determine the acceleration of a 25 kg crate being dragged across a floor by a 150 N force at a 42 degree angle above the floor where the kinetic coefficient of friction is .52.

ma = F•cosα – F(fr) =

= F•cosα – k•N =
= F•cosα – k•mg.
a = F•cosα/m - k•g.

To determine the acceleration of the crate being dragged across the floor, we need to take into account the net forces acting on the crate.

1. First, let's find the force of friction acting on the crate:
The force of friction can be calculated using the formula:
Force of friction = coefficient of friction × normal force

The normal force is equal to the weight of the crate, which can be calculated as:
Weight = mass × gravity
Weight = 25 kg × 9.8 m/s²
Weight = 245 N

Now, let's calculate the force of friction:
Force of friction = 0.52 × 245 N
Force of friction = 127.4 N

2. Next, we need to resolve the applied force into its horizontal and vertical components. Since the force is at an angle of 42 degrees above the floor, the horizontal component can be calculated as:
Force_horizontal = Force × cos(angle)
Force_horizontal = 150 N × cos(42°)
Force_horizontal = 150 N × 0.7431
Force_horizontal = 111.465 N

3. The net force in the horizontal direction is the difference between the applied force and the force of friction, which can be calculated as:
Net force_horizontal = Force_horizontal - Force of friction
Net force_horizontal = 111.465 N - 127.4 N
Net force_horizontal = -15.935 N

Note: The negative sign indicates that the force of friction is greater than the applied force, resulting in a net force in the opposite direction.

4. Finally, we can calculate the acceleration using Newton's second law of motion:
Net force = mass × acceleration

In this case, the net force in the horizontal direction is equal to the mass of the crate multiplied by the acceleration:
-15.935 N = 25 kg × acceleration

Thus, the acceleration of the crate is:
acceleration = -15.935 N / 25 kg
acceleration = -0.6374 m/s²

Note: The negative sign indicates that the crate is experiencing deceleration (opposite direction to the applied force).