When you push a 2.05 kg book resting on a tabletop it takes 2.45 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? static? kinetic?
F1 = force to start movement
μs = coefficient of static friction
F2 = force to maintain movement
μk = coefficient of kinetic friction
m = mass
The coefficients of friction are defined as follows:
F1 = μs*mg
F2 = μk*mg
To find the coefficients of static and kinetic friction between the book and the tabletop, we can use the given information and the formula for friction.
The formula for friction is given by:
Friction = coefficient of friction * Normal force
Where:
- Friction is the force opposing the motion.
- Coefficient of friction (represented by the Greek letter "mu") is a dimensionless constant that depends on the nature of the surfaces in contact.
- Normal force is the force exerted by a surface to support the weight of an object resting on it.
In this case, the normal force is equal to the weight of the book because it is resting on the tabletop. The weight is given by:
Weight = mass * gravity
Where:
- Mass is the mass of the book, given as 2.05 kg.
- Gravity is the acceleration due to gravity, approximately 9.8 m/s^2.
Now, let's calculate the coefficients of static and kinetic friction step by step:
1. Calculation of the static friction:
We know that it takes 2.45 N of force to start the book sliding. Since this force is equal to the maximum static friction force before sliding occurs, we can set up the equation:
2.45 N = coefficient of static friction * Normal force
The normal force is equal to the weight of the book, so let's calculate it:
Weight = mass * gravity
Weight = 2.05 kg * 9.8 m/s^2
Next, substitute the value of the weight into the equation:
2.45 N = coefficient of static friction * (2.05 kg * 9.8 m/s^2)
Now, solve the equation to find the coefficient of static friction.
2.45 N = coefficient of static friction * 20.0 N
Coefficient of static friction = 2.45 N / 20.0 N
2. Coefficient of kinetic friction:
We are given that it takes 1.50 N to keep the book moving with constant speed. This force is equal to the kinetic friction force, so we can set up the equation:
1.50 N = coefficient of kinetic friction * Normal force
Again, substitute the value of the weight into the equation:
1.50 N = coefficient of kinetic friction * (2.05 kg * 9.8 m/s^2)
Now, solve the equation to find the coefficient of kinetic friction.
1.50 N = coefficient of kinetic friction * 20.0 N
Coefficient of kinetic friction = 1.50 N / 20.0 N
After performing the calculations, the coefficients of static and kinetic friction between the book and the tabletop can be found.