A 50.0-kg box is resting on a horizontal floor. A force of 250 N directed at an angle of 20.7° below the horizontal is applied to the box. The coefficient of kinetic friction between the box and the surface is 0.300. What is the acceleration of the box?

1.77m/s^2? Im not sure

5.89m/s2

I got 1.21m/s2

To find the acceleration of the box, we need to analyze the forces acting on it. There are three main forces involved: the applied force, the force of gravity, and the frictional force.

1. Applied force: Given that a force of 250 N is applied at an angle of 20.7° below the horizontal, we need to determine the horizontal and vertical components of this force.

The horizontal component of the applied force can be found using the formula:

Force_horizontal = Applied force * cos(θ)

where θ is the angle below the horizontal.

Force_horizontal = 250 N * cos(20.7°) = 231.8 N

2. Force of gravity: The force of gravity acting on the box can be calculated using the formula:

Force_gravity = mass * acceleration due to gravity

where the mass of the box is 50.0 kg and the acceleration due to gravity is approximately 9.8 m/s².

Force_gravity = 50.0 kg * 9.8 m/s² = 490 N

3. Frictional force: The frictional force can be determined using the formula:

Frictional force = coefficient of friction * normal force

The normal force is the perpendicular force exerted by the floor on the box, which is equal in magnitude to the force of gravity.

Frictional force = 0.300 * 490 N = 147 N

Now, let's calculate the net force acting on the box in the horizontal direction:

Net force = Force_horizontal - Frictional force

Net force = 231.8 N - 147 N = 84.8 N

Finally, we can use Newton's second law of motion to determine the acceleration of the box:

Net force = mass * acceleration

84.8 N = 50.0 kg * acceleration

acceleration = 84.8 N / 50.0 kg

acceleration ≈ 1.70 m/s²

Therefore, the acceleration of the box is approximately 1.70 m/s².