Thermal Expansion of a gold ring

AI Thread Summary
To remove a gold ring with an inner diameter of 2.26 cm from a finger with a knuckle diameter of 2.3 cm, the ring must be heated to expand sufficiently. The coefficient of linear expansion for gold is 1.42 E -5. The circumference of the ring, calculated using the formula C = π * diameter, is approximately 7.09 cm, which represents the initial length for expansion calculations. The key challenge lies in determining how to apply the linear expansion formula, delta L = alpha * Lo * delta T, to find the required temperature increase. Properly applying these principles will yield the necessary temperature to free the ring.
thaixicedxtea
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Homework Statement


You somehow manage to get a gold ring with inner diameter 2.26 cm stuck on your finger, even though your knuckle has a diameter of 2.3 cm. The temperature of the ring is 23 degrees C.
To what temperature would you have to heat the ring in order to get it off your finger? The coefficient of linear expansion of gold is 1.42 E -5. Answer in units of C.


Homework Equations


delta L = alpha/coefficient * Lo * delta T



The Attempt at a Solution


Since I'm given the linear expansion coefficient, I figured that I'm going to use the delta L equation. What I'm stuck with is what to do with the diameters given, like how do I figure out the initial length from the diameter...
 
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thaixicedxtea said:

Homework Statement


You somehow manage to get a gold ring with inner diameter 2.26 cm stuck on your finger, even though your knuckle has a diameter of 2.3 cm. The temperature of the ring is 23 degrees C.
To what temperature would you have to heat the ring in order to get it off your finger? The coefficient of linear expansion of gold is 1.42 E -5. Answer in units of C.


Homework Equations


delta L = alpha/coefficient * Lo * delta T



The Attempt at a Solution


Since I'm given the linear expansion coefficient, I figured that I'm going to use the delta L equation. What I'm stuck with is what to do with the diameters given, like how do I figure out the initial length from the diameter...

What is the circumference of the ring?
 
C equals pi * diameter, so the circumference of the ring is 2.26 cm * pi = 7.09.
Is that the length? If it is, why?
I must be thinking too hard...
 
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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