Lab partners: Charles, Anthony
Date performed: 09/12/16
In this lab, we are given a non-constant acceleration problem to solve. The analytical, step-by-step process and solution are also given in the manual, but our goal is to solve the problem with the help of excel.
By using excel, we essentially split the problem into its variables by column. Then, all we had to do was write out functions for excel to solve, and get the answer. The analytical approach gets x=248.7.
We first set up a few constants, and below those, we have our variables that we need to fill. We have a column for time, acceleration, average acceleration, change in velocity, velocity, velocity average, change in position, and position. We start with ∆t=1. The time at which we want the position is approximately 19.69 seconds (solved with analytical approach).
Excel sheet with ∆t=1
As one can see, our value of x with this numerical approach is fairly accurate. However, we will vary ∆t to see if it will make a difference. First, we changed it to 0.1 seconds, and then to 0.05 seconds.
On the left: First half of excel sheet with ∆t=0.1
On the right: Second half of excel sheet with ∆t=0.1
Again, the value of x that we get with this variation is still fairly accurate compared to the answer from the analytical approach. In comparison to our values obtained with ∆t=1, the smaller variation of ∆t gives us a more precise value. Having looked over the steps of the analytical approach in the manual, one can tell that it can be very tedious to solve, and there are a lot more chances for errors in the problem solving. With excel, we save a lot of time.
If you wanted to know if your value of ∆t was small enough without knowing the analytical approach's result, you can just look at your values of x. Looking at the excel sheet with ∆t=0.1, you can see that when the x values reach about 248, there are a lot of times at which the answer is that. So to make sure that your time interval is small enough, check to see if you can spot out the value of x at which it repeats (so it stands out). The values of x will begin to decrease after that point. Finally, we will practice one more time using excel to solve a similar problem with different given values.
On the left: First half of excel sheet with M0=7000, b=40, F=-13000
On the right: Second half of excel sheet with M0=7000, b=40, F=-13000
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