Final answer:
The force of friction acting on the 435 N box sliding down a 40.0° incline is calculated by first determining the gravitational force component parallel to the incline and then subtracting the force due to the box's acceleration. The resulting force of friction is 269.1 N.
Step-by-step explanation:
To find the force of friction acting on the box, we must consider the forces parallel and perpendicular to the surface of the incline. First, we calculate the gravitational force component parallel to the incline. This can be found by multiplying the weight of the box (435 N) by the sine of the angle of the incline (sin(40.0°)). The force parallel to the incline is then:
Fₚ = mg sin(θ) = 435 N * sin(40.0°) = 280.2 N
Now, using Newton's second law (F = ma), we can determine the total force exerted along the incline due to the acceleration:
F = ma = 435 N / 9.8 m/s² * 0.250 m/s² = 11.1 N
To find the force of friction, subtract the force due to acceleration from the gravitational force component parallel to the incline:
Fₒ = Fₚ - F = 280.2 N - 11.1 N = 269.1 N
Therefore, the frictional force is 269.1 N, opposing the motion of the box.