When you push a 1.82-kg book resting on a tabletop, it takes 2.30 N to start the book sliding. Once it is sliding, however, it takes only 1.46 N to keep the book moving with constant speed.
Q1. What is the coefficient of static friction between the book and the tabletop?
Q2. What is the coefficient of kinetic friction between the book and the tabletop?
Q1. What is the coefficient of static friction between the book and the tabletop?
A1. Well, you know what they say, friction is kind of like a stubborn relationship - it takes some effort to get things moving! In this case, you need a force of 2.30 N to overcome the static friction and start the book sliding. So, the coefficient of static friction between the book and the tabletop is given by:
μs = F / N
μs = 2.30 N / (1.82 kg × 9.8 m/s²)
μs ≈ 0.132
So, the coefficient of static friction is approximately 0.132. Let's hope the book wasn't planning on staying put for too long!
Q2. What is the coefficient of kinetic friction between the book and the tabletop?
A2. Now that the book is sliding around, it takes a smaller force of 1.46 N to keep it moving with constant speed. This force is related to the coefficient of kinetic friction, which we can calculate as:
μk = F / N
μk = 1.46 N / (1.82 kg × 9.8 m/s²)
μk ≈ 0.080
So, the coefficient of kinetic friction is approximately 0.080. Looks like once that book gets going, it just can't resist sliding around!
To find the coefficient of static friction (μs) and the coefficient of kinetic friction (μk) between the book and the tabletop, we can use the following formulas:
For static friction:
Fs = μs * N
For kinetic friction:
Fk = μk * N
where Fs is the static friction force, Fk is the kinetic friction force, and N is the normal force.
- First, we need to find the normal force (N) acting on the book. The normal force is equal to the weight of the book, which can be calculated using the formula:
N = mg
where m is the mass of the book and g is the acceleration due to gravity.
Given:
m = 1.82 kg
g = 9.8 m/s^2
Calculating N:
N = 1.82 kg * 9.8 m/s^2
N ≈ 17.836 N
- Next, let's find the static friction coefficient (μs). We know that it takes 2.30 N of force to start the book sliding. So, we can set up the equation:
2.30 N = μs * 17.836 N
Solving for μs:
μs = 2.30 N / 17.836 N
μs ≈ 0.1287
Therefore, the coefficient of static friction between the book and the tabletop is approximately 0.1287.
- Finally, let's find the kinetic friction coefficient (μk). We know that it takes 1.46 N of force to keep the book moving at a constant speed. So, we can set up the equation:
1.46 N = μk * 17.836 N
Solving for μk:
μk = 1.46 N / 17.836 N
μk ≈ 0.0817
Therefore, the coefficient of kinetic friction between the book and the tabletop is approximately 0.0817.
To find the coefficient of static friction, we can use the equation for static friction:
fs = μs * N
where fs is the force of static friction, μs is the coefficient of static friction, and N is the normal force.
To find the coefficient of kinetic friction, we can use the equation for kinetic friction:
fk = μk * N
where fk is the force of kinetic friction, μk is the coefficient of kinetic friction, and N is the normal force.
In this case, we are given the forces required to start the book sliding and to keep it moving with constant speed. The force required to start the book sliding is the force of static friction, and the force required to keep it moving with constant speed is the force of kinetic friction.
Q1. To find the coefficient of static friction (μs), we can use the formula:
fs = μs * N
From the given information, we know that fs (force of static friction) is 2.30 N. We need to find the normal force (N) acting on the book.
The normal force (N) is equal to the weight of the book, which can be calculated by multiplying the mass (m) of the book by the acceleration due to gravity (g). So, N = m * g.
Given:
Mass of the book, m = 1.82 kg
Acceleration due to gravity, g = 9.8 m/s^2
Calculating the normal force (N):
N = (1.82 kg) * (9.8 m/s^2)
N = 17.836 N
Now we have the values of fs (2.30 N) and N (17.836 N). Substituting these values into the equation:
2.30 N = μs * 17.836 N
Rearranging the equation, we can solve for μs:
μs = 2.30 N / 17.836 N
μs ≈ 0.129
Therefore, the coefficient of static friction between the book and the tabletop is approximately 0.129.
Q2. To find the coefficient of kinetic friction (μk), we can use the formula:
fk = μk * N
From the given information, we know that fk (force of kinetic friction) is 1.46 N, and the normal force (N) acting on the book is 17.836 N (as calculated above).
Now we have the values of fk (1.46 N) and N (17.836 N). Substituting these values into the equation:
1.46 N = μk * 17.836 N
Rearranging the equation, we can solve for μk:
μk = 1.46 N / 17.836 N
μk ≈ 0.082
Therefore, the coefficient of kinetic friction between the book and the tabletop is approximately 0.082.
Q1: 2.30 = M*g*mus
mus = 2.30/(M*g) = 0.129
Q2: 1.46 = M*g*muk
muk = 1.46/(M*g) = ___