![]() ![]() Now the distance fallen in an interval delta_t is equal to the average velocity during the time interval multiplied by delta_t. ![]() We’ll measure distance downwards from the initial position. Now consider plotting distance fallen as a function of time. That’s quite true, but our more complicated approach generalizes easily to the case where there’s air resistance. It has probably occurred to the reader at this point that we’re making heavy weather of a simple problem, we could have just put " =g*B12" in C12 and copied that formula down to give the same result. Then, as with the times, we copy this formula down to C31, filling in the series of velocities corresponding to the times. Taking the initial velocity to be zero, we enter 0 in C12, then in C13 put " =C12 + g*delta_t". This means that in a time interval delta_t, the velocity will increase by g times delta_t. The discretized version of this might be written delta_v = g.delta_t. Excel will copy the formula down, and fill in the values in cells to B31, a list of times delta_t apart.Īs a warm-up exercise, to get practice with using the spreadsheet, we consider the trivial case of zero air resistance. Put the cursor on the small bottom right-hand corner square, the cursor will turn into a cross. Now click on B13 so that it is surrounded by a square, with a small solid square covering the bottom right-hand corner of the frame around B13. When you enter this, 0.0333 should appear in B13. B13 will be the time after the first time interval, so in B13 write " =B12 + delta_t". (We’re leaving some space for later stuff.)ī12 will be the initial time, enter 0. These cells are at the head of our table. In B11 write " time", in C11 " velocity" and in D11 " distance". We also will need the value of g, so write g = in A6, do the usual Insert/Name/Define, etc., let's take g = 10. If we’re trying to reproduce the motion observed on the video, the interval delta_t would be one-thirtieth of a second, so enter 0.0333 in B5. (Maybe later we’ll figure out how to put D t, right now it’s too much trouble.) In A3, write: We plot the position of a falling ball at time intervals delta_t. (I'll write in bold things you should enter in the spreadsheet, although of course you don't need them to be in bold type in the spreadsheet.)įirst, open up a spreadsheet and write Falling Motion under Gravity in cell A1. The plan here is to use Excel to plot velocity against time and distance against time for a falling ball, plotting a sequence of graphs starting with the simplest. ![]()
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