CAIE A-Level Further Mathematics 3.2.6 Toppling and Sliding

Practise testing limiting equilibrium by locating the centre of mass, taking moments about the contact edge and combining normal reaction with limiting friction.

Exam points

for impending toppling, place the weight line through the contact edge or take moments there
for impending sliding, use limiting friction with horizontal and vertical force balance
compare the centre-of-mass projection with the support boundary before stating stability

[Maximum number: 3]

Figure for Question 3.2.6—Toppling and sliding question 1 — CAIE A-Level Further Math A2

A uniform square lamina ABCD has sides of length 10 cm. The point E is on BC with $E C=7.5 \mathrm{~cm}$ , and the point F is on DC with $C F=x \mathrm{~cm}$ . The triangle EFC is removed from ABCD (see diagram). The centre of mass of the resulting shape ABEFD is a distance $\bar{x} \mathrm{~cm}$ from CB and a distance $\bar{y} \mathrm{~cm}$ from CD.

Find the greatest possible value of x, giving your answer in the form $a+b \sqrt{2}$ , where a and b are constants to be determined.

Use condition: $\bar{x} \geqslant x$

B1

$2 x^{2}-80 x+400 \geqslant 0$

M1

$x=20-10 \sqrt{2}$

A1

4b 3

All question bank results loaded

3.2.6—Toppling and sliding question 1