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$\bullet$ A Foucault pendulum consists of a brass sphere with a diameter of 35.0 $\mathrm{cm}$ suspended from a steel cable 10.5 $\mathrm{m}$ long (both measurements made at $20.0^{\circ} \mathrm{C} ) .$ Due to a design oversight, the swinging sphere clears the floor by a distance of only 2.00 $\mathrm{mm}$ when the temperature is $20.0^{\circ} \mathrm{C}$ . At what temperature will the sphere begin to brush the floor?

$T=T_{0}+\Delta T=20^{\circ} C+15^{\circ}=35^{\circ} C$

Physics 101 Mechanics

Chapter 14

Temperature and Heat

Thermal Properties of Matter

The First Law of Thermodynamics

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Hey, everyone, this is question number 68 from Chapter 14 and this problem were given that we have a pet pendulum with a brass sphere of diameter 35 centimetres in a steel cable of length. 10.5 meters. We're told that the sphere clears the floor by two millimeters at 20 degrees Celsius, were then asked to find the temperature at which the sphere brushes the floor. So we're giving a starting temperature. Were given a diameter, length and stuff, and it's it's a little more obscure because this is a general problem, not specific. But what is you need to think about what is going to make this fear brush the floor and obviously it's going to be that it's going to expand. What temperature? So we should be thinking of thermal expansion, which is Delta l Change in length is equal to Alfa, which is our expansion coefficient times. L not okay, but in this case, we have two things that we have to take into account. We have to take in account the expansion of the cable and the expansion of the sphere. So then our delta l becomes alsa be brass. L not do capital l l not plus Alfa Steel for the cable. L'm not. And I actually forgot our delta t over here. Um times delta t. So what we're looking for us is Delta team. We actually have the delta L because it's we're told that it's two millimeters off the ground and were asked to find what temperature will start to brush so that our delta l is going to become 22 millimeters. So he said this sum equal to two millimetres and we saw for Delta T and that is going to give us the equation Don't t equals. It's just dividing this over to the other side. So this is going to become is underdone Delta l So two millimetres. We've gotta change out two meters. So two times 10 to the minus three divided by 1,000 meters. And then we have Alfa of brass is too times 10 to the minus 50. Okay, the minus. One times our diameters. Your 0.35 meters Wass What? Plus alf of steel 1.2 times. 10 to the minus five came the minus one and then our length 10.5 meters R l not okay and if you play that into your calculator, he had a delta T equal to 15 degrees Celsius. But that's not worry end because this is Delta. So we have two d'oh, 15 degrees C plus what we started with, which is 20 degrees C. So then, at 35 degrees Celsius, this sphere will start to brush the floor.

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