A 5 kg book sliding on the floor with initial speed 20 m/s comes to rest in 100 m. What is the magnitude of the frictional force acting on the book?

The answer is 10 N, but how do you arrive at this answer?

To calculate the magnitude of the frictional force acting on the book, we can use the principles of Newton's laws of motion.

First, we need to determine the acceleration of the book. We can use the equation for uniform acceleration:

v^2 = u^2 + 2as

Where:
v = final velocity (0 m/s, since the book comes to rest)
u = initial velocity (20 m/s)
a = acceleration
s = distance (100 m)

Rearranging the equation gives us:

a = (v^2 - u^2) / (2s)

Substituting the given values:

a = (0^2 - 20^2) / (2 * 100)
a = -400 / 200
a = -2 m/s^2

The negative sign indicates that the acceleration is in the opposite direction to the initial velocity. This negative acceleration is due to the frictional force acting in the opposite direction to the motion of the book.

Next, we can calculate the frictional force using Newton's second law of motion:

F = ma

Where:
F = frictional force
m = mass of the book (5 kg)
a = acceleration (-2 m/s^2)

Substituting the given values:

F = 5 kg * (-2 m/s^2)
F = -10 N

Here, the negative sign indicates that the frictional force is in the opposite direction to the motion.

However, since the question asks for the magnitude of the frictional force, we ignore the negative sign and take the absolute value:

Magnitude of the frictional force = |-10 N| = 10 N

Hence, the magnitude of the frictional force acting on the book is 10 N.