The illustrated shaft has an overall length...

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Question 1 of 205eccef9bbacbc34ba4d452a5

The illustrated shaft has an overall length of 18 inches. If the diameter of "E" = 2.5" and "F" = 3.5", with an indicated radius of "R" = .125" and the length of the tapered section "X" is to be 8"; then the amount of tailstock offset should be _________. See illustration GS-0133.

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🔍 Key Concepts

• Relationship between taper per unit length and tailstock offset when turning between centers • Using similar triangles between the full workpiece length (18") and the tapered length (X = 8") • Remember that taper is usually given as change in diameter, but offset is a change in radius

💭 Think About

• First, compute how much the diameter changes from E to F over the 8-inch tapered section. Then convert that to a change in radius. • Think about how that same angular setup must carry all the way along the full 18-inch length between centers. How does the offset scale when the length increases from 8" to 18"? • Set up a proportion using similar triangles: one triangle for the taper portion (8" long) and one for the full shaft (18" long). Where in that proportion does the offset appear?

✅ Before You Answer

• Confirm the taper amount: D_large − D_small over 8 inches of length. • Convert the taper from diameter difference to radius difference before using it as the “opposite side” in your triangle. • Apply the length ratio (full length / taper length) correctly to that radius difference to find the tailstock offset; your answer must match one of the given choices.

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