An object that has a mass of 36.0 kg is pushed along a horizontal surface with a force of 85.0 N at 30 degrees. If the force of friction is 52.0 N, what is the magnitude of the acceleration of the object?

Fn = Fap - Ff,

Fn = 85cos30 - 52 = 21.6N = Net force.

Fn = ma,
a = Fn / m = 21.6 / 4.5 = 4.80m/s^2.

To find the magnitude of the acceleration of the object, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration:

Net force = mass × acceleration

First, let's resolve the force of 85.0 N into its horizontal and vertical components using trigonometry. Since the object is pushed at an angle of 30 degrees, the horizontal component of the force will be:

Force horizontal = Force × cos(angle)
= 85.0 N × cos(30°)

Similarly, the vertical component of the force will be:

Force vertical = Force × sin(angle)
= 85.0 N × sin(30°)

Now, let's calculate the net force acting on the object. Since the force of friction opposes the motion, it will act in the opposite direction of the applied force:

Net force = Force horizontal - Force of friction

Next, substitute the given values into the equation:

Net force = (85.0 N × cos(30°)) - 52.0 N

By rearranging the equation, we can solve for acceleration:

Net force = mass × acceleration

acceleration = Net force / mass

Substitute the known values:

acceleration = (85.0 N × cos(30°)) - 52.0 N) / 36.0 kg

Using a calculator, calculate the value inside the brackets, then divide it by 36.0 kg to find the magnitude of acceleration.

Note: Make sure to convert the angle to radians by using the appropriate conversion factor if your calculator requires angles to be in radians.