Understanding the Forces

* Gravity: The box experiences a downward force due to gravity (weight), which is calculated as:

* Weight (W) = mass (m) * acceleration due to gravity (g) = 2.0 kg * 9.8 m/s² = 19.6 N

* Normal Force: The wall exerts an upward force on the box perpendicular to the wall. Since the box is sliding at a constant speed, this force is equal in magnitude to the component of the weight perpendicular to the wall.

* Friction: The wall also exerts a frictional force opposing the box's motion, acting parallel to the wall.

* Applied Force: You are applying a force at a 45-degree angle. This force has two components:

* Horizontal component: This component helps oppose the friction force.

* Vertical component: This component helps reduce the normal force from the wall.

Setting Up the Equations

Since the box is moving at a constant speed, the net force on it is zero. This means the forces in both the horizontal and vertical directions must balance.

Horizontal Forces:

* Applied force (horizontal) = Friction force

* F_applied * cos(45°) = μ * Normal force (where μ is the coefficient of friction)

Vertical Forces:

* Normal force = Weight - Applied force (vertical)

* Normal force = 19.6 N - F_applied * sin(45°)

Solving for the Applied Force

1. Substitute the expression for Normal force from the vertical equation into the horizontal equation:

* F_applied * cos(45°) = μ * (19.6 N - F_applied * sin(45°))

2. Solve for F_applied:

* F_applied * cos(45°) + μ * F_applied * sin(45°) = 19.6 N * μ

* F_applied * (cos(45°) + μ * sin(45°)) = 19.6 N * μ

* F_applied = (19.6 N * μ) / (cos(45°) + μ * sin(45°))

Important Note: You need to know the coefficient of friction (μ) between the wood box and the wall to calculate the exact force applied.

Example:

Let's assume a coefficient of friction (μ) of 0.3.

* F_applied = (19.6 N * 0.3) / (cos(45°) + 0.3 * sin(45°))

* F_applied ≈ 5.88 N

Therefore, you would need to apply approximately 5.88 N of force at a 45-degree angle to keep the box sliding at a constant speed, assuming a coefficient of friction of 0.3.