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Problem 44 Hard Difficulty

An object with mass $ m $ moves with position function $ \textbf{r}(t) = a \sin t \, \textbf{i} + b \cos t \, \textbf{j} + ct \textbf{k} $, $ 0 \leqslant t \leqslant \pi/2 $. Find the work done on the object during this time period.

Answer

Work done $$=\frac{m\left(b^{2}-a^{2}\right)}{2}$$

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Video Transcript

so Well, we have a funeral. The force, which should be m times seven derivative. So what is the first derivative first derivative ISS a co sign t negative B sign t see the second derivative it is. Uh, nephew Fae. Cy Inti. Negative. Beacause i nt zero. So the force should be just m times this and we have a force, so f d r should be just the If we change it to t will be will be the product off f end our prime. The thought for thou. So there will be we put him in front, Detective. A square scientific society minus B square scientific society. Oh, t t so minus. And hey, score plus p squared holmes zero to tie over too. Is this size square tea over to easily obtained by new substitution? If we probably pie over to get one over one divided by two and you're probably zero because zero. So this should be minus and Pace Corps Prosperi square over two