A single block brake with a short shoe and torque capacity

A single block brake with a short shoe and torque capacity of 250 N-m is shown. The cylindrical brake drum rotates anticlockwise at 100 rpm and the coefficient of friction is 0.25. The value of a, in mm (round off to one decimal place), such that the maximum actutating force P is 2000 N, is_____.

T = 250 Nm
F × r = 250

⇒ F =	250
	a

P × 2.5a = F ×	a	=	F	× a
	4		μ

2000 × 2.5a =	250 × a	+	250	×	a
	a × 0.25		a		4

a =	1000 + 62.5
	5000

=	1062.5	= 212.5 mm
	5000