Question

which is the correct free body diagram for a box being pushed across a smooth frictionless level floor?
a
friction
applied force
b
normal force
weight
applied force
c
applied force
d
normal force
friction
applied force
weight

Explanation:

Step1: Recall free - body diagram rules

For a box on a frictionless level floor being pushed, the forces acting on it are: gravitational force (weight) downward, normal force upward (balanced with weight), and the applied pushing force. Since the floor is frictionless, there is no friction force.

Step2: Analyze each option

• Option A: Shows a friction force, but the floor is frictionless, so this is incorrect.
• Option B: Has weight (downward), normal force (upward, balanced with weight), and applied force (downward? Wait, no, when pushing a box horizontally, the applied force should be horizontal? Wait, maybe the diagram has vertical and horizontal? Wait, no, re - examining: Wait, the problem says "pushed across a smooth frictionless level floor". So vertical forces: weight (mg) down, normal force (N) up (N = mg). Horizontal force: applied force (F) in the direction of push. But in the diagrams, let's check the forces:
• Option B: Forces are weight (up? No, weight should be down, normal force up, applied force down? Wait, maybe the diagram's arrows: Wait, in option B, weight is upward? No, weight is a downward force. Wait, maybe I misread. Wait, the diagram for B: weight is upward? No, that can't be. Wait, no, maybe the vertical forces: normal force up, weight down (balanced), and applied force (let's say horizontal). Wait, maybe the diagrams have vertical and horizontal. Wait, option D has friction, which is wrong. Option A has friction, wrong. Option C has only applied force, no weight or normal force, wrong. Option B: Let's re - check. If the box is on a level floor, vertical forces: normal force (up) and weight (down, balanced). Horizontal force: applied force. But in the diagram of B, the applied force is downward? Wait, maybe the diagram is simplified. Wait, the key is: frictionless, so no friction. So among the options, option B has no friction force, and has weight (wait, maybe the weight is upward? No, that's a mistake, but maybe the diagram's arrow for weight is upward as a reaction? No, weight is a force on the box, so it should be downward. Wait, maybe the diagram has normal force up, weight down (balanced), and applied force (maybe the applied force is in the direction of push, and the other forces: normal and weight. Option B: the forces are normal force (up), weight (up? No, that's incorrect. Wait, maybe I made a mistake. Wait, the correct free - body diagram for a box on a frictionless horizontal surface with an applied force (pushing) should have:
• Vertical: weight (down) and normal force (up), equal in magnitude.
• Horizontal: applied force (in the direction of push), no friction.

Looking at the options:

• Option A: Friction force (wrong, frictionless).
• Option B: No friction force, has normal force, weight, and applied force (even if the applied force direction seems odd, but others have friction or missing forces).
• Option C: Only applied force, no weight or normal (wrong).
• Option D: Has friction (wrong).

So the correct option is B.

Answer:

B. (The diagram labeled B)