Math Problem Statement

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

Solution

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

fk=μkNf_k = \mu_k \cdot N

where:

  • fkf_k is the kinetic frictional force,
  • μk\mu_k is the coefficient of kinetic friction (given as 0.15),
  • NN is the normal force, which, on a horizontal surface, is equal to the weight of the object (mgmg).

Since the book is on a horizontal surface, the normal force NN is equal to the gravitational force mgmg. Therefore:

fk=μkmgf_k = \mu_k \cdot mg

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

fk=0.15mgf_k = 0.15 \cdot m \cdot g

If we assume g=9.8m/s2g = 9.8 \, \text{m/s}^2 (the acceleration due to gravity), the force of friction fkf_k becomes:

fk=0.15m9.8f_k = 0.15 \cdot m \cdot 9.8

Thus, the frictional force fk1.47mNf_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.

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Math Problem Analysis

Mathematical Concepts

Kinetic Friction
Newton's Laws
Forces and Motion

Formulas

f_k = μ_k * N
f_k = μ_k * m * g

Theorems

Newton's Second Law of Motion

Suitable Grade Level

Grades 9-11