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Calculate the value for g for 10 oscillations and then for 20 oscillations Compare your 2 results with the expected result of g= 9.80 m/sec Explain why we used 10 and 20 oscillations to determine the acceleration due to gravity.

Calculate the value for g for 10 oscillations and then for 20 oscillations Compare your 2 results with the expected result of g= 9.80 m/sec Explain why we used 10 and 20 oscillations to determine the acceleration due to gravity.

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**Experiment 1:** Tie the string to the heavy object. Tie the loose end of the string to a hook, a bar, or any other sturdy object you can suspend it from. First, let the object hang motionless from the suspended string. Measure the distance from the point where it is suspended to the middle of the heavy object (essentially the length of the string – L). Now pull the heavy object sideways a few inches while keeping the string straight. Let go and let the object oscillate back and forth 10 times. Measure how long it takes for 10 complete oscillations. Then repeat with 20 oscillations. Use the following equation to determine g (the acceleration due to gravity). The time for 1 oscillation is called the period (T). \[ T = 2 \pi \sqrt{\frac{L}{g}} \] Calculate the value for g for 10 oscillations and then for 20 oscillations. Compare your 2 results with the expected result of g = 9.80 m/sec². Explain why we used 10 and 20 oscillations to determine the acceleration due to gravity.
Transcribed Image Text:**Experiment 1:** Tie the string to the heavy object. Tie the loose end of the string to a hook, a bar, or any other sturdy object you can suspend it from. First, let the object hang motionless from the suspended string. Measure the distance from the point where it is suspended to the middle of the heavy object (essentially the length of the string – L). Now pull the heavy object sideways a few inches while keeping the string straight. Let go and let the object oscillate back and forth 10 times. Measure how long it takes for 10 complete oscillations. Then repeat with 20 oscillations. Use the following equation to determine g (the acceleration due to gravity). The time for 1 oscillation is called the period (T). \[ T = 2 \pi \sqrt{\frac{L}{g}} \] Calculate the value for g for 10 oscillations and then for 20 oscillations. Compare your 2 results with the expected result of g = 9.80 m/sec². Explain why we used 10 and 20 oscillations to determine the acceleration due to gravity.
**Experiment 1** **Time (sec):** - Oscillate 10 times = 13.61 - Oscillate 20 times = 27.06 Length of string = 18 inches --- \[ T = 2\pi \sqrt{\frac{L}{g}} \] - L = length - g = gravity This formula represents the period (T) of a pendulum, where the period is the time it takes for one complete cycle of oscillation. The length (L) is in inches, and gravity (g) is the acceleration due to gravity.
Transcribed Image Text:**Experiment 1** **Time (sec):** - Oscillate 10 times = 13.61 - Oscillate 20 times = 27.06 Length of string = 18 inches --- \[ T = 2\pi \sqrt{\frac{L}{g}} \] - L = length - g = gravity This formula represents the period (T) of a pendulum, where the period is the time it takes for one complete cycle of oscillation. The length (L) is in inches, and gravity (g) is the acceleration due to gravity.
Expert Solution
Step 1

Given,

length of the string is, L= 18 in = 0.4572m

the time is taken to complete 10 oscillations is, t1=13.61s

And the time is taken to complete 20 oscillations is, t2=27.06s

 

So, the time period for 10 oscillation is,

T1=13.61s10=1.361s

And the time period for 20 oscillation is,

T2=27.06s20=1.353s

 

And time period can be written as,

T=2πLg

So, for the 10 oscillations, acceleration due to gravity will be,

g1=L2πT12=0.4572m×2π1.361s2=9.744m/s2

Similarly, for the 20 oscillations, acceleration due to gravity will be,

g2=L2πT22=0.4572m×2π1.353s2=9.86m/s2

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