A box has a mass of 0.345 kg. It is on a very smooth (frictionless) horizontal surface and is acted upon by a force of 3.76 N at an angle of θ = 57.1° with the horizontal. The magnitude of the acceleration of the box is m/s2?

To find the magnitude of the acceleration of the box, we can use Newton's second law of motion, which states that the net force on an object is equal to the mass of the object multiplied by its acceleration.

Given:
Mass of the box (m) = 0.345 kg
Force acting on the box (F) = 3.76 N
Angle of the force with the horizontal (θ) = 57.1°

To calculate the magnitude of the acceleration, we need to resolve the force into its horizontal and vertical components.

The horizontal component of the force (F_horizontal) can be calculated using the formula:
F_horizontal = F * cos(θ)

The vertical component of the force (F_vertical) can be calculated using the formula:
F_vertical = F * sin(θ)

Now, we can calculate the acceleration (a) using Newton's second law of motion:
a = F_horizontal / m

Let's calculate the magnitudes step-by-step.

1. Calculate the horizontal component of the force:
F_horizontal = F * cos(θ)
F_horizontal = 3.76 N * cos(57.1°)

2. Calculate the vertical component of the force:
F_vertical = F * sin(θ)
F_vertical = 3.76 N * sin(57.1°)

3. Calculate the acceleration:
a = F_horizontal / m
a = F_horizontal / 0.345 kg

Now, you can calculate the values using a calculator or a computer program:

F_horizontal = 3.76 N * cos(57.1°) ≈ 1.687 N
F_vertical = 3.76 N * sin(57.1°) ≈ 3.174 N
a = 1.687 N / 0.345 kg ≈ 4.89 m/s²

Therefore, the magnitude of the acceleration of the box is approximately 4.89 m/s².

To find the magnitude of the acceleration of the box, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration (F = m * a).

Given:
Mass of the box (m) = 0.345 kg
Force acting on the box (F) = 3.76 N
Angle of the force with the horizontal (θ) = 57.1°

Since the force is acting at an angle to the horizontal surface, we need to resolve the force into its horizontal and vertical components. The horizontal component of the force will be responsible for accelerating the box, while the vertical component does not affect the motion on the horizontal surface.

The horizontal component of the force can be calculated using the formula:
F_horizontal = F * cos(θ)

Substituting the given values:
F_horizontal = 3.76 N * cos(57.1°)

Calculating the horizontal force:
F_horizontal = 3.76 N * 0.5597 ≈ 2.10 N

Now, we can use the formula F = m * a to find the acceleration (a) of the box:
a = F_horizontal / m

Substituting the calculated values:
a = 2.10 N / 0.345 kg

Calculating the acceleration:
a ≈ 6.09 m/s²

Therefore, the magnitude of the acceleration of the box is approximately 6.09 m/s².