2 more thermal expansion questions

[F|234K]

1.) a steel rod is 3 cm in diameter at 25 C. a brass ring has an interior diameter of 2.992 cm at 25 C. at what common temperture will the ring just slide into the rod?

for this Q, i am not too sure which equation to use. i think it's the volume change one, which is delta V= beta(Vo)(delta T)

but i don't know how the temperature and the diameter is going to fit in...

2.) a grandfather's clock is calibrated at a temperature of 20 C. the pendulum is a think brass rod with a heavy mass attached to the end. on a hot day, when the temperature is 30 C, does the clock run fast or slow? how much time does it gain or lose in a 24 hour period?

this Q...i just have no idea how to start...

thanks in advance, any suggestions/comments are greatly appreciated.

 

[Doc Al]

1.) a steel rod is 3 cm in diameter at 25 C. a brass ring has an interior diameter of 2.992 cm at 25 C. at what common temperture will the ring just slide into the rod?

for this Q, i am not too sure which equation to use. i think it's the volume change one, which is delta V= beta(Vo)(delta T)

but i don't know how the temperature and the diameter is going to fit in...

Forget about volume; the rod will just slide into the ring when their diameters are the same. You need to find the $\Delta T$ that will have them end up with the same diameter.

2.) a grandfather's clock is calibrated at a temperature of 20 C. the pendulum is a think brass rod with a heavy mass attached to the end. on a hot day, when the temperature is 30 C, does the clock run fast or slow? how much time does it gain or lose in a 24 hour period?

Hint: How does the period of a pendulum depend on its length?

 

[F|234K]

for number one, are u suggesting taht i should use the linear equation instead of the volume one?

linear equation being delta L=alpha(Lo)(delta T)

 

[F|234K]

"Hint: How does the period of a pendulum depend on its length?"

taht the thing i don't no...so i can't do the Q...

 

[Doc Al]

for number one, are u suggesting taht i should use the linear equation instead of the volume one?

Absolutely.

Regarding the pendulum: Look it up!

 

[F|234K]

thanks alot.