Madison pushes with a 160-N horizontal force on a 20-kg crate of coffee resting on a warehouse floor.the floor of friction force of 24N.show that the box accelerates is 4m/s²

a = (Fap-Fk)/m = (160-24)/20 = 6.8 m/s^2

To show that the box accelerates at 4 m/s², 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.

First, let's calculate the gravitational force acting on the crate. The gravitational force, also known as the weight, is given by the equation:

Weight = mass × acceleration due to gravity

Given that the mass of the crate is 20 kg and the acceleration due to gravity is approximately 9.8 m/s², we can calculate the weight:

Weight = 20 kg × 9.8 m/s² = 196 N

Next, let's calculate the net force acting on the crate. The net force is the vector sum of all the forces acting on the crate. In this case, we have two forces: the horizontal pushing force applied by Madison and the friction force exerted by the floor.

The net force on the crate can be calculated as:

Net Force = Applied Force - Friction Force

Applied Force = 160 N (given)
Friction Force = 24 N (given)

Net Force = 160 N - 24 N = 136 N

Now, we have the net force and the mass of the crate, so we can calculate the acceleration using Newton's second law:

Net Force = mass × acceleration

136 N = 20 kg × acceleration

To find the acceleration, rearrange the equation:

acceleration = Net Force / mass

acceleration = 136 N / 20 kg = 6.8 m/s²

The calculated acceleration is 6.8 m/s², which is not equal to 4 m/s² as stated in the question.

Therefore, the information provided does not support the claim that the box accelerates at 4 m/s².