When you push a 1.95 kg book resting on a tabletop it takes 2.40 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?
To find the coefficients of static and kinetic friction between the book and the tabletop, we need to understand the relationship between the applied force, the normal force, and the frictional force.
The normal force (N) 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, which can be calculated as the mass (m) of the book multiplied by the acceleration due to gravity (g).
The frictional force (F) can be divided into the static frictional force (Fs) and the kinetic frictional force (Fk). The static frictional force is the force that opposes the start of motion, while the kinetic frictional force is the force that opposes the motion of an object moving at a constant speed.
The static frictional force can be calculated using the equation Fs <= µsN, where µs is the coefficient of static friction. The kinetic frictional force can be calculated using the equation Fk = µkN, where µk is the coefficient of kinetic friction.
Let's calculate the coefficients of static and kinetic friction step by step:
1. Find the normal force (N):
N = m * g, where m is the mass of the book and g is the acceleration due to gravity (9.8 m/s^2).
2. Calculate the static frictional force (Fs):
Since it takes 2.40 N to start the book sliding, the static frictional force must be equal to this value:
Fs = 2.40 N
3. Calculate the kinetic frictional force (Fk):
Since it takes 1.50 N to keep the book moving at a constant speed, the kinetic frictional force must be equal to this value:
Fk = 1.50 N
4. Calculate the coefficients of static and kinetic friction:
µs = Fs / N
µk = Fk / N
Now, let's plug in the given values to find the coefficients:
µs = 2.40 N / (1.95 kg * 9.8 m/s^2)
µk = 1.50 N / (1.95 kg * 9.8 m/s^2)
Calculating these values will give you the coefficients of static and kinetic friction between the book and the tabletop.
To find the coefficients of static and kinetic friction, we'll use the following equations:
1. For static friction: F_static = μ_s * N
2. For kinetic friction: F_kinetic = μ_k * N
Where:
- F_static is the force of static friction
- F_kinetic is the force of kinetic friction
- μ_s is the coefficient of static friction
- μ_k is the coefficient of kinetic friction
- N is the normal force
First, let's calculate the normal force:
Since the book is resting on the tabletop and not accelerating vertically, the vertical forces must be balanced. Therefore, the normal force is equal to the weight of the book, which can be calculated as:
N = m * g
Where:
- m is the mass of the book (1.95 kg)
- g is the acceleration due to gravity (9.8 m/s^2)
N = 1.95 kg * 9.8 m/s^2
N = 19.11 N
Now let's calculate the coefficient of static friction:
F_static = μ_s * N
2.40 N = μ_s * 19.11 N
μ_s = 2.40 N / 19.11 N
μ_s ≈ 0.125
The coefficient of static friction is approximately 0.125.
Next, let's calculate the coefficient of kinetic friction:
F_kinetic = μ_k * N
1.50 N = μ_k * 19.11 N
μ_k = 1.50 N / 19.11 N
μ_k ≈ 0.078
The coefficient of kinetic friction is approximately 0.078.
2.40=muStatic*mg
1.50=muKinetic*mg
solve for each.