# AP Physics 2: 1.3 Changes and Conservation Laws

AP Physics 2: 1.3 Changes and Conservation Laws. To what temperature does the aluminum sheet need to be heated in order for the square peg to fit through the hole?

AP | AP Physics 2 |

AP Physics 2 | Changes and Conservation Laws |

Language | English Language |

Science Practice 2 | Using math appropriately |

Test Prep | AP Physics 2 |

### Transcript

linear coefficient of iron is 11.8 times 10 to the negative 6 centimeters per [Aluminum and iron linear coefficiencies]

degree celsius according to a common expression square pegs can't fit into

round holes however it doesn't take thermal expansion coefficients into [Man points to thermal expansion coefficient]

account. Well a square iron peg has sides of two times square root of two

centimeters and needs to pass through an aluminum sheet with a round hole of [Square block of aluminum and a metal sheet]

diameter 3.99 centimeters both objects are initially 20 degrees Celsius...To what

temperature does the aluminum sheet need to be heated in order for the square peg

to fit through the hole and here are the potential answers... All right well this

question really speaks to our attitude whenever taking on a DIY project if [Woman doing DIY project]

something doesn't fit beat it into shape or in this case, heat it into shape

alright which may be why everything we build falls apart after about five [Color block tower falls down]

minutes first of all we need to know how much bigger this hole needs to be the

dimensions of the peg will remain the same and the widest part of the peg will

be the diagonal the minimum diameter of a whole. To find the length of the

diagonal we multiply the length of one side times the square root of two which [Formula for length of diagonal]

gives us a diagonal of four centimeters that means the diameter the hole has to

increase by point 01 centimeters an equation for linear thermal expansion is

the change in length equals the product of the linear coefficient the original

length and the change in temperature so we need to find the change in [Thermometer increases]

temperature that equals the point 0 1 centimeter change in length we can

rearrange the equation to solve for the change in temperature and plug in our [A plug and a light bulb switches on]

numbers we were given a linear coefficient for

aluminum at the start which is 23 times 10 to the negative 6 centimeters per

degree celsius we'll round that down to 20 to make it a little easier and we'll

round the diameter of the hole up to 4 centimeters now let's solve this thing [Person solving a rubiks cube]

the change in temperature equals the change in length over the coefficient

times the starting length that means point 01 centimeters over 20 times 10

to the negative 6 degrees Celsius times 4 centimeters when we do the math we

find that the change in temperature equals 125 degrees Celsius since the [Aluminum block and thermometer rising in temperature]

starting temp was 20 degrees the final temp needed for this peg to fit is 145

degrees Celsius which means our answer is none of the options match 145 degrees

but remember we ballparked the number on the linear coefficient since we made the [linear coefficients on a ball park]

denominator a little smaller our result was a little bigger than it should have

been the only answer close to 145 degrees 129 degrees and we can be

confident that B is the correct choice and remember if you're in a situation

like this trust physics to make it work don't just brute force it that's [girl wearing a face mask using a blow torch]

assuming you have a blowtorch handy if not, just grab a hammer and well go

nuts... [woman hammering an aluminum block]