Unit 3 / Practice Drills
Unit 3 Practice Drills
Friction and Trusses
A mixed unit: friction is direction-sensitive, while trusses are method-heavy and repetitive.
Unit 3 Practice Drills
Friction and trusses, organised by the repeated SPPU setups.
Drills 1 and 2 cover the repeated ladder-friction pattern. Drill 3 covers the wedge setup. Drills 4 and 5 use the same truss so students can compare the method of joints with the method of sections.
Drill 1 - Ladder Friction: Minimum Angle
Problem
A uniform ladder 5 m long and weighing 200 N leans against a smooth vertical wall. The coefficient of static friction between the ladder and the floor is μₛ = 0.4. Find the minimum angle the ladder makes with the floor for it to stay in equilibrium.
Figure 1A
Ladder against a smooth wall with floor friction
Q1 - Support reactions and force directions
There are three support reactions: N_A upward at the floor, F_A horizontally toward the wall, and N_B horizontally away from the smooth wall.
The wall is smooth, so no friction acts at B.
Q2 - Apply ΣFy = 0
N_A − W = 0, so N_A = W = 200 N.
Q3 - Apply ΣFx = 0
F_A − N_B = 0, so F_A = N_B.
Q4 - Take moments about A
N_B × (5 sinθ) − 200 × (2.5 cosθ) = 0
N_B = 100 cotθ
Q5 - Impending slip condition
At the minimum angle, F_A = μₛN_A = 0.4 × 200 = 80 N.
Since F_A = N_B, set 80 = 100 cotθ.
cotθ = 0.8, so tanθ = 1.25 and θ = 51.3°.
Worked Diagram Hidden
Reveal worked diagram
Open this only after you have attempted the setup yourself.
Worked Diagram Hidden
Reveal worked diagram
Open this only after you have attempted the setup yourself.
Figure 1B
Worked ladder FBD with limiting reactions
Where students lose marks
The moment arm of the wall reaction is the vertical height 5 sinθ, while the moment arm of the ladder weight is the horizontal distance to its midpoint 2.5 cosθ. Students often use 5 and 2.5 directly instead of using the perpendicular distances.
Drills 2 to 5 stay premium
The minimum-angle ladder problem stays open as the sampler. The person-on-ladder, wedge-friction, and both truss-method drills unlock with the premium pass.