A box has a mass of 0.220 kg. It is on a very smooth (frictionless) horizontal surface and is acted upon by a force of 2.36 N at an angle of θ = 44.8° with the horizontal. The magnitude of the acceleration of the box is m/s2?

a = F/m

a = (2.36 cos 44.8 ) /.22

To find the magnitude of the acceleration of the box, we can break down the force into its horizontal and vertical components.

The horizontal component of the force can be found using the formula: Fx = F * cos(θ)
where F is the magnitude of the force and θ is the angle with the horizontal.

Substituting the given values into the formula:
Fx = 2.36 N * cos(44.8°)

Similarly, the vertical component of the force can be found using the formula: Fy = F * sin(θ)
where F is the magnitude of the force and θ is the angle with the horizontal.

Substituting the given values into the formula:
Fy = 2.36 N * sin(44.8°)

Since there is no friction and the horizontal surface is smooth, the net horizontal force (Fx) is equal to the mass of the box (m) multiplied by the acceleration in the horizontal direction (ax). So, Fx = m * ax.

Since the vertical component of the force (Fy) is acting vertically upward and the box is on a horizontal surface, the net vertical force in the y-direction is zero, meaning the acceleration in the vertical direction (ay) is zero.

Using the formula F = m * a and substituting the values, we can equate the horizontal components of the forces:

m * ax = 2.36 N * cos(44.8°)

Now, we can solve for the acceleration (ax):

ax = (2.36 N * cos(44.8°)) / m

Substituting the given mass (m = 0.220 kg) into the equation:

ax = (2.36 N * cos(44.8°)) / 0.220 kg

Calculating this value will give us the magnitude of the acceleration of the box.