Equilibrium of a laminaEdexcel International A Level Further Maths: Flashcards

What these 12 flashcards ask

Where is G when a lamina hangs freely from a point?
Forces on a freely suspended lamina?
Rectangle 0.6\times0.4 hangs from a corner: angle between the long edge and the vertical?
How do you find the hanging angle of a composite lamina?
What does a particle attached to a lamina do to G?
Why take moments about a smooth pivot?
Condition for a lamina on an incline to be about to topple?
For G at d along the edge and h above the plane, when does it topple?
Condition for sliding on a rough plane?
A lamina is on the point of toppling but not sliding: what do you know about \mu?
Resolving for a body on a slope of angle \alpha and weight W?
Moment equation for a horizontal force F holding a lamina at rest?

Exam questions on Equilibrium of a lamina

A uniform rectangular lamina $ABCD$ has $AB=0.6$ m and $BC=0.4$ m, and mass $3$ kg. Take $g=9.8$ m s $^{-2}$ . The lamina is freely suspended from a fixed point and hangs in equilibrium in a vertical plane.
The lamina is suspended from $A$ . Find the vertical distance of $G$ below $A$ .2 marks
A uniform rectangular lamina $PQRS$ has $PQ=40$ cm, $QR=30$ cm and mass $2$ kg. It is free to rotate in a vertical plane about a smooth fixed horizontal axis through $P$ , and hangs in equilibrium.
The particle is removed. Find the angle that $PQ$ makes with the vertical.2 marks
A uniform rectangular lamina $ABCD$ has $AB=30$ cm and $BC=50$ cm. It stands in a vertical plane with the edge $AB$ in contact with a rough plane inclined at an angle $\alpha$ to the horizontal. $AB$ lies along a line of greatest slope, with $A$ the lower end.
The lamina is on the point of toppling. Find the greatest value of $\alpha$ .3 marks

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).