When you push a 1.70 kg book resting on a tabletop it takes 2.60 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?

Wb = mg = 1.7kg * 9.8N/kg = 16.66N.

Fb = (16.66N,0deg) = Force of book..

Fp = 16.66sin(0) = 0 = Force parallel to table.

Fv = 16.66cos(0) = 16.66N. = Force perpendicular to table.

1. Fap - Ff = 0, Fap = Force applied.
2.60 - Ff = 0, Ff = Force of friction.
Ff = 2.60,
u*Fv = 2.60,
16.66u = 2.60,
u = 0.156. = Static coefficient of friction.

2. 1.5 - Ff = 0,
Ff = 1.5,
u*Fv = 1.50,
16.66u = 1.5,
u = 0.09 = Kinetic coefficient of friction.

To find the coefficients of static and kinetic friction between the book and the tabletop, we need to use the given information and apply the concept of friction.

First, let's consider the force required to start the book sliding, which is the static friction. We know that the force required to start the book is 2.60 N. According to the equation of static friction, the maximum static friction force (F_static_max) can be calculated as:

F_static_max = μ_static * N

where μ_static is the coefficient of static friction and N is the normal force exerted on the book. The normal force can be calculated as the product of mass (m) and the acceleration due to gravity (g).

N = m * g

Substituting the values, we have:

N = 1.70 kg * 9.8 m/s^2 = 16.66 N

Now, we can rearrange the equation to find the coefficient of static friction:

μ_static = F_static_max / N

μ_static = 2.60 N / 16.66 N ≈ 0.156

So, the coefficient of static friction between the book and the tabletop is approximately 0.156.

Next, let's consider the force required to keep the book moving at a constant speed, which is the kinetic friction. We know that the force required to keep the book moving is 1.50 N. According to the equation of kinetic friction, the kinetic friction force (F_kinetic) can be calculated as:

F_kinetic = μ_kinetic * N

where μ_kinetic is the coefficient of kinetic friction. Substituting the values, we have:

1.50 N = μ_kinetic * 16.66 N

Now, we can rearrange the equation to find the coefficient of kinetic friction:

μ_kinetic = 1.50 N / 16.66 N ≈ 0.090

So, the coefficient of kinetic friction between the book and the tabletop is approximately 0.090.

In summary:

Coefficient of static friction (μ_static) ≈ 0.156
Coefficient of kinetic friction (μ_kinetic) ≈ 0.090