A student investigates why doors are easier to open when pushed in certain ways
PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
A student investigates why doors are easier to open when pushed in certain ways. The door is 0.90m wide and mounted on frictionless hinges. The student applies the same 20N horizontal push in three different trials:
• Trial I – at the midpoint of the latch side, pushing perpendicular to the plane of the door.
• Trial II – at the top edge of the latch side, pushing straight toward the hinges (parallel to the plane of the door).
• Trial III – at the midpoint of the latch side, but the push is directed 30∘ away from perpendicular so it has both perpendicular and parallel components.
Use this information to explore how rotational effectiveness depends on where and how the force is applied.
(a) For each trial, qualitatively describe whether the door starts rotating easily, rotates with difficulty, or fails to rotate. Base your description on the relationship between the line of action of the force and the hinges.
(b) Explain why trials that place the line of action farther from the hinges tend to produce greater rotational effectiveness, even when the force magnitude is unchanged.
(c) The student proposes mounting a vertical handle only 0.15m from the hinges to save space. Explain, without numerical calculation, how this design choice would change the effort required to open the door compared with the current handle location near the latch.
(d) Draw a clearly labeled force diagram for Trial III, showing the components of the applied force relative to the door. Indicate which component does and which component does not contribute to the door’s rotation, and justify your identification.