2) Show all the steps involved to reduce the equation on the first page to: Ln(x

Question

2)   Show all the steps involved to reduce the equation on the first page to:

Ln(x) = 2Ln(t) + Ln(a/2)

3) What is the slope of the Ln(x) vs Ln(t) graph? How does this compare with the expected slope (determined in the previous question or from looking at the original equation)?

4) Determine the value for %u2018a%u2019 from the intercept of the Ln-Ln graph. %u2018a%u2019 represents the acceleration (m/s^2) down the incline.

5) From the position vs time squared graph, determine the value of %u2018a %u2018. This graph should be linear and you should determine where %u2018a%u2019 is hidden in analyzing this graph.

6) Compare the accelerations from each graph.  Hopefully they are the same.  The acceleration along the incline is related to %u2018g%u2019. Do you think %u2018a%u2019 depends on the incline angle?  If so, you might determine a trigonometric relationship that exists between %u2018a%u2019 and %u2018g%u2019.  See your test for help (or your instructor may explain how to get the relationship). Compare the value for %u2018g%u2019 from your experiment to the accepted value.

The graph of position vs time is not (should not be) linear. Explain why (see the theoretical expression on the first page of this handout). Show all the steps involved to reduce the equation on the first page to: What is the slope of the Ln(x) vs Ln(t) graph? How does this compare with the expected slope (determined in the previous question or from looking at the original equation)? Determine the value for %u2018a%u2019 from the intercept of the Ln-Ln graph. %u2018a%u2019 represents the acceleration (m/s^2) down the incline. From the position vs time squared graph, determine the value of %u2018a %u2018. This graph should be linear and you should determine where %u2018a%u2019 is hidden in analyzing this graph. Compare the accelerations from each graph. Hopefully they are the same. The acceleration along the incline is related to %u2018g%u2019. Do you think %u2018a%u2019 depends on the incline angle? If so, you might determine a trigonometric relationship that exists between %u2018a%u2019 and %u2018g%u2019. See your test for help (or your instructor may explain how to get the relationship). Compare the value for %u2018g%u2019 from your experiment to the accepted value.

Explanation / Answer

1) The graph of position vs time is not (should not be) linear. Explain why (see the theoretical expression on the

first page of this handout).

x = 1/2 a t^2 is not linear because the power of t is not 1, it is 2.

2) Show all the steps involved to reduce the equation on the first page to: Ln(x) = 2Ln(t) + Ln(a/2)

x = 1/2 a t^2

==> Ln(x) = Ln(t^2 (a/2))

==> Ln(x) = Ln(t^2) + Ln(a/2)

==> Ln(x) = 2 Ln(t) + Ln(a/2)

3) What is the slope of the Ln(x) vs Ln(t) graph? How does this compare with the expected slope (determined in the previous question or from looking at the original equation)?

expected slope = 2

from the diagram: 1.2529

4) Determine the value for "a" from the intercept of the Ln-Ln graph. "a" represents the acceleration (m/s2) down the incline.

from the graph ==> Ln(a/2) = 4.2111

==> a/2 = e^(4.2111)

==> a/2 = 67.431

==> a = 135 cm/s^2

==> a = 1.35 m/s2

5) From the position vs time squared graph, determine the value of a. This graph should be linear and you should determine where a is hidden in analyzing this graph.

x = 0.5 a t^2

==> the slope = 0.5 a

==> 26.549 = 0.5 a

==> a = 53.1

==> a = 0.53 m/s2

6) Compare the accelerations from each graph. Hopefully they are the same. The acceleration along the incline is related to g. Do you think

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