Question

A book is pulled to the right at constant velocity by a 10 N force acting 30° above the horizontal. The coefficient of kinetic friction between the book and the horizontal surface is 0.5. What is the weight of the book and the normal force?

Answer 1

To solve this problem, we need to break down the forces acting on the book and analyze the equilibrium.

1. Weight of the book: The weight of an object is given by the formula: Weight = mass * acceleration due to gravity (g)

However, since the book is at constant velocity, there is no net force in the vertical direction, and the weight is balanced by the normal force.

2. Normal force: The normal force is the force exerted by a surface to support the weight of an object resting on it. It acts perpendicular to the surface.

3. Force of friction: The force of friction opposes the motion of the book and acts parallel to the surface.

Now, let's calculate the weight and normal force.

Given: Force applied, F = 10 N Angle above the horizontal, θ = 30° Coefficient of kinetic friction, μk = 0.5

First, we need to resolve the applied force into its vertical and horizontal components.

Vertical component: F_vertical = F * sin(θ) F_vertical = 10 N * sin(30°) F_vertical ≈ 5 N

Horizontal component: F_horizontal = F * cos(θ) F_horizontal = 10 N * cos(30°) F_horizontal ≈ 8.66 N

The weight of the book is balanced by the vertical component of the applied force and the normal force:

Weight = F_vertical + Normal force

Since the book is at constant velocity, the force of friction must be equal and opposite to the horizontal component of the applied force:

Force of friction = F_horizontal

Now, we can calculate the weight and normal force:

Weight = F_vertical + Normal force Weight = 5 N + Normal force

Force of friction = F_horizontal Force of friction = 8.66 N

According to the coefficient of kinetic friction (μk = 0.5), the force of friction is equal to the coefficient of friction multiplied by the normal force:

Force of friction = μk * Normal force 8.66 N = 0.5 * Normal force

Now we can solve for the normal force:

Normal force = 8.66 N / 0.5 Normal force ≈ 17.32 N

The weight of the book is equal to the sum of the vertical component of the applied force and the normal force:

Weight = F_vertical + Normal force Weight = 5 N + 17.32 N Weight ≈ 22.32 N

Therefore, the weight of the book is approximately 22.32 N, and the normal force exerted by the surface is approximately 17.32 N.