A book with a mass of 1350 g is sitting on a desk. The ukf between the book and the desk is .45 and the ukf between the book and the desk is .30.
a. how much horizontal force is required to start the book moving across the desk?
b. Once it starts moving, what is the acceleration of the book?
c. If we want the book to move at constant velocity, how much do we need to reduce our original applied force.
a. M*g = 1.35 * 9.8 = 13.2 N. = Wt. of book. = Normal force(Fn).
Fs = us*Fn = 0.45 * 13.2 = 5.95 N.
F-Fs = M*a. F = Fs+M*a = 5.95+M*0 = 5.95 N.
b. Fk = uk*Fn = 0.30 * 13.2 = 3.96 N.
F-Fk = M*a. a = (F-Fk)/M.
c. Fap-Fk = M*a.
Fap = Fk+M*a = 3.96 + M*0 = 3.96 N. = Force applied.
Reduction = 5.95-3.96 =
To answer these questions, we need to understand the concepts of friction, force, mass, and acceleration. Let's break down each question step by step:
a. To calculate the horizontal force required to start the book moving across the desk, we need to use the concept of static friction. The formula for static friction is:
F_friction = μ_s * F_normal
where F_friction is the force of friction between two surfaces, μ_s is the coefficient of static friction, and F_normal is the normal force acting on the object in question.
In this case, the normal force is equal to the weight of the book, which can be calculated using the formula:
F_normal = m * g
where m is the mass of the book and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Plugging in the given values, we have:
F_normal = 1.35 kg * 9.8 m/s^2 = 13.23 N
Now, we can calculate the force required to start the book moving:
F_friction_start = μ_s * F_normal
Plugging in the coefficient of static friction (μ_s = 0.45) and the normal force, we get:
F_friction_start = 0.45 * 13.23 N ≈ 5.94 N
Therefore, approximately 5.94 Newtons of force is required to start the book moving across the desk.
b. Once the book starts moving, the force of friction changes from static friction to kinetic friction. The formula for kinetic friction is:
F_friction_kinetic = μ_k * F_normal
where F_friction_kinetic is the force of kinetic friction between two surfaces, μ_k is the coefficient of kinetic friction, and F_normal is the normal force acting on the object.
In this case, the coefficient of kinetic friction (μ_k) is given as 0.30, and the normal force (F_normal) remains the same as before (13.23 N).
Plugging in these values, we get:
F_friction_kinetic = 0.30 * 13.23 N ≈ 3.97 N
Therefore, the force of kinetic friction acting on the book once it starts moving is approximately 3.97 Newtons.
c. If we want the book to move at a constant velocity (which means there is no net force acting on it), the force applied must equal the force of kinetic friction. Using the formula F_applied = F_friction_kinetic, we can calculate how much the applied force needs to be reduced.
F_applied = F_friction_kinetic
F_applied = 3.97 N
As a result, the originally applied force needs to be reduced to approximately 3.97 Newtons to keep the book moving at a constant velocity.
By following these calculations and understanding the concepts of friction, force, mass, and acceleration, you can find the answers to the given questions.