Diff Eq (Fall 2012)

Projects

Ryan Reza, Lydia Liu, Philip Taffet, Andrei Osypov

Investigate the rate at which a string with a weight on the end unwinds from a spool. To collect the data, we would attach the spool to a smart pulley in order to measure the rotational velocity of the spool. We would perform multiple trials with different weights to decrease error in our measurements. As the string unwinds, the radius of the spool becomes smaller, thereby decreasing the torque that the weight applies on the spool, which in turn affects the acceleration of the spool. Depending on how heavy the string is, we may also see the effect of the mass of the hanging string on the velocity as well, but this may be to small to be measured.

Xavier Gonzalez, Elaine Dong, Meredith Lawrence, Annie Duncan

We're thinking of two ideas:

1. We're going to mark off heights on a bottle (http://imageshack.us/photo/my-images/242/pom.jpg/sr=1 ; it's clear plastic), place it under a running tap, and measure the change of water level (h for height) in centimeters over time (seconds). Acceleration can also be determined and would be interesting to see because of the bottle's shape. Multiple trials.

2. We're going to hang weights on springs and use a PASCO sensor to determine the position, speed, and acceleration of the weight as it oscillates over time (these factors would be affected by both the spring force and the force of gravity). The weight would be pulled down a specific, constant length during each trial. To counter the effect of eventual loss of mechanical energy, we would only measure the first few oscillations of each trial. Multiple trials. We may vary the masses and springs.

Vincent Zhang, Katie Beittenmiller, Maddie Clayton, Scott Hereford

Investigate the rate at which the swing of a pendulum decreases. To collect data we have obtained a string and a weight from Mr. Friedman which we will hang from some sort of fulcrum to create a pendulum. We plan on performing several trials by placing some sort of measuring device behind the pendulum to measure the angle and use a video camera to record the movement of the pendulum as well as the time.

Ben Stein, Jake Peacock, and Brett Gutstein

We're going to investigate the rate at which a cup of water cools. We will use a thermometer to measure the temperature of the water and a stopwatch to measure time.

Aaron Chu, Alezeh Rauf, William Breckwoldt, and Tommy Cowell

We are going to determine the rate at which a car driven at a certain speed will decelerate when put into neutral. While the car is being driven, the speedometer will be recorded in order to approximate the car's speed throughout the process.

Elliot Cheung, John Kim, Jason Shyu, and Anirudh Suresh

We are planning to place an empty liter bottle under a water faucet and measure the change in height of the waterline on the side of the bottle with respect to time. In addition to multiple trials, we might also compare varying bottle shapes and sizes.