A book sliding across a horizontal table top at a speed of 5 m/s starts slowing down due to friction. The coefficient of kinetic friction between the book and the table top is 0.15. The force of friction on the book is

To find the force of friction acting on the book, we can use the formula:

\[
f_k = \mu_k \cdot N
\]

where:
- \( f_k \) is the kinetic frictional force,
- \( \mu_k \) is the coefficient of kinetic friction (given as 0.15),
- \( N \) is the normal force, which, on a horizontal surface, is equal to the weight of the object (\( mg \)).

Since the book is on a horizontal surface, the normal force \( N \) is equal to the gravitational force \( mg \). Therefore:

\[
f_k = \mu_k \cdot mg
\]

However, to find the exact numerical value of \( f_k \), we need the mass (\( m \)) of the book, which isn't provided. Without it, we can only express the frictional force in terms of \( m \):

\[
f_k = 0.15 \cdot m \cdot g
\]

If we assume \( g = 9.8 \, \text{m/s}^2 \) (the acceleration due to gravity), the force of friction \( f_k \) becomes:

\[
f_k = 0.15 \cdot m \cdot 9.8
\]

Thus, the frictional force \( f_k \approx 1.47 m \, \text{N} \).

To find the exact numerical answer, please provide the mass of the book.

Would you like to go over more on this or have any questions? Here are some related questions to consider:

1. How would the frictional force change if the coefficient of friction increased?
2. What if the book’s speed initially was different? Would it affect the frictional force?
3. How can we calculate the deceleration caused by friction?
4. What is the work done by the friction force as the book slows down?
5. How long would it take for the book to stop given this frictional force?

**Tip:** Remember, on flat surfaces, the normal force equals the gravitational force if no other vertical forces are acting.

Learn how to calculate the force of friction acting on a book sliding across a horizontal surface with a coefficient of kinetic friction of 0.15. This problem covers key concepts of kinetic friction, Newton's Laws, and force calculations. Suitable for students in Grades 9-11.

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