To find the horizontal acceleration of the box, we need to consider the forces acting on it and apply Newton's second law of motion.
The given force of 15 N is acting to the right. There is also a force of friction opposing the motion. The frictional force can be calculated using the coefficient of dynamic friction.
The formula for calculating the frictional force is:
Frictional force = coefficient of dynamic friction * normal force
The normal force is the force exerted by a surface to support the weight of an object resting on it. In this case, the normal force is equal to the weight of the box, which can be calculated as:
Weight = mass * gravitational acceleration
Where the mass is 30 kg and the gravitational acceleration is approximately 9.8 m/s².
Weight = 30 kg * 9.8 m/s² = 294 N
Now we can calculate the frictional force:
Frictional force = 0.25 * 294 N = 73.5 N
Since the force pulling the box to the right is 15 N and the frictional force opposes the motion, the net force acting on the box can be calculated as:
Net force = applied force - frictional force
Net force = 15 N - 73.5 N = -58.5 N
Note that the net force is negative because it acts in the opposite direction of the applied force.
Finally, we can apply Newton's second law of motion to find the acceleration:
Net force = mass * acceleration
-58.5 N = 30 kg * acceleration
Solving for acceleration:
acceleration = -58.5 N / 30 kg
acceleration ≈ -1.95 m/s²
The negative sign indicates that the box is accelerating in the opposite direction of the applied force, meaning it is decelerating or moving to the left. Therefore, the horizontal acceleration of the box is approximately -1.95 m/s².