A magician pulls a tablecloth from under a 200g mug located 30.0cm from the edge

Question

A magician pulls a tablecloth from under a 200g mug located 30.0cm from the edge of the cloth.  The cloth exerts afriction force of .100N on the mug, and the cloth is pulled with aconstant acceleration of 3.00m/s2.   How far does this mug move relative to the horizontal tabletop before the cloth is completely out from under it?  Note that thecloth must move more than 30cm relative to the tabletop during theprocess.
Please explain well, and use units! A magician pulls a tablecloth from under a 200g mug located 30.0cm from the edge of the cloth.  The cloth exerts afriction force of .100N on the mug, and the cloth is pulled with aconstant acceleration of 3.00m/s2.   How far does this mug move relative to the horizontal tabletop before the cloth is completely out from under it?  Note that thecloth must move more than 30cm relative to the tabletop during theprocess.
Please explain well, and use units!

Explanation / Answer

The distance the cloth travels in t seconds is:
x(cloth) = (1/2)*a(cloth)*t^2
So, the time it takes the cloth to travel 30 cm is:
t = sqrt(2*x(cloth)/a(cloth)) = sqrt(2*(0.30m)/(3.00m/s^2)) = 0.4472s
The acceleration of the mug is:
a(mug) = F(mug)/m(mug) = (0.100N)/(0.200kg) = 0.50m/s^2
So the distance the mug travels is:
x(mug) = (1/2)*a(mug)*t^2 = (1/2)*(0.50m/s^2)*(0.4472s)^2 = 0.0499m = 4.99cm

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