A well-known technique for achieving a very tight fit between two components is to expand by heating and then cool to shrink fit. For example, an aluminum ring of inner radius 5.98 cm needs to be firmly bonded to a cylindrical shaft of radius 6.00 cm measurements are at 20°C). Calculate the minimum temperature to which the aluminum ring needs to be heated before it can be slipped over the shaft for fitting.Coefficient of linear expansion for Al = 24 × 10⁻⁶/K.)

Question

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We need to find the minimum temperature to which the aluminum ring needs to be heated before it can be slipped over the shaft for fitting. Let the required temperature be T.

The aluminum ring needs to expand by a certain amount to fit over the cylindrical shaft. This expansion can be calculated using the formula:

ΔL = αLΔT

where ΔL is the change in length, α is the coefficient of linear expansion, L is the original length, and ΔT is the change in temperature.

In this case, the aluminum ring needs to expand by 0.02 cm (the difference between the inner radius of the ring and the radius of the shaft) to fit over the shaft. Therefore,

0.02 cm = (24 × 10^-6 K^-1) (5.98 cm) ΔT

ΔT = 20.08 K

This is the minimum temperature to which the aluminum ring needs to be heated. Adding this to the initial temperature of 20°C gives a final temperature of:

Tfinal = 20°C + 20.08 K = 160.08°C

Therefore, the answer is D) 160°C.

A Well-Known Technique for Achieving a Very Tight Fit Between