2. To estimate the depth of an abandoned well, a piece of stone is dropped from rest into it and a stopwatch is started. The stopwatch is stopped as soon as the stone hits the water surface. Let d be the distance between the well's entrance and the water surface and T be the reading on the stopwatch. (a) Express d in terms of T and g. Check that the expression has equal units on both sides of the equation. [Note: Neglect air resistance.] (b) The reading on the stopwatch is 5.5 s, with an uncertainty AT = 0.5 s. Calculate the measured d and its uncertainty Ad. [Hint: For f = aA¹, its uncertainty is given by |4f| labAb-¹AA).] ≈ (c) You drop another stone and obtain 5.5 s, with the same uncertainty. The average of the two measurements is taken as dnew. What is the new uncertainty Adnew? [Hint: For f = aA + bB, its uncertainty is given by |4f|≈ √a²4A² + b²4B².]
2. To estimate the depth of an abandoned well, a piece of stone is dropped from rest into it and a stopwatch is started. The stopwatch is stopped as soon as the stone hits the water surface. Let d be the distance between the well's entrance and the water surface and T be the reading on the stopwatch. (a) Express d in terms of T and g. Check that the expression has equal units on both sides of the equation. [Note: Neglect air resistance.] (b) The reading on the stopwatch is 5.5 s, with an uncertainty AT = 0.5 s. Calculate the measured d and its uncertainty Ad. [Hint: For f = aA¹, its uncertainty is given by |4f| labAb-¹AA).] ≈ (c) You drop another stone and obtain 5.5 s, with the same uncertainty. The average of the two measurements is taken as dnew. What is the new uncertainty Adnew? [Hint: For f = aA + bB, its uncertainty is given by |4f|≈ √a²4A² + b²4B².]
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![2.
To estimate the depth of an abandoned well, a piece of stone is dropped from rest into it
and a stopwatch is started. The stopwatch is stopped as soon as the stone hits the water
surface. Let d be the distance between the well's entrance and the water surface and T
be the reading on the stopwatch.
(a) Express d in terms of T and g. Check that the expression has equal units on both
sides of the equation. [Note: Neglect air resistance.]
(b) The reading on the stopwatch is 5.5 s, with an uncertainty AT = 0.5 s. Calculate
the measured d and its uncertainty Ad.
[Hint: For f = aA¹, its uncertainty is given by |4f| labA¹-¹AA\.]
≈
(c) You drop another stone and obtain 5.5 s, with the same uncertainty. The average of
the two measurements is taken as dnew. What is the new uncertainty Adnew?
[Hint: For f = aA + bB, its uncertainty is given by |4f|≈ √a²4A² + b² AB².]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8a6376af-076b-46db-ad44-654584889b97%2F0417862c-eef6-46bb-9fb0-6d601a5c6e4c%2F8i3z23_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2.
To estimate the depth of an abandoned well, a piece of stone is dropped from rest into it
and a stopwatch is started. The stopwatch is stopped as soon as the stone hits the water
surface. Let d be the distance between the well's entrance and the water surface and T
be the reading on the stopwatch.
(a) Express d in terms of T and g. Check that the expression has equal units on both
sides of the equation. [Note: Neglect air resistance.]
(b) The reading on the stopwatch is 5.5 s, with an uncertainty AT = 0.5 s. Calculate
the measured d and its uncertainty Ad.
[Hint: For f = aA¹, its uncertainty is given by |4f| labA¹-¹AA\.]
≈
(c) You drop another stone and obtain 5.5 s, with the same uncertainty. The average of
the two measurements is taken as dnew. What is the new uncertainty Adnew?
[Hint: For f = aA + bB, its uncertainty is given by |4f|≈ √a²4A² + b² AB².]
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