- #1

- 8

- 1

## Homework Statement

Here is a link to the problem: https://imgur.com/a/0T9sF

I am having trouble finding the time it takes the loop to leave the field in part a.

## Homework Equations

## emf=-\frac{d \Phi}{dt} ##

## \Sigma F=ma=mg-BIl ##

## \frac{dv}{dt}-\gamma v=g ## where ## \gamma=826.72##.

Solution to that DE: ## v(t)= \frac{g}{\gamma}(1-e^{-\gamma t}) ##

## The Attempt at a Solution

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In part a, I determined that ##v_{term}=\frac{g}{\gamma}=.012## m/s, and that ##t_{90}=.0028## s.

I used separation of variables on the differential equation and integrated to get position as a function of time:

## y-y_{o}=\frac{1}{2}(g-\gamma v)t^2 ##

I tried letting ##y_{o}=0## and ##y_{o}=l## to solve for t. But I am not given ##l##. My professor claims I do not need to know it but I am having a hard time seeing how I can find the time at which the loop leaves the field without it. I also integrated ##v(t)## to get position as a function of time but I am running into the same probloem.