a wooden box weighing 286N is pushed across the floor by a workman who exerts a horizontal force of 143N. If the force of friction between the box and the floor is 28N, what is the acceleration (in meters per second) of the box?

To find the acceleration of the box, we can use Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration. In this case, the net force is the difference between the horizontal force applied by the workman and the force of friction.

First, we need to calculate the net force:
Net force = Applied force - Force of friction
Net force = 143N - 28N
Net force = 115N

Next, we can use Newton's second law to find the acceleration:
Net force = Mass × Acceleration
Acceleration = Net force / Mass

To find the mass of the wooden box, we can use the equation for weight:
Weight = Mass × Acceleration due to gravity

Given that the weight of the wooden box is 286N, and the acceleration due to gravity is approximately 9.8 m/s^2, we can rearrange the equation to find the mass:
Mass = Weight / Acceleration due to gravity
Mass = 286N / 9.8 m/s^2
Mass ≈ 29.2 kg

Now, we can substitute the values into the equation for acceleration:
Acceleration = Net force / Mass
Acceleration = 115N / 29.2 kg
Acceleration ≈ 3.95 m/s^2

Therefore, the acceleration of the box is approximately 3.95 m/s^2.

To find the acceleration of the box, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration.

Here's how we can break down the problem step by step:

1. First, we need to calculate the net force acting on the box. The net force is the vector sum of all the forces acting on the box.
Net force = Force applied - Force of friction
Net force = 143N - 28N
Net force = 115N

2. Next, we need to convert the weight of the box into mass. The weight of an object can be calculated using the equation:
Weight = mass × acceleration due to gravity
In this case, the weight of the box is given as 286N. Acceleration due to gravity is approximately 9.8 m/s^2.
286N = mass × 9.8 m/s^2
Solving for mass: mass = 286N / 9.8 m/s^2
mass ≈ 29.18 kg

3. Now we can calculate the acceleration using Newton's second law of motion.
Net force = mass × acceleration
115N = 29.18 kg × acceleration
Solving for acceleration: acceleration = 115N / 29.18 kg
acceleration ≈ 3.94 m/s^2

Therefore, the acceleration of the box is approximately 3.94 m/s^2.