9-Mar-2015 Non-Constant Acceleration

Purpose
The purpose of this lab was to practice solving problems with a non-constant acceleration which would require calculus. However we find out that the integral needed to solve this problem becomes too difficult to solve; therefore, we used excel to help us solve the non-constant acceleration problem.

Experiment
For this experiment we are trying to solve a problem with a non-constant acceleration where an elephant on a frictionless roller skate going down a hill. Then the elephant is slowed down when it hits the bottom of a hill with a rocket slowing down the elephant, and the mass varying since the rocket gets lighter as the fuel is being used up.

Since we know that F=ma then when we solve for acceleration we get a=F/m, but since we know that the mass is varying this therefore means that the acceleration is non-constant. To solve this problem would require the use of integrating the acceleration function, then that would give us a velocity function. From the velocity function we can find out how long it takes for the elephant to stop, this is done by setting the velocity function to zero.

We then use the velocity function to find the displacement by integrating it like we did for the acceleration function. We then take the time found for the velocity and sub it into the displacement to find out how far the elephant would go before it stops.

However this method was rather tedious therefore we decided to use excel showing that as long as we understand how to set up the problem and how each part of the problem works the problem can be solved much faster with a program such as excel. The columns entered into excel are time, acceleration, average acceleration, change in velocity, speed, change in position and position. For time it is increasing by increments of .01 seconds, acceleration is calculated by using the formula found by using the force and mass earlier, the average acceleration is the acceleration plus the current acceleration at the time being calculated and divided by two, the change in velocity is calculated by taking the average velocity multiplied by the change in time, speed is is calculated by adding the change in velocity plus the initial velocity, the change in position is calculated by taking the average speed times the change in time, and the position is calculated by taking the initial position and adding the change in position to it. We also put at the top a specified column for time so that we can alter is as we go if we need the interval to be either larger or smaller

After all the formula have been entered into the spread sheet we then drag it down until we the velocity reaches zero and then that would also tell us how far the elephant went before it came to a stop. In this case the elephant stopped in about 19.7 seconds and went about 248.6981 meters before coming to a stop. We also changed the time interval to .05 because the previous .01 was too small.