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Problem 40 Hard Difficulty

A spring of force constant $k$ is compressed by a distance $x$ from its equilibrium length. (a) Does the mass of the spring change when the spring is compressed? Explain. (b) Find an expression for the change in mass of the spring in terms of $k$ ,$x,$ and $c.$ (c) What is the change in mass if the force constant is $2.0 \times 10^{2} \mathrm{N} / \mathrm{m}$ and $x=15 \mathrm{cm} ?$


a) $t=\frac{2 d}{c+v}$
b) $\Delta m=\frac{k \cdot x^{2}}{2 c^{2}}$
c) $2.5 \times 10^{-17} k g$


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Video Transcript

But let's to part here. Well, the answer to part is yes. And according to E is equal to M C square. Well, mass and energy on Sam, uh, things because mass and energy are equal. We can say that Moss has been added to the sibling since, uh, Moss. Since moss and anarchy are the same or equal, we can say that Moss has been aided to the Sebring. So we can so we can see that Moss has bean add it to the supreme is being added Added to the sip ring to the separate No, let's do part B. Well, we know date, uh e equals M C square. So he's the risk Moss energy. And let's see risk more sinners use don't Tayyar and Delta M C Square massing. This case is dealt, um, you know, live sold for don't m changing mess. It's a cool too one divided by two times to Kate on X clear case, the super inconstant divided by, uh C Square sees the speed of light you did for chanting moss. Is they called too. Okay, X Creator divided by two times he square Olympics. Ingredient X is the displacement all right now, let's to part see, um well, we know that change in mass is equal to K. Times X squared, divided by two times C square. Let's plug in the values we have Sebring constant. It's equal to Ah, 200 multiplied by X x is your 0.15 uh meters old square divided by to multiply by ah three Multiply by 10 to the power it holds square and then for changing mass is equal to 2.5 multiplied by attempted on minus 17 kilograms.

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