Question 1170795
Let's break down this problem step by step.

**1. Finding the Pushing Force**

* **Forces Involved:**
    * Applied force (F) at 30 degrees to the horizontal.
    * Frictional force (f) = 52 N, opposing motion.
    * Since the cart moves at a constant velocity, the net force in the horizontal direction is zero.
* **Horizontal Component of Applied Force:**
    * F_x = F * cos(30°)
* **Equilibrium Condition:**
    * F_x = f
    * F * cos(30°) = 52 N
* **Solving for F:**
    * F = 52 N / cos(30°)
    * F = 52 N / (√3 / 2)
    * F ≈ 60.04 N

**2. Work Done by the Pushing Force**

* **Work Done Formula:**
    * W = F * d * cos(θ)
    * Where:
        * W is work done.
        * F is the force.
        * d is the distance.
        * θ is the angle between the force and the displacement.
* **Calculation:**
    * W = 60.04 N * 33 m * cos(30°)
    * W ≈ 1716.9 J
    * W ≈ 1.72 × 10³ J

**3. Work Done by the Frictional Force**

* **Frictional Force:**
    * f = 52 N, opposing motion.
* **Work Done by Friction:**
    * W_f = f * d * cos(180°)
    * The angle between the frictional force and the displacement is 180 degrees because they are in opposite directions.
    * W_f = 52 N * 33 m * (-1)
    * W_f = -1716 J
    * W_f ≈ -1.72 × 10³ J

**4. Work Done by the Gravitational Force**

* **Gravitational Force:**
    * Fg = mg (where m is mass and g is acceleration due to gravity).
* **Work Done by Gravity:**
    * W_g = Fg * d * cos(θ)
    * The gravitational force acts vertically downwards, while the displacement is horizontal.
    * Therefore, the angle between the gravitational force and the displacement is 90 degrees.
    * W_g = Fg * d * cos(90°)
    * W_g = Fg * d * 0
    * W_g = 0 J

**Summary of Answers:**

* **Pushing Force:** 60.04 N
* **Work Done by Pushing Force:** 1.72 × 10³ J
* **Work Done by Frictional Force:** -1.72 × 10³ J
* **Work Done by Gravitational Force:** 0 J