PhysicsLAB: Test Scenario: Position vs Time

This test scenario was based on the APB free response question 2006B1.

Refer to the following information for the next question.

A group of students wish to determine experimentally the acceleration g due to gravity has an apparatus that holds a small steel sphere above a recording plate, as shown above. When the sphere is released, a timer automatically begins recording the time of fall. The timer automatically stops when the sphere strikes the recording plate.

The students measure the time of fall for different values of the distance D shown above and record their data in the table below. These data points are then plotted on the graph.

(a) On the grid above, sketch the smooth curve that best represents the student's data

Refer to the following information for the next seven questions.

The students must now use this data for distance D and time t to produce a second graph from which the acceleration g due to gravity can be determined.

(b) What quantities should the students graph in order to produce a linear relationship between the two quantities? Fill in one of the blank rows with the required adjusted data.

(c) On the grid below, plot the data points for the quantities you have identified in part (b), and sketch the best straight-line fit to the points. Label your axes and show the scale that you have chosen for the graph.

(d) Calculate the slope of your graph in part (c). Show all steps.

(e) What is the slope’s relationship to g, the acceleration due to gravity?

(f) What is the group’s experimental value for g, the acceleration due to gravity?

(g) What was the accuracy of the group’s value for g?

(h) State one way in which the student could improve the accuracy of the results if the experiment were to be performed again. Explain why this would improve the accuracy.