Final answer:
The acceleration of the box being pulled against friction can be calculated by considering the horizontal and vertical components of the applied force and the force of kinetic friction. By applying Newton's second law and solving the equation, we find that the acceleration is approximately 2.1 m/s².
Step-by-step explanation:
To calculate the acceleration of the box being pulled against friction, we need to consider the forces acting on it. The force pulling the box, Fp, can be broken down into its horizontal and vertical components. The horizontal component, Fp cos θ, is in the same direction as the motion and helps accelerate the box, while the vertical component, Fp sin θ, is perpendicular to the motion and does not affect the acceleration. The force of kinetic friction, , can be calculated by multiplying the coefficient of kinetic friction, μk, by the normal force, which is equal to the weight of the box multiplied by cos θ. Using Newton's second law, F = ma, we can set up an equation: Fp cos θ - = ma. Substituting the given values, we have (45.0 N)(cos 40.0°) - (0.30)(10.0 kg)(9.8 m/s²)(cos 40.0°) = (10.0 kg)a. Solving for a, we find that the acceleration is approximately 2.1 m/s².