Homework Help: Physics

Posted by Steve on Friday, March 25, 2011 at 10:47pm.

How do i get the answer
A steel ball of diameter Lb = 4.196 cm is placed on a hole of diameter Lh = 4.042 cm on an aluminium plate. The initial temperature is 14 ˘XC. What would be the minimum temperature so that the ball will fit through the hole if both are heated? The linear expansion coefficients for steel and aluminium are Ł\steel = 1.100 ĄŃ 10ĄV5 KĄV1 and Ł\alu = 2.200 ĄŃ 10ĄV5 KĄV1, respectively. ans 3610 degrees celcius

Physics - drwls, Friday, March 25, 2011 at 11:58pm
First let's use symbols people can read.
a1 = 1.1*10^-5 C^-1 (thermal expansion cefficient of steel)
a2 = 2.2*10^-5 C^-1 (thermal expnsion cefficient of aluminum)

The hole and the ball will both expand in proportion to the linear expansion coefficient and the temperature rise, dT. The diameters will be equal when
4.042(1 + a2*dT) = 4.196(1 + a1*dT)
0.154 = (8.892 - 4.616)*10^-5*dT
= 4.276*10^-5*dT

dT = 3602 C

Add that to the initial temperature of 14 C and you get 3616 C

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