TI-M: Re: Re: RE: physics
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TI-M: Re: Re: RE: physics
Ooops, that should be .231481 meters, I just missed the decimal in my
typing.
----- Original Message -----
From: "Mike Grass" <mike_grass@hotmail.com>
To: <ti-math@lists.ticalc.org>
Sent: Thursday, November 09, 2000 11:45 PM
Subject: TI-M: Re: RE: physics
>
> I'll bite....
>
> Ki is initial kinetic energy for the block at the top of the ramp, so 0.
> Kf is final kinetic energy for the block right after it leaves the ramp.
> Kfh is the final velocity on the horizontal surface, so 0.
> Kih is the initial kinetic energy on the horizontal surface.
> vf is the final velocity of the block after it leaves the ramp.
> vi is the initial velocity on the horizontal surface.
> m is the mass of the first block.
> M is the mass of the second block.
> N is the normal force.
> h is the height.
> g is gravity.
> d is distance traveled on the horizontal surface (what we want to solve
> for).
> W is work
> Wg is work done by gravity
> Wn is work done by normal force (0, since normal force is perpendicular to
> the change in the position)
> Wf is work done by friction (0 for the ramp, -(mu)*N*d for the horizontal
> surface)
> Up is positive y
> Right is positive x
>
> First, for the block sliding down the ramp:
> (Work-kinetic energy theorem)
> Kf-Ki = Sigma(W) with Ki = 0
> = Wg + Wn + Wf
> = Wg
> Kf = Wg
> Wg = m*g*h
> Kf = 1/2*m*vf^2
> 1/2*m*vf^2 = m*g*h
> vf = sqrt(2*g*h)
>
> Now, because this is assumed to be a completely inelastic collision and
> momentum is conserved:
> m*vf = (m+M)*vi
> m*(sqrt(2*g*h)) = (m+M)*vi
> vi = (m*sqrt(2*g*h))/(m+M)
>
> So, we have the initial velocity of the system and we use the Work-kinetic
> energy theorem again:
> Kfh-Kih = sigma(W) with Kfh = 0
> -Kih = Wg + Wn + Wf, Wg = 0, Wn = 0
> -Kih = -(mu)*N*d, with N = m*g
> 1/2*(m+M)*vi^2 = (mu)*(m+M)*g*d
> d = vi^2/(2*g*(mu))
> = (m*sqrt(2*g*h)/(m+M))^2 * (2*g*(mu))
> = (m^2*h)/((mu)(m+M)^2)
>
> And plugging in the values for m, h, (mu), and M, we get.....
> 231481 meters
>
> I think that's right :)
>
>
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