Gravity causes the metal balls in today\'s lab to fall from ball release devices

Question

Gravity causes the metal balls in today's lab to fall from ball release devices to target pads. The following mathematical formula theoretically relates d (how far the ball has fallen, in units of meters), t (the time it takes it to fall that far, in units of seconds), and 8 (the gravitational acceleration that causes it to fall, in units of m/s^2): d = -1/2 gt^2 Determine if the following statements are True or False. Residuals have the same units as the dependent variable. According to this formula, a graph of d versus t (i.e. a plot of d as a function of t) would be a straight line. Residuals have the same units as the independent variable. According to this formula, a graph of d versus t^2 (i.e. a plot of d as a function of t^2) would be a straight line. Suppose that the formula above correctly describes the way objects fall, and that the numerical value of the slope of a graph of d versus t^2 from your results in today's lab is -4.05. What are the units for this slope? From this result, find the experimental value for g_exp. Calculate the percent error for this g_exp.

Explanation / Answer

since the value of slope = -4.05

and d = -1/2 * g *t^2

therefore ............-1/2*gexp = -4.05

gexp = 8.1 m/s2

percentage error = (9.8 - 8.1)/ 9.8 * 100% = 17.346%

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