- #1
titansarus
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Homework Statement
We have a cart (It is very long) and a box on it.They are at first stationary but at ##t=0##, cart begins to move with ##v## such that:
##v = \alpha t^\beta ; t\leq t_0## and ##\dot v = c; t>t_0 ##
where ##\alpha ,\beta ,c## are constants.
At the time ##t1 (t_1<t_0)## the box is at the verge of movement (I don't know the exact translation of this in English, it means that at ##t_1 + \delta t## (very small ##\delta t>0##) it will move). At the (t_2 > t_0) it will get stationary relative to the cart (both move at the same speed).
I)Find dimension of ##\alpha,\beta,c##
II)Find ##c## in term of ##\alpha, \beta , t_0##
III)Find ##\mu_s ,\mu_k## (Static and Kinetic coefficient of friction) between box and cart.
IV) Find the distance the box traveled on the cart between (t_1 to t_2).
The Attempt at a Solution
I) For the first part, we can simply find that ##\beta## is dimensionless, ##v = L / T##so ##alpha = L * T^ -(\beta +1) ## also c is ##L / T^2##
II) we can say that at ##t = t_0## the accelerations must get equal (Because it's physics, not some strange math functions) so ##\alpha \beta t_0^{\beta-1} = c##
III) We can say that at ##t_2## we have static friction and acceleration of cart and box are equal, so ##\mu_s g = c## and we get ##\mu_s = c/g##. I don't know how to find ##\mu_k## and also how to solve part IV .