To find the acceleration of the box, we need to consider the forces acting on it. The main forces involved are the applied force, the force of friction, and the gravitational force.
Given: Applied force (F_applied) = 50 N Mass of the box (m) = 6 kg Coefficient of friction (μ) = 0.3 Acceleration due to gravity (g) = 10 m/s²
Gravitational force: The gravitational force acting on the box is given by: Force_gravity = mass * acceleration_due_to_gravity = 6 kg * 10 m/s² = 60 N (downward direction)
Force of friction: The force of friction can be calculated using the coefficient of friction and the normal force. The normal force is equal to the weight of the box since it is on a horizontal surface.
Normal force (N) = Force_gravity = 60 N
Force_friction = coefficient_of_friction * Normal_force = 0.3 * 60 N = 18 N (opposite to the direction of motion)
Net force: The net force acting on the box is the difference between the applied force and the force of friction: Net_force = F_applied - Force_friction = 50 N - 18 N = 32 N (in the direction of motion)
Acceleration: Using Newton's second law of motion, we know that the net force is equal to the mass of the object multiplied by its acceleration: Net_force = mass * acceleration
Therefore, we can solve for the acceleration: acceleration = Net_force / mass = 32 N / 6 kg = 5.33 m/s²
Hence, the acceleration of the box will be 5.33 m/s².