A student investigated the relationship between the period and the length of a simple pendulum - Leaving Cert Physics - Question 1 - 2017
Question 1
A student investigated the relationship between the period and the length of a simple pendulum.
The student measured the length l of the pendulum which was then allo... show full transcript
Worked Solution & Example Answer:A student investigated the relationship between the period and the length of a simple pendulum - Leaving Cert Physics - Question 1 - 2017
Step 1
Why did the student use a small angle?
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Answer
The student used a small angle because the formula for the period of a pendulum is only valid for small angles. At larger angles, the motion no longer approximates simple harmonic motion (SHM), leading to inaccuracies in the measured period.
Step 2
How did the student ensure that the pendulum was suspended from a fixed point?
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The student ensured the pendulum was suspended from a fixed point by using a cork or two coins to hold the pendulum and allow it to swing freely.
Step 3
Between which points was the length of the pendulum measured?
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The length of the pendulum was measured from the bottom of the cork or coins to the middle of the bob.
Step 4
Which t value is most accurate? Explain your answer.
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The most accurate t value is 77.3 s. This is because it has the smallest percentage error when compared to the other measured time values.
Step 5
Draw a suitable graph to show the relationship between the length of a pendulum and its period.
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First, divide the t values by 40 and square them. Then, label the axes with 'l (m)' on the x-axis and 'T² (s²)' on the y-axis. Plot the points based on the calculated values and draw a straight line through the origin.
Step 6
Use your graph to calculate g, the acceleration due to gravity.
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To calculate g, determine the slope of the line using two points on the line. Then, substitute the slope into the formula:
T2=g4π2l
Rearranging gives:
g=slope4π2
Substituting the slope will yield the value for g, which is approximately 9.8 m/s².
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