To load a 100 kg refrigerator onto the moving truck, a 40° ramp, calculate the friction force and the force required to move the refrigerator inside the truck. Coefficient of friction of rubber against metal 0.8 and 0.4

**1. Calculate Gravitational Force Components:**

The gravitational force (F_g) on the refrigerator is: F_g = mg, where m = 100 \, \text{kg} and g = 9.8 \, \text{m/s}^2.

F_g = 100 \times 9.8 = 980 \, \text{N}.

**2. Resolve Components of Gravitational Force:**

The component parallel to the ramp is F_{\parallel} = mg \sin \theta = 980 \cdot \sin 40^\circ.

F_{\parallel} = 628.84 \, \text{N}.

The component perpendicular to the ramp is F_{\perp} = mg \cos \theta = 980 \cdot \cos 40^\circ.

F_{\perp} = 750.56 \, \text{N}.

**3. Calculate Static Friction Force:**

Static friction force (f_s) when the refrigerator is not moving: f_s = \mu_s F_{\perp}, where \mu_s = 0.8.

f_s = 0.8 \times 750.56 = 600.45 \, \text{N}.

**4. Calculate Force Required to Move the Refrigerator:**

The force required to overcome static friction: F_{\text{required, static}} = F_{\parallel} + f_s.

F_{\text{required, static}} = 628.84 + 600.45 = 1229.29 \, \text{N}.

**5. Calculate Kinetic Friction Force:**

Kinetic friction force (f_k) when the refrigerator is in motion: f_k = \mu_k F_{\perp}, where \mu_k = 0.4.

f_k = 0.4 \times 750.56 = 300.22 \, \text{N}.

**6. Calculate Force Required to Keep the Refrigerator in Motion:**

The force to keep it moving: F_{\text{required, kinetic}} = F_{\parallel} + f_k.

F_{\text{required, kinetic}} = 628.84 + 300.22 = 929.06 \, \text{N}.

Thus, the initial force required to start moving the refrigerator is 1229.29 \, \text{N}, and once in motion, it is 929.06 \, \text{N}.