When you push a 1.55 kg book resting on a tabletop it takes 2.10 N to start the book sliding. Once it is sliding, however, it takes only 1.50 N to keep the book moving with constant speed. What are the coefficients of static and kinetic friction between the book and the tabletop?

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65 To determine the coefficients of static and kinetic friction between the book and the tabletop, we can use the given information about the force required to start and keep the book sliding.

The force required to start the book sliding, also known as the force of static friction, can be calculated as:

F_static = μ_static * N

where:
- F_static is the force of static friction
- μ_static is the coefficient of static friction
- N is the normal force between the book and the tabletop

The normal force, N, is equal to the weight of the book (mg), which can be calculated as:

N = m * g

where:
- m is the mass of the book
- g is the acceleration due to gravity (approximately 9.8 m/s^2)

Substituting this expression for N into the equation for static friction, we get:

F_static = μ_static * m * g

where F_static is 2.10 N.

Now, let's calculate the coefficient of static friction:

μ_static = F_static / (m * g)

Substituting the given values:

μ_static = 2.10 N / (1.55 kg * 9.8 m/s^2)

μ_static ≈ 0.140

The coefficient of static friction between the book and the tabletop is approximately 0.140.

Next, we can determine the coefficient of kinetic friction. The force required to keep the book moving with constant speed is the force of kinetic friction, which can be calculated as:

F_kinetic = μ_kinetic * N

where:
- F_kinetic is the force of kinetic friction
- μ_kinetic is the coefficient of kinetic friction
- N is the normal force between the book and the tabletop

Substituting the expression for N, this equation becomes:

F_kinetic = μ_kinetic * m * g

and we know that F_kinetic is 1.50 N.

To find the coefficient of kinetic friction, we can use:

μ_kinetic = F_kinetic / (m * g)

Substituting the given values:

μ_kinetic = 1.50 N / (1.55 kg * 9.8 m/s^2)

μ_kinetic ≈ 0.098

The coefficient of kinetic friction between the book and the tabletop is approximately 0.098.

Therefore, the coefficients of static and kinetic friction between the book and the tabletop are approximately 0.140 and 0.098, respectively.