When you push a 1.92 kg book resting on a tabletop, you have to exert a force of 2.0 N to start the book sliding. Once it is sliding, however, you can use a force of only 1.0 N to keep the book moving with constant speed. What are the coefficients of static and kinetic friction between the book and the tabletop?
the weight of the book is 1.92 * 9.81 = 18.8N
Now, how is friction determined?
To find the coefficients of static and kinetic friction between the book and the tabletop, we can use the formula:
μ = F / N
where:
- μ is the coefficient of friction,
- F is the force of friction acting on the book, and
- N is the normal force exerted by the tabletop on the book.
Let's break down the problem step by step:
Step 1: Finding the normal force
The normal force (N) is the force exerted by the tabletop on the book, which is equal in magnitude but opposite in direction to the weight of the book (mg). We can find the weight using the equation:
Weight = mass * acceleration due to gravity
In this case, the mass of the book is given as 1.92 kg. We'll assume the acceleration due to gravity is 9.8 m/s². Thus,
Weight = 1.92 kg * 9.8 m/s²
Step 2: Finding the coefficient of static friction (μs)
To start the book sliding, a force of 2.0 N is required. This force is equal to the maximum force of static friction. Therefore,
μs = F / N
Substituting the values,
μs = 2.0 N / (1.92 kg * 9.8 m/s²)
Step 3: Finding the coefficient of kinetic friction (μk)
Once the book is sliding, the force required to keep it moving at a constant speed is 1.0 N. This force is equal to the force of kinetic friction. Therefore,
μk = F / N
Substituting the values,
μk = 1.0 N / (1.92 kg * 9.8 m/s²)
Solving these equations will give you the coefficients of static and kinetic friction between the book and the tabletop.