Understanding the Concepts

* Static Friction: This force prevents an object from starting to move. It's only relevant when the object is at rest.

* Kinetic Friction: This force opposes the motion of an object that's already moving.

* Constant Velocity: An object moving at constant velocity has zero acceleration. This means the forces acting on it must be balanced.

Solution

1. Focus on Kinetic Friction: Since the box is already moving at a constant velocity, we only need to consider the kinetic friction.

2. Balance of Forces: For the box to move at a constant velocity, the pushing force must be equal and opposite to the kinetic friction force.

3. Convert Units: The problem provides friction in pounds (lb). We need to convert this to Newtons (N) since we're working with meters per second. Use the conversion: 1 lb ≈ 4.45 N

* Static Friction: 5 lb * 4.45 N/lb ≈ 22.25 N

* Kinetic Friction: 4 lb * 4.45 N/lb ≈ 17.8 N

4. Pushing Force: Therefore, the pushing force needed to keep the box moving at a constant 8 m/s is 17.8 N.

Key Point: Even though the static friction is higher than the kinetic friction, it's not relevant in this scenario because the box is already in motion.