You push a couch across a carpeted (rough) living room floor. Identify all the forces acting on the couch.

• A. Weight, normal, friction
• B. Weight, applied, friction
• C. Weight, applied, normal, tension
• D. Weight, applied, normal, friction

Answer: (D)

Verified step by step guidance

1. Begin by identifying the forces acting on the couch. The first force is the weight of the couch, which acts downward due to gravity. This force can be represented as \( F_{\text{gravity}} = m \cdot g \), where \( m \) is the mass of the couch and \( g \) is the acceleration due to gravity.
2. Next, consider the normal force. This force acts perpendicular to the surface and supports the couch against gravity. It is exerted by the floor on the couch and is equal in magnitude and opposite in direction to the gravitational force when the couch is not accelerating vertically.
3. Identify the applied force, which is the force you exert on the couch to push it across the floor. This force is horizontal and is responsible for moving the couch.
4. Consider the frictional force. Since the floor is carpeted and rough, friction opposes the motion of the couch. The frictional force can be calculated using \( F_{\text{friction}} = \mu \cdot F_{\text{normal}} \), where \( \mu \) is the coefficient of friction between the couch and the carpet.
5. Finally, verify that all relevant forces have been identified: weight (gravity), normal, applied, and friction. These forces together describe the dynamics of the couch as it is pushed across the carpeted floor.