Physics I Lab Manual 2011 91

# Physics I Lab Manual 2011 91 - the following equations into...

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EXPERIMENT 13. NUMERICAL ANALYSIS for air at STP. The constant (0.22) has units of kg/m 3 so that when MKS units are used for diameter and velocity the resulting force is in Newtons. When the sphere reaches its terminal velocity v T , the net force on the sphere is zero, so from Newtons second law we have 0 . 22 kg m 3 d 2 v 2 - mg = 0 . If a baseball is at hand, measure the diameter and mass of the baseball and compute its terminal velocity. If a baseball is not available, assume its mass is 0.14 kg and its diameter is 0.072 m. 2. Free Fall from Rest . A baseball is dropped from rest. Use the spreadsheet program Excel to evaluate the motion over a large number of small time steps. Enter the n =0 row of initial values. Define the n =1 elements as equations using previous values and constants. Then use the fill down command (in the Edit menu) to repeat the calculations for as long and as far as you want the baseball to fall. Program each of
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Unformatted text preview: the following equations into the following columns, using references to cells containing the value for Δ t , v T , g , and m . You can use a time step of Δ t = 0 . 1 v T /g which is one tenth of a characteristic time v T /g describing how long before the eﬀects of drag become signiﬁcant. In step 3 we will investigate the signiﬁcance of this value. The ﬁrst couple of rows in your spreadsheet should look similar to this Figure 13.2: Example of the ﬁrst row of the spreadsheet where the values mg and g reference the cells where these constants have been deﬁned. The value of successive cells in the n th row of data should be calculated from the following formulas: (a) Index: n (b) Time: t n = t n-1 + Δ t (c) Exact solution to velocity without a drag force acting: v n =-gt n (d) Exact solution to distance without a drag force acting: y n =-1 2 gt 2 n 81...
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