A light rod of length is hinged at the end so that it can rotate freely in a vertical…

PHYSICS · Subjective · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

A light rod

AB

of length

1.2\,\text{m}

is hinged at the end

A

so that it can rotate freely in a vertical plane. Two coplanar forces act on the rod: (i) a force

F_1 = 25\,\text{N}

acting at the midpoint

C

of the rod, making an angle of

30^{\circ}

with

AC

on the side that tends to rotate the rod anticlockwise about

A

. (ii) a force

F_2

acting at the free end

B

, making an angle of

\alpha

with

AB

on the side that tends to rotate the rod clockwise about

A

. (a) Taking anticlockwise torque as positive, write an expression for the net torque about

A

in terms of

F_2

and

\alpha

. (b) Hence obtain the condition for rotational equilibrium of the rod. (c) If

F_2 = 40\,\text{N}

, determine the angle

\alpha

(to the nearest degree) required for equilibrium. (d) The force

F_2

is now kept at

60^{\circ}

while its magnitude is varied. Calculate the value of

F_2

that will bring the rod into rotational equilibrium.