Final answer:
The question is about calculating the force of friction on a ladder that is sliding against a wall. The force of friction is determined using the normal force from the weight of the ladder at a given angle and the coefficient of kinetic friction between the ladder and the floor.
Step-by-step explanation:
The student is asking about the force of friction acting on a ladder that is sliding against a wall. To solve this, we need to first calculate the normal force acting on the ladder, which can be found using the weight of the ladder and the angle θ at which it rests against the wall. The weight (W) acting downward has a component (W*cos(θ)) that acts perpendicular to the surface of the floor, which is the normal force (N). Since the ladder weighs 42 lbs and θ = 40°, the normal force is given by N = W*cos(θ).
Next, we use the coefficient of kinetic friction (μ) and the normal force (N) to find the force of friction (f k). The force of friction is calculated as f k = μ * N. Given the coefficient of kinetic friction is 0.2, we calculate f k = 0.2 * N.
Calculating the exact value requires the conversion of pounds to newtons and the calculation of the cosine for the given angle. The calculated force of friction is what prevents the ladder from sliding out further and is a result of the interaction between the ladder and the floor surface.