Ph105free Fall Exercise

PH105Free Fall Exercise

A ball is thrown straight up from the edge of a building 20 m tall with an initial velocity of 13 m/s and lands at the base of the building. Use Excel to plot the position and velocity of the ball as a function of time.

Procedure

Set up your spreadsheet as shown on the next page. Begin by entering the constants describing the motion into cells.

Now set up a column of times ranging from 0 to 4 sec in intervals of 0.2 sec. Enter 0 and 0.2 in the first two cells of the time column. To extend the range of times, highlight the first two cells, then click on the lower right corner of the highlighted region and drag down until the series reaches 4.

You can “name” your constants for easier reference (y0, v0, g) in the following way. Suppose, for example, the number 9.8 is in cell B8. If you click on this cell then B8 will be displayed in the Name Box in the upper left corner of the screen. If you then click on the Name Box you can enter the letter g in place of B8. Then whenever you want to refer to the value of g given in cell B8, you only need to type the letter g. Likewise, you can name all the times in the time column by highlighting the entire column of times and entering t in the Name Cell.

Now enter the formulas for v and y in the first cells of the 2nd and 3rd columns. A formula must begin with = or +. Thus, for v you enter +v0-g*t and for y enter +y0+v0*t-1/2*g*t^2. You can then copy these formulas into the other cells in the v and y column by clicking and dragging on the lower right corner of the cell.

Now plot on a single graph v and y versus t. Highlight all three columns (including the headings), click on the Chart Wizard icon, and proceed by following your nose.

Calculations:

1) Refer to your graph and to your table of numbers to find the:

a) maximum elevation of the ball

b) time for the ball to reach its maximum elevation

c) total time for the ball to reach the ground

d) velocity of the ball just before it strikes the ground.

2)Determine the above analytically and compare with your Excel answers.

3)Now assume that the ball is thrown down instead of up with the same speed and repeat the above calculations.

Questions:

1) Are the final velocities the same if thrown up or thrown down with the same speed? Is this what you would expect?

2) When the ball is thrown up, what is its acceleration at the top of the trajectory?

3) Compare the slopes of the velocity versus time curves when thrown up and when thrown down. Are they the same? What does this mean?

4) Turn in the results of the numerical and analytical calculations (both thrown up and thrown down) and the answers to the questions. Each team turns in one set of results, and all team members sign the hand-in.