a 20 N force pulls a 5kg box at a 60 degree angle above horizontal along the floor. If the Kinetic friction between contact surfaces is 2N. what is the acceleration of the box?

To find the acceleration of the box, we need to consider the forces acting on it. In this case, there are three forces at play: the applied force (20 N), the force due to gravity (weight), and the force of kinetic friction.

1. Calculate the force of gravity (weight):
The weight of an object is given by the formula:
weight = mass × acceleration due to gravity

Here, the mass of the box is 5 kg, and the acceleration due to gravity is approximately 9.8 m/s² (unless specified otherwise). Therefore:
weight = 5 kg × 9.8 m/s²

2. Resolve the applied force into its horizontal and vertical components:
The force applied to the box can be broken down into horizontal and vertical components. The vertical component just balances out the weight, while the horizontal component overcomes friction:

horizontal component of force = applied force × cos(angle)
vertical component of force = applied force × sin(angle)

Here, the angle given is 60 degrees. Therefore:
horizontal component of force = 20 N × cos(60°)
vertical component of force = 20 N × sin(60°)

3. Calculate the net force:
The net force acting on the box is the sum of the horizontal forces. Subtract the force of friction from the horizontal component of the applied force:

net force = horizontal component of force - force of friction

4. Determine the acceleration:
The acceleration of an object is given by Newton's second law:
acceleration = net force / mass

Here, the mass of the box is 5 kg. Therefore:
acceleration = net force / 5 kg

Now, let's substitute the values and calculate the acceleration:

weight = 5 kg × 9.8 m/s²
horizontal component of force = 20 N × cos(60°)
force of friction = 2 N
net force = horizontal component of force - force of friction
acceleration = net force / 5 kg

By following these steps, you can find the numerical value for the acceleration of the box.