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Concept explainers
(a)
To Prove:The experimental magnitude of the free-fall acceleration is given by
(a)
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Explanation of Solution
Introduction:
The distance
Here,
The marble is dropped from a point at a negligible distance from the first light gate. Therefore, the distance travelled by the marble in the measured time interval
Therefore, substitute 0 for
Simplify for
Conclusion:
Thus, it is proved that the experimental value of the free fall acceleration is given by the expression,
(b)
The expected value of
(b)
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Answer to Problem 113P
The expected value of the time
Explanation of Solution
Given:
The position of the first light gate (at the edge of the table)measured from the floor
The position of the second light gate when measured from the floor
The standard value of the free-fall acceleration
Formula used:
The time taken for the marble to fall between the two light gates is given from equation (2) and is written as
Where,
Calculation:
From equations (3) and (4)
Substitute the given values of variables in equation (5).
Conclusion:
Thus, the expected value of the time
(c)
The value of the
(c)
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Answer to Problem 113P
The value of the free fall acceleration determined in the current experimental setup would be
Explanation of Solution
Given:
The height of the edge of the table from the floor
The position of the first light gate (at the edge of the table) measured from the table
The position of the second light gate when measured from the table
The standard value of the free-fall acceleration
Formula used:
The marble is dropped from the edge of the table with a velocity
Assume the origin to be located on the table and the initial velocity is zero.
The time
Here,
The value of the free fall acceleration that would be obtained from this experiment (with errors) is given by the following expression
The percentage difference between the calculated and the standard values of the free fall acceleration is given by
Calculation:
Calculate the speed of the marble when it passes through the first light gate by substituting the values of the variables in equation (6).
Calculate the distance between the light gates using equation (8).
Substitute the values of the variables (calculated and given) in equation (7) and write a quadratic equation in
Solve for
Taking the positive root alone
The person performing the experiment does not take into account the difference in the positioning of the light gates. Hence, the value of free fall acceleration
Substitute the values of variables in equation (9) and calculate the experimental value of the free fall acceleration.
Calculate the percentage difference between the measured value and the standard value is found using equation (10).
Conclusion:
Thus, the value of the free fall acceleration determined in the current experimental setup would be
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Chapter 2 Solutions
Physics for Scientists and Engineers
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