Question

Help needed. >_<

Answer 1

I know N=mv^2/R but how do I account for changing v?

Answer 2

thinking out loud, do part 2 first and see where you go. you should have tangential deceleration.... \(mr \ddot \theta = - \mu N\) which should tie in with \(N = m \dot \theta^2 r\)

leading to **something like** this \(m r \ddot \theta = -\mu m \dot \theta^2 r\) , check it for yourself....:p

then solve in steps first as \(\dfrac{d \omega}{dt} = -\mu \omega^2\)

Answer 3

How do I do part (c)? Could you elaborate a little? I'm completely lost. @IrishBoy123

Answer 4

i suspect the problem you are having is in solving the diffeential equation

you seem comfortable with \(N = \dfrac{mv^2}{r}\) in the radial direction

in tangential direction, you will know from b) that \(ma = - \mu N\)

so \(ma = - \mu \dfrac{mv^2}{r}\)
\(a = - \mu \dfrac{v^2}{r}\)
or \(\dfrac{dv}{dt} = - \mu \dfrac{v^2}{r}\)

solving this is the problem, right? well it becomes....
\(\large \dfrac{1}{v^2}\dfrac{dv}{dt} = - \dfrac{\mu}{r}\)

\(\large \int\limits_{v_o}^{v(t)} \dfrac{1}{v^2} \;dv = - \dfrac{\mu}{r} \; \int\limits_{0}^{t} dt\)

can you solve that?

Answer 5

\[\frac{ 1 }{ v }-\frac{ 1 }{ v _{o} }=\frac{ -\mu t }{ r }\]