What is the Force Exerted by a Heated Steel Beam with Clamped Ends?

AI Thread Summary
A 20-meter steel beam clamped at both ends is heated from 0°C to 40°C, causing it to expand to 20.0088 meters. The discussion centers on calculating the force exerted by the beam due to this thermal expansion, using the coefficient of linear expansion and Young's modulus for steel. Young's modulus (Ysteel) is crucial for determining the stress and resulting force needed to compress the beam back to its original length. Participants clarify the significance of Young's modulus and share equations necessary for the calculations. The conversation concludes with a participant expressing understanding after receiving guidance on the topic.
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Homework Statement


Suppose the ends of a 20-m-long steel beam are rigidly clamped at 0°C to prevent expansion. The rail has a cross-sectional area of 30 cm^2. What force does the beam exert when it is heated to 40°C? ( αsteel = 1.1 × 10−5/C°, Ysteel = 2.0 × 1011 N/m2).


Homework Equations



delta L =alpha Li delta T

The Attempt at a Solution


I solve for the new length and get 20.0088m. I don't know what Ysteel is used for or were to start after finding the new lenght.
 
Last edited:
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The answer is one of these if that helps
a. 2.6 × 105 N
b. 5.6 × 104 N
c. 1.3 × 103 N
d. 6.5 × 102 N
e. 2.5 × 102 N
 
Do you know what the Young's elastic modulus Y signifies and how to work with it? If so, how much stress (and then, how much force) is required to compress the length back to 20 m?
 
no i haven't seen it before, what is the equation?
 
You might want to read http://en.wikipedia.org/wiki/Young%27s_modulus" .
 
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thanks i got it now
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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