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Chapter 3: Problem 12

An ion in a mass spectrometer follows a semicircular path of radius \(15.2 \mathrm{cm} .\) What are (a) the distance it travels and (b) the magnitude of its displacement?

Short Answer

Expert verified
The distance traveled by the ion is half the circumference of the semicircle calculated in step 1 and the displacement is the diameter of the semicircle as calculated in step 2

Step by step solution

01

Calculate distance

The distance traveled by the ion will be half the circumference of the circle with radius 15.2 cm. The formula for the circumference of a circle is \( C = 2 \pi r \), substituting the given radius \( r = 15.2 cm \), we find \( C = 2 \pi \times 15.2 cm \). As the ion is only covering half of this distance, the actual distance covered by the ion will be \( \frac{1}{2} \times C \).
02

Calculate displacement

Displacement is the shortest distance from the starting point to the end point, and in this case, it's the diameter of the semicircular path. Since diameter of a circle is twice the radius, \( D = 2r \). Substituting the given radius (r=15.2cm), we get \( D = 2 \times 15.2 cm \).
03

Solve the calculations

Substitute the given value of radius into the formulas derived in steps 1 and 2 to get the numeric values of distance traveled and displacement.

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