Calculating Force on an Aluminum Beam with Temp Change

[theskyisgreen]

Homework Statement

An aluminum beam 79 m long and with a cross-sectional area of 0.095 m2 is used as part of a bridge. The beam is clamped rigidly at both ends.

(a) If the temperature of the beam is increased by 29°C, what is magnitude of the extra force exerted by the beam on one of its supports?

(b) What is the magnitude of the force if the temperature of the beam is decreased by 43°C?

Homework Equations

delta L = alpha of alum (a constant) * L * temp
Force = Young's Modulus of alum * area * delta L / L

The Attempt at a Solution

For a)
delta L = (22.2x10^-6)*(79m)*(302 K) = .53m

F= (7.0x10^10)*(.095m^2)*(.53m)/(79m) = 4.46x10^7

Unfortunately, that was incorrect.

Because I couldn't get the first part correct, I haven't been able to attempt b, but I'm assuming you do the same thing but change the temp in the first equation.

Any help?

 

[Mapes]

Check your first equation; it should include the change in temperature.

 

[rl.bhat]

delta L = (22.2x10^-6)*(79m)*(302 K) = .53m
ΔT = 29 degrees, not 302 K

 

[theskyisgreen]

I thought I did that..
Although I did convert the celsius to Kelvin, but 29+273 = 302 K.
Am I not supposed to convert it to K?

 

[Mapes]

I thought I did that..
Although I did convert the celsius to Kelvin, but 29+273 = 302 K.
Am I not supposed to convert it to K?

A temperature of 29°C is a temperature of 302 K, but a temperature change of 29°C is a temperature change of 29 K. A degree Celsius is equivalent to a Kelvin, but their reference points, their zeros, are different. Does this make sense?