When you push a 1.80-kg book resting on a tabletop, it takes 2.05 N to start the book sliding. What is the frictional force exerted on the book when you push on it with a force of 0.80 N?
The book will not slide if a force that low is applied, so the friction force equals the applied force in that case.
To determine the frictional force exerted on the book when you push on it with a force of 0.80 N, we can use the concept of static friction.
Static friction is the force that opposes the motion of an object when it is at rest. It is determined by the equation:
f_s = μ_s * N
where f_s is the static frictional force, μ_s is the coefficient of static friction, and N is the normal force.
In this scenario, the normal force (N) is equal to the weight of the book, which can be calculated using the formula:
N = m * g
where m is the mass of the book (1.80 kg) and g is the acceleration due to gravity (approximately 9.8 m/s^2).
N = 1.80 kg * 9.8 m/s^2
N = 17.64 N
Next, we need to determine the coefficient of static friction (μ_s). The coefficient of static friction represents the roughness between two surfaces in contact. Unfortunately, we do not have this value provided.
However, we can find the coefficient of static friction by using the relationship between the applied force, the force required to start the book sliding, and the coefficient of static friction. The equation is:
f_s = μ_s * N
Since the force required to start the book sliding is given as 2.05 N, we can solve the equation for μ_s:
2.05 N = μ_s * 17.64 N
μ_s = 2.05 N / 17.64 N
μ_s ≈ 0.116
Now that we have found the coefficient of static friction, we can determine the frictional force (f_s) when you push the book with a force of 0.80 N:
f_s = μ_s * N
f_s = 0.116 * 17.64 N
f_s ≈ 2.04 N
Therefore, the frictional force exerted on the book when you push on it with a force of 0.80 N is approximately 2.04 N.
To calculate the frictional force exerted on the book when a force of 0.80 N is applied, we need to determine the frictional force coefficient (μ) between the book and the tabletop.
The equation that relates the force of friction (f) to the normal force (N) and the frictional force coefficient (μ) is:
f = μN
Given that the force required to start the book sliding is 2.05 N, we can calculate the normal force (N) acting on the book using the equation above.
f = μN
2.05 N = μN
Next, we need to find the normal force (N). The normal force is equal to the weight of the book, which can be calculated using the equation:
N = mg
where m is the mass of the book and g is the acceleration due to gravity (approximately 9.8 m/s^2).
The mass of the book is given as 1.80 kg, so:
N = mg
N = 1.80 kg * 9.8 m/s^2
N = 17.64 N
Now we can substitute the value of N into the equation for f:
2.05 N = μ * 17.64 N
Solving for μ:
μ = 2.05 N / 17.64 N
μ = 0.1162
So, the frictional force coefficient (μ) between the book and the tabletop is approximately 0.1162.
To find the frictional force exerted on the book when a force of 0.80 N is applied, we can now use the equation:
f = μN
f = 0.1162 * 17.64 N
f = 2.0477 N
Therefore, the frictional force exerted on the book when a force of 0.80 N is applied is approximately 2.05 N.