Need Help With Physics Absolute Uncertaintes

Isaac Physics has two questions which appear contradictory.

The first:

You measure the time taken for a pendulum to complete 20 full swings, using an electronic timer accurate to the nearest 0.1s. You then divide your answer by 20 to get the time for just 1 swing. What is the absolute uncertainty on your value for just 1 swing?

Apparently the answer is 0.003s, which makes sense. This is presumably because the absolute uncertainty in 20 full swings is 0.05. Therefore, the uncertainty in 1 swing would be 0.05/20=0.003 (1 s.f.).

The second:

A later question then says "Using a micrometer that reads the diameter of a wire to the nearest 0.01mm, you obtain the results: 3.46mm, 3.55mm, 3.42mm. What is the absolute uncertainty in the radius of the wire?"

Apparently the answer is 0.065mm. I'm assuming they have arrived at this answer because the range of values is 3.55-3.42=0.13. You then divide this answer by 2 to find the uncertainty, which is 0.13/2=0.065mm. Although, according to the previous question, you would then have to divide this by 2, because the micrometer measures diameter, and it asks for the uncertainty in the radius.

These answers appear contradictory, and it is really confusing me. Please explain the answers to both of these questions, and why in the first one you are supposed to divide by 20, but in the second one you are not supposed to divide by 2. I know this is a long read, but any help would be very appreciated as my exam is next Tuesday. Thank you!

Reply 1

lmg1

7

Original post by Rubberbandit

Isaac Physics has two questions which appear contradictory.

The first:

You measure the time taken for a pendulum to complete 20 full swings, using an electronic timer accurate to the nearest 0.1s. You then divide your answer by 20 to get the time for just 1 swing. What is the absolute uncertainty on your value for just 1 swing?

Apparently the answer is 0.003s, which makes sense. This is presumably because the absolute uncertainty in 20 full swings is 0.05. Therefore, the uncertainty in 1 swing would be 0.05/20=0.003 (1 s.f.).

The second:

A later question then says "Using a micrometer that reads the diameter of a wire to the nearest 0.01mm, you obtain the results: 3.46mm, 3.55mm, 3.42mm. What is the absolute uncertainty in the radius of the wire?"

Apparently the answer is 0.065mm. I'm assuming they have arrived at this answer because the range of values is 3.55-3.42=0.13. You then divide this answer by 2 to find the uncertainty, which is 0.13/2=0.065mm. Although, according to the previous question, you would then have to divide this by 2, because the micrometer measures diameter, and it asks for the uncertainty in the radius.

These answers appear contradictory, and it is really confusing me. Please explain the answers to both of these questions, and why in the first one you are supposed to divide by 20, but in the second one you are not supposed to divide by 2. I know this is a long read, but any help would be very appreciated as my exam is next Tuesday. Thank you!

To find the uncertainty you usually take uncertainty/actual result x 100. In this case the uncertainty would be 1/2(range). That is the way I found uncertainties on the physics practical relating to questions on oscillations

Reply 2

lmg1

7

Original post by Rubberbandit

Isaac Physics has two questions which appear contradictory.

The first:

You measure the time taken for a pendulum to complete 20 full swings, using an electronic timer accurate to the nearest 0.1s. You then divide your answer by 20 to get the time for just 1 swing. What is the absolute uncertainty on your value for just 1 swing?

Apparently the answer is 0.003s, which makes sense. This is presumably because the absolute uncertainty in 20 full swings is 0.05. Therefore, the uncertainty in 1 swing would be 0.05/20=0.003 (1 s.f.).

The second:

A later question then says "Using a micrometer that reads the diameter of a wire to the nearest 0.01mm, you obtain the results: 3.46mm, 3.55mm, 3.42mm. What is the absolute uncertainty in the radius of the wire?"

Apparently the answer is 0.065mm. I'm assuming they have arrived at this answer because the range of values is 3.55-3.42=0.13. You then divide this answer by 2 to find the uncertainty, which is 0.13/2=0.065mm. Although, according to the previous question, you would then have to divide this by 2, because the micrometer measures diameter, and it asks for the uncertainty in the radius.

These answers appear contradictory, and it is really confusing me. Please explain the answers to both of these questions, and why in the first one you are supposed to divide by 20, but in the second one you are not supposed to divide by 2. I know this is a long read, but any help would be very appreciated as my exam is next Tuesday. Thank you!