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Chapter 1: Problem 95

The circumference of the Cornell Electron Storage Ring is \(768.4 \mathrm{~m}\). Express the diameter in inches, to the proper number of significant figures.

Short Answer

Expert verified
Answer: The diameter of the Cornell Electron Storage Ring in inches is 9628 inches.

Step by step solution

01

Find the diameter in meters

Using the formula for the circumference of a circle: \(C = \pi d\), where \(C\) is the circumference and \(d\) is the diameter. We are given \(C = 768.4 \mathrm{~m}\). To find the diameter, we can rearrange the formula as follows: \(d = \frac{C}{\pi}\) Substitute the given circumference value, and calculate the diameter in meters: \(d = \frac{768.4}{\pi} \approx 244.6 \mathrm{~m}\)
02

Convert the diameter to inches

Now that we have the diameter in meters, we need to convert it to inches. We will use the conversion factor: \(1\mathrm{~m} = 39.37\mathrm{~in}\). Multiply the diameter in meters by the conversion factor to get the diameter in inches: \(d_{in} = 244.6 \times 39.37 \approx 9628 \mathrm{~in}\)
03

Determine the correct number of significant figures

The given circumference has four significant figures, so our final answer should also have four significant figures. The calculated diameter in inches is \(9628\mathrm{~in}\), which already has the proper number of significant figures. The diameter of the Cornell Electron Storage Ring in inches, to the proper number of significant figures, is \(9628\mathrm{~in}\).

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Most popular questions from this chapter

A flea hops in a straight path along a meter stick, starting at \(0.7 \mathrm{~cm}\) and making successive jumps, which are measured to be \(3.2 \mathrm{~cm}, 6.5 \mathrm{~cm}, 8.3 \mathrm{~cm}, 10.0 \mathrm{~cm}, 11.5 \mathrm{~cm}\) and \(15.5 \mathrm{~cm} .\) Express the answers to the following questions in scientific notation, with units of meters and an appropriate number of significant figures. What is the total distance covered by the flea in these six hops? What is the average distance covered by the flea in a single hop?

The Earth's orbit has a radius of \(1.5 \cdot 10^{11} \mathrm{~m},\) and that of Mercury has a radius of \(4.6 \cdot 10^{10} \mathrm{~m} .\) Consider these orbits to be perfect circles (though in reality they are ellipses with slight eccentricity). Write down the direction and length of a vector from Earth to Mercury (take the direction from Earth to Sun to be \(0^{\circ}\) ) when Mercury is at the maximum angular separation in the sky relative to the Sun.

A position vector has a length of \(40.0 \mathrm{~m}\) and is at an angle of \(57.0^{\circ}\) above the \(x\) -axis. Find the vector's components.

The force \(F\) a spring exerts on you is directly proportional to the distance \(x\) you stretch it beyond its resting length. Suppose that when you stretch a spring \(8.00 \mathrm{~cm},\) it exerts a 200. N force on you. How much force will it exert on you if you stretch it \(40.0 \mathrm{~cm} ?\)

Is it possible to add three equal-length vectors and obtain a vector sum of zero? If so, sketch the arrangement of the three vectors. If not, explain why not.
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