A traffic light of mass is hung from a point on the ceiling by two light

PHYSICS · Subjective · AP · Physics 1: Algebra-based · Force and Translational Dynamics · Force and Translational Dynamics

Problem

A traffic light of mass

12\,\text{kg}

is hung from a point

O

on the ceiling by two light, inextensible cords

OA

and

OB

. Cord

OA

is fastened to the ceiling such that it makes an angle of

30^{\circ}

with the horizontal on the left side of

O

, while cord

OB

makes an angle of

45^{\circ}

with the horizontal on the right side of

O

. (i) Draw a clear free-body diagram of the traffic light, showing all external forces acting on it. (ii) Derive algebraic expressions for the tensions

T_1

OA

and

T_2

OB

in terms of the weight

W

of the light and the given angles. (iii) Calculate the numerical values of

T_1

and

T_2

. (iv) Using a suitable scale (e.g.

1\,\text{cm}

represents

20\,\text{N}

), construct a vector triangle for the three forces and verify graphically that the light is in equilibrium.

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