4. The illustration shows a steel rod is fixed between two...

4. The illustration shows a steel rod is fixed between two walls. The rod has a length (L=10 m) and a circular cross sectional area with radius (r=0.03 m). How much force is generated by the rod on the wall if the temperature increases from 20°C to 40°C ? ?????? ?????? ??? ??? ?? ?????? ????? ???? ???? ?????? ????? 10 ?? ? ???? ???? ????? ????? 0.03 ??. ?? ??? ????? ??????? ?? ????? ?? ????? ??? ???? ?????? ????? ?? 20 ???? ????? ??? 40 ???? ????? ? r=0.03 m L = 10 m F F A. 1.34 × 10^5 N B. 3.05 × 10^5 N C. 2.88 × 10^5 N D. 5.70 × 10^5 N

Transcript

00:01 In this example, they tell us that we have a steel rod and it's heated 70 degrees celsius, right? and once it's heated, it's attached to two supports and it's allowed to cool.

00:17 What they want to know is what the tension on this rod is, what the force on this rod is as it's cooling, as it's contracting.

00:26 So we know the expansion coefficient for steel.

00:31 We're told to assume the young's modulus for steel to be 20 .6 times 10 to the 10 newton meters squared.

00:38 I'm going to tell us the diameter of the rod is four centimeters or four times 10 to the negative two meters.

00:47 So our goal here is to try and find the force.

00:50 The two equations we're going to need to use are going to be our change in length equation, which states that the change in length is equal to the expansion coefficient for steel times its initial length times its change in temperature.

01:06 Then also the young's modulus equation, which states the young's modulus is equal to the force times the cross -sectional area over the change in length time, error divided by the initial length.

01:27 So we can rearrange both these equations to solve for the change.

01:32 In length over the initial length and we do that for our change in length equation we get the change in length divided by the initial length is equal to the expansion coefficient times the change in temperature for our young's modulus equation we get the change in length over the initial length is equal to the force over the cross -sectional area divided by young's modulus.

02:02 Oops.

02:04 We can combine these two equations together so that we get the expansion coefficient of steel times the change in temperature is equal to the force divided by the cross -sectional area divided by young's modulus.

02:23 Now, we're trying to calculate the force as this rod is cooling, right? so we can rearrange this equation to solve for the force.

02:33 When we do that, we get the force as equal to...

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