for the pulse. Keep the foot at the same position and change the distance you pull the middle portion of the spring. Record the time it takes for the pulse to go to the other end and return.

Next record data for velocity vs. pulse length. The same setup is used as previously. For this experiment, keep the amplitude constant and move the group members foot at various distances. Record the distances and corresponding time for the pulse to return.

Next, to record velocity vs. distance hold the spring length constant and setup the same as before. Instead of timing the pulse from start to return, now time the pulse from start to half length, start to full length, start to full and one half length, and start two two full lengths to record any change in velocity.

Finally use a force measuring device to determine the force on the spring by the fixed end. Move the spring to get various force values and record the time for the pulse from start to return to determine velocity for each value. Keep the amplitude and pulse length constant.

Data Table:

Graphs:

Velocity vs. Amplitude

Velocity vs. Pulse Length

Velocity vs. Distance

Velocity vs. Force

Conclusion: (no relationship in any except V vs. F.  Despite what appears to be a linear relationship, the data set accidentally followed that general trend, but the numbers were scattered.  Due to experimental error, the data appears to have a relationship despite having none)

In the graph of V vs. F, the relationship is parabolic; therefore V is squared to linearize making the graph V^2 vs. F. Based on this graph we see the relationship V^2=( m/kg)F.

Sources of error include difficulty in pinpointing the exact time one wavelength has traveled the entire length of the spring, and difficulty in keeping the spring in the exact same position throughout the experimental trials. The procedure could be improved if there were more stable fixed positions at the ends of the spring. It could also be improved if the pulses were more accurately recorded. For example, using ones foot works but contributes in error of the experiment due to the width of the foot in contact with the spring.

AP Physics Lab 9

Ryan Partain, Tyler Kolby, Daniel Hanna, Trey Seabrooke

Oscillating Particle Lab

Objective: To determine the graphical and mathematical relationships among mass, amplitude, spring constant, and period for a bouncing mass hanging by a spring.

Picture of Apparatus:

Materials:

• Spring
• Stand w/ latch
• Hanging mass
• 10 Washers
• Timer
• Ruler
• Electronic Balance

Procedure:

Obtain all materials listed above and set up the materials to resemble the picture of the apparatus above.

Begin data collection for the various quantities listed in the objective.

To determine force vs. height, set up the apparatus like pictured, and allow the hanging mass to hang freely without oscillation. Record the distance the spring is stretched. Repeat this for 8-10 different masses.

To determine mass vs. period, set up the apparatus like pictures, and allow the hanging mass to hang freely, then stretch the spring to allow oscillation. Keep the amplitude, or distance you stretch the spring constant and record the time of 10 oscillations to find the period for 8-10 different masses.

To determine amplitude vs. period, keep the hanging mass constant. Stretch the spring and record the time for 10 oscillations. Stretch the spring every half centimeter from .5cm to 6cm.

To determine period vs. spring constant, calculate your group's k value from the force vs. height graph and then combine your k with every other group to get the values for the graph.

Data Table:

Graphs:

Force vs. Height

Period vs. Mass

Period^2 vs. Mass

Period vs. Amplitude

Period vs. Spring Constant

Period vs. 1/Spring Constant

Period^2 vs. 1/Spring Constant

Conclusion: For the graph of weight vs. extension, the relationship is linear and the slope is the k value or spring constant.

For the graph of period vs. mass, the relationship is parabolic. The period is squared to linearize this graph.

For the graph of period vs. amplitude, there is no relationship.

For the graph of period vs. spring constant, the relationship is inverse. The inverse of the spring constant is taken and the relationship is parabolic. The period is then squared to linearize the graph.

Based on the relationships we see in our graphs, we see the relationship that T(period)=2π(the square root of (m/k))

When experimenting, the timekeeping is a source of error because one person has to communicate to the other that the particle has oscillated ten times (in our case) in order for him to stop the time. Another source of error is that it is difficult to pinpoint exactly when the particle reaches the end of its period making timing more inconsistent and slightly less accurate.Using a motion detector to track the particle would be more effective and accurate in this experiment because it can keep accurate time and also knows exactly when ten periods have elapsed when it's data is graphed.