To find the coefficient of kinetic friction, we first need to find the work done by the friction force. We can use the work-energy theorem, which states that the work done on an object is equal to the change in its kinetic energy.

Step 1: Calculate the final kinetic energy of the book.
The kinetic energy (KE) of an object is given by the formula KE = 1/2 * m * v^2, where m is the mass and v is the velocity.

KE_final = 1/2 * m_b * v_b^2
= 1/2 * 2.5 kg * (1.5 m/s)^2
= 2.8125 J

Since the book started from rest, its initial kinetic energy is 0. So, the change in kinetic energy is just the final kinetic energy, which is 2.8125 J.

Step 2: Calculate the work done by the cat.
The work done (W) by a force is given by the formula W = F * d, where F is the force and d is the distance.

W_cat = F_c * D_B
= 25.0 N * 1.5 m
= 37.5 J

Step 3: Calculate the work done by the friction force.
According to the work-energy theorem, the total work done on the book is equal to the change in its kinetic energy. The total work done on the book is the sum of the work done by the cat and the work done by the friction force. So, we can find the work done by the friction force by subtracting the work done by the cat from the change in kinetic energy.

W_friction = KE_final - W_cat
= 2.8125 J - 37.5 J
= -34.6875 J

The negative sign indicates that the friction force does negative work, which is expected because it acts in the opposite direction to the motion of the book.

Step 4: Calculate the friction force.
The work done by a force is also equal to the force times the distance. So, we can find the friction force (F_friction) by dividing the work done by the friction force by the distance.

F_friction = W_friction / D_B
= -34.6875 J / 1.5 m
= -23.125 N

Step 5: Calculate the coefficient of kinetic friction.
The friction force is also equal to the coefficient of kinetic friction (μ_k) times the normal force (F_N). Since there is no vertical motion, the normal force is just equal to the weight of the book, which is m_b * g, where g is the acceleration due to gravity (9.8 m/s^2).

F_friction = μ_k * F_N
-23.125 N = μ_k * (2.5 kg * 9.8 m/s^2)

Solving for μ_k gives:

μ_k = -23.125 N / (2.5 kg * 9.8 m/s^2)
= -0.94

The negative sign is not physically meaningful for a coefficient of friction, so we take the absolute value to get μ_k = 0.94.

So, the coefficient of kinetic friction between the book and the floor is 0.94.

Question

To find the coefficient of kinetic friction, we first need to find the work done by the friction force. We can use the work-energy theorem, which states that the work done on an object is equal to the change in its kinetic energy.

Step 1: Calculate the final kinetic energy of the book.
The kinetic energy (KE) of an object is given by the formula KE = 1/2 * m * v^2, where m is the mass and v is the velocity.

KE_final = 1/2 * m_b * v_b^2 
= 1/2 * 2.5 kg * (1.5 m/s)^2 
= 2.8125 J

Since the book started from rest, its initial kinetic energy is 0. So, the change in kinetic energy is just the final kinetic energy, which is 2.8125 J.

Step 2: Calculate the work done by the cat.
The work done (W) by a force is given by the formula W = F * d, where F is the force and d is the distance.

W_cat = F_c * D_B 
= 25.0 N * 1.5 m 
= 37.5 J

Step 3: Calculate the work done by the friction force.
According to the work-energy theorem, the total work done on the book is equal to the change in its kinetic energy. The total work done on the book is the sum of the work done by the cat and the work done by the friction force. So, we can find the work done by the friction force by subtracting the work done by the cat from the change in kinetic energy.

W_friction = KE_final - W_cat 
= 2.8125 J - 37.5 J 
= -34.6875 J

The negative sign indicates that the friction force does negative work, which is expected because it acts in the opposite direction to the motion of the book.

Step 4: Calculate the friction force.
The work done by a force is also equal to the force times the distance. So, we can find the friction force (F_friction) by dividing the work done by the friction force by the distance.

F_friction = W_friction / D_B 
= -34.6875 J / 1.5 m 
= -23.125 N

Step 5: Calculate the coefficient of kinetic friction.
The friction force is also equal to the coefficient of kinetic friction (μ_k) times the normal force (F_N). Since there is no vertical motion, the normal force is just equal to the weight of the book, which is m_b * g, where g is the acceleration due to gravity (9.8 m/s^2).

F_friction = μ_k * F_N 
-23.125 N = μ_k * (2.5 kg * 9.8 m/s^2)

Solving for μ_k gives:

μ_k = -23.125 N / (2.5 kg * 9.8 m/s^2) 
= -0.94

The negative sign is not physically meaningful for a coefficient of friction, so we take the absolute value to get μ_k = 0.94.

So, the coefficient of kinetic friction between the book and the floor is 0.94.

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