A.) A 1.5 kg book is placed on a board and the angle that the board makes with t

Question

A.) A 1.5 kg book is placed on a board and the angle that the board makes with the flat ground is increased slowly. At what angle does the book begin to slip if the coefficient of static friction for these surfaces is 0.45?

B.) The angle is then increased by 10 additional degrees. If the book begins at rest, how much time does it take to travel 1.2 meters down the ramp? The coefficient of kinetic friction for these two surfaces is 0.15.

*Please show details of how you arrived at your answer. Thanks!

Explanation / Answer

(A)
us = 0.45
Let the angle at which it starts slipping =

m*g*sin() = us*mg*cos()
tan() = us
= tan^-1(0.45)
= 24.23o

(B)
New Angle, = 34.2
uk = 0.15

Let us find acceleration of the book,
m*g*sin() - uk*mg*cos() = m*a
a = g*sin() - uk*g*cos()
a = 9.8 * sin(34.2) - 0.15 * 9.8 * cos(34.2)
a = 4.29 m/s^2

Now,
s = u*t + 1/2*a*t^2
1.2 = 0 + 1/2 * 4.29 * t^2
t = 0.75 s

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