Answer: To find the coefficient of static friction:
Frictional force needed to start the book sliding:
f_s = F_applied = 5.0 N
The maximum force of static friction can be found using:
f_s,max = μ_s N
where N is the normal force between the book and the table.
To find N, we need to consider the forces acting on the book:
The force of gravity acting downwards (weight)
The normal force from the table acting upwards
Since the book is not accelerating vertically, we can say:
N - mg = 0
N = mg
where m is the mass of the book, and g is the acceleration due to gravity.
So, N = (1.0 kg + 100 kg) x 9.81 m/s^2 = 1089.9 N
Now we can find μ_s:
f_s,max = μ_s N
5.0 N = μ_s x 1089.9 N
μ_s = 0.0046
Therefore, the coefficient of static friction between the book and the table is 0.0046.
To find the coefficient of kinetic friction:
Frictional force needed to keep the book sliding at a constant velocity:
f_k = F_applied = 4.0 N
The force of kinetic friction is given by:
f_k = μ_k N
where N is the normal force, which we already found to be 1089.9 N.
So, μ_k = f_k / N
μ_k = 4.0 N / 1089.9 N
μ_k = 0.0037
Therefore, the coefficient of kinetic friction between the book and the table is 0.0037.
To find the distance the book slides before coming to rest:
When the teacher stops pushing the book, the only force acting on it is the force of kinetic friction, which acts to slow down the book. The book will eventually come to rest when its velocity is zero.
We can use the equation of motion:
v^2 = u^2 + 2as
where u is the initial velocity, v is the final velocity (which is zero), a is the acceleration (which is the same as the deceleration due to friction), and s is the distance travelled.
Rearranging the equation, we get:
s = (v^2 - u^2) / 2a
Substituting the given values:
u = 0.30 m/s (since the book is moving at a constant velocity before the teacher stops pushing it)
v = 0 m/s (since the book comes to rest)
a = - μ_k g (since the force of friction acts in the opposite direction to the book's motion)
a = - 0.0037 x 9.81 m/s^2 = -0.0363 m/s^2
Plugging in the values, we get:
s = (0 - (0.30 m/s)^2) / (2 x (-0.0363 m/s^2))
s = 0.41 m
Therefore, the book slides 0.41 meters before coming to rest.
Step-by-step explanation: