A steel sphere sits on top of an aluminum ring.The steel sphere (a = 1.10 x 10^-5/C $\degree$)has a diameter of 4.000 0 cm at 0 $\degree$C.The aluminum ring (a = 2.40 x 10^-5/C $\degree$)has an inside diameter of 3.994 0 cm at 0 $\degree$C.Closest to which temperature given will the sphere just fall through the ring?

Question

Quizplus · Accepted Answer

The sphere will fall through the ring when the inside diameter of the ring is equal to or greater than the diameter of the sphere, taking into account the coefficients of thermal expansion for each material. To calculate the temperature at which this occurs, we can use the formula:

ΔT = (D₂ - D₁)/(α₂ - α₁)

where ΔT is the temperature difference between the two objects, D₁ and D₂ are the diameters of the sphere and ring respectively, and α₁ and α₂ are the coefficients of thermal expansion for the steel and aluminum.

Plugging in the given values, we get:

ΔT = (4.0000 - 3.9940)/(1.10 x 10^-5 - 2.40 x 10^-5) = 116.67°C

Therefore, the sphere will just fall through the ring at a temperature of 116°C or higher. The closest option is C) 116°C.

A Steel Sphere Sits on Top of an Aluminum Ring °\degree°

A Steel Sphere Sits on Top of an Aluminum Ring $\degree$