Problem

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Problem 52 Hard Difficulty

Hold a pencil in front of your eye at a position where its blunt end just blocks out the Moon (Fig. 15$)$ . Make appropriate measurements to estimate the diameter of the Moon, given that the Earth-Moon distance is $3.8 \times 10^{5} \mathrm{km}$ .

Answer

3500 $\mathrm{km}$

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Physics 101 Mechanics

Physics for Scientists and Engineers with Modern Physics

Chapter 1

Introduction, Measurement, Estimating

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Christina K.

Rutgers, The State University of New Jersey

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Video Transcript

Okay. Our question says Hold a pencil in front of your eye at a position where it's blunt. End just blocks out the moon. Figure 15 Make appropriate measurements to estimate ah, the diameter of the moon Given that the Earth moon distance is 3.8 times 10 to the fifth kilometres. So if you're blocking out the the moon with the pencil, that means you're gonna be able to use the ratio of the distance. The pencil is away from your arm relative to the diameter of the pencils. Blunt end Ah and you, Khun, relate that ratio to the distance. The moon is away from your from your eye and the diameter of the moon. Okay, so here I wrote out what we were given. We have decent p which is the distance or I'm sorry, the diameter of the pencil, 0.7 centimeters or about 0.7 meters. Since you have write this out one meter because people do 100 centimetres so you could just move the decimal place over two and you have 0.7 meters. We also have that the distance the pencil is away from the eye, which I write as A s A P is equal to 0.75 meters. We also are told that the distance the moon is away from the individual which is s of Emma's 3.8 times 10 to the five meters or I'm sorry, that is 3.8 times 10 to the five kilometres. So I need to write Write this as K M Kilometers. Okay. And so the question then is what is the diameter of the moon By using the by using the following ratio Since the moon is being completely covered by the blunt in the deepest pencil, we have the ratio of the diameter of the pencil relative to the distance. The pencil is away is equal to the ratio. All of the diameter of the moon relative to the distance the moon is away, which we write as s o them. Okay, well, let's go ahead and solve this equation for, uh the diameter of the moon because that's what we're trying to find. We find that the diameter of the moon is equal to three show Lisa P divided by S a p on DH that is going to be multiplied by seven. Okay. All right, let's go ahead and plug in all the values that we have. Decent PR. 0.7 meters. Okay. It's important for this ratio of decent P to S and P B. And the same units of measurements that they cancel out and s a p a 0.75 meters. Okay. And then we're going to multiply this by 3.8 times 10 to the five commoners. So our solution will also be in kilometers. Okay? And if you carry out this calculation, this comes out to be about 3,000 500 kilometers diameter the mitt. Come here, owners. Oxygen is our solution.

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