Some students used a plank to make a bridge to cross a stream - Edexcel - A-Level Physics - Question 13 - 2023 - Paper 1

To find the force exerted by the wall on the plank, we apply the principle of moments.
The total moments around the point where the plank touches the wall must balance the moments created by the weight of the plank.

Taking moments about the wall:

• The weight of the plank acts at its midpoint (2.5m from the rock), thus the moment due to the weight is:

$ext{Moment from weight} = W imes d = 245 ext{ N} imes 2.5 ext{ m} = 612.5 ext{ Nm}$

Let $F$ be the force exerted by the wall, acting at a distance of 1.4m from the wall. Thus,

$F imes 1.4 ext{ m} = 612.5 ext{ Nm}$

Solving for $F$:

ightarrow F eq 0, ext{ since the weight pushes downwards while the wall helps balance it.} $$

To justify the student's statement, we need to analyze the forces acting on the plank.
The plank will tip when the moment caused by the student's weight exceeds the moment that counteracts it.

• If the student weighs 550N and walks to the end of the plank, this creates a moment about the pivot point at the rock:

$ext{Moment from student} = 550 ext{ N} imes 5.0 ext{ m} = 2750 ext{ Nm}$

• In comparison, the maximum moment before tipping occurs is 612.5 Nm created by the weight of the plank.
  Since 2750 Nm > 612.5 Nm, the plank will indeed tip if the student walks to the other end.