can anyone solve this?

Question

if you have courage and a tight grip you can yank a tablecloth out from under the dishes on a table. What is the longest time in which the cloth can be pulled out so that a glass 6 inches from the edge comes to rest before falling off the table? Assume that the coefficient of friction of the glass sliding on the tablecloth or sliding on the tabletop is .5

Answer 1

I could solve it, but I'm an engineer, so I just googled the correct answer and will repeat it here. I'm all about efficiency.

The idea is that as the tablecloth is pulled forward, with the glass on it, the glass is accelerated forward by the sliding friction. Then when the glass is on the table, because the tablecloth is gone, the glass is slowed by the friction between it and the table.

What this means is that of the 10 cm distance, the glass can accelerate for 5 cm and then decelerate for 5 cm (because the forces are equal... you are told the coeff of friction is the same for the glass on cloth and glass on table).

So the problem is reduced to... the cloth accelerates the glass forward in a distance of 5 cm. How much time does it take?

Well, we know the acceleration of the glass can be found by using the friction force, u m g, and Newtons second law

F = ma

u m g = ma

a = ug

And now, using basic kinematics

d = (1/2) a t2 or

t = √2d /a = √2d/ug = √ 2* 0.05 / 9.8 * 0.5 = 0.143 seconds yep, you gotta be quick.

Edit-
Shoot, I realized after posting that I mixed units. 6in = 15.24cm so divide that by 2 to give 7.62cm and then plug that into the final equation instead of 0.05 use 0.0762 to give 0.22 seconds.

Answer 2

The tablecloth has to be out from under the glass in 3 inches so it can come to a stop before the edge. The moving tablecloth will give the glass a force
Ff = mu*m*g
The glass will accelerate according to Newton's 2nd
Ff = m*a
a = Ff/m = mu*m*g / m
a = mu*g

x = (1/2)*a*t^2
where x = 3 inches

The glass will decelerate due to Ff pointing in the other direction once the tablecloth is out from under, and the glass's speed will decay to zero by the end of the 2nd 3 inches.