A box is being with a velocity v by a force P (parallel to to v) along a level horizontal floor. the normal force is Fn, the kinetic frictional force if fk, and the weight of the box is mg.
Decide which forces do positive, zero or negative work and why?
To determine which forces do positive, zero, or negative work, we need to consider the definition of work. In physics, work is defined as the product of force and displacement in the direction of the force. Mathematically, work (W) is given by W = F * d * cosθ, where F is the applied force, d is the displacement, and θ is the angle between the applied force and displacement.
In this scenario, we have the following forces at play:
1. Applied Force (P): This force is parallel to the displacement (v), so the angle θ between them is 0 degrees. The work done by the applied force is positive because both force and displacement are in the same direction.
2. Normal Force (Fn): The normal force is exerted perpendicular to the surface of the floor. Since the displacement of the object is horizontal, the normal force does zero work. This is because the angle θ between the force and the displacement is 90 degrees, resulting in cosθ = 0.
3. Kinetic Frictional Force (fk): The kinetic frictional force always acts in the direction opposite to the motion or displacement. In this case, it acts to oppose the applied force (P) and the velocity (v). Therefore, the displacement and the kinetic frictional force are in opposite directions, resulting in an angle θ of 180 degrees. The work done by the kinetic frictional force is negative because the force and displacement are in opposite directions.
4. Weight Force (mg): The weight force acts vertically downward, perpendicular to the displacement. Since the displacement is horizontal, the weight force does zero work. Similar to the normal force, the angle θ between the force and displacement is 90 degrees, resulting in cosθ = 0.
To summarize:
- The applied force (P) does positive work.
- The normal force (Fn) and weight force (mg) do zero work.
- The kinetic frictional force (fk) does negative work.
It is important to note that work is a scalar quantity, meaning it only represents the magnitude of the force-component in the direction of displacement.