In this lesson, we will learn how to solve problems using Lami's theorem.

Q1:

A home-built swing is suspended by a rope passing through two pulleys, π΅ and πΆ , whose ends meet at point π΄ where the swing is attached. The rope segments π΄ π΅ and π΄ πΆ make angles of 4 0 β and 4 5 β with the horizontal, respectively. When a child sits still on the seat, the tension in π΄ π΅ is 199 N. Given that, in this condition, the system is in equilibrium, find the combined weight of the child and the seat π and the tension π in the rope π΄ πΆ , giving your answers to the nearest two decimal places.

Q2:

A particle is in equilibrium under the action of three coplanar forces of magnitudes πΉ N, 15 N, and 25 N. Given that the last two forces are perpendicular to each other, determine the value of πΉ .

Q3:

The diagram shows a body weighing 6.1 N suspended in equilibrium by two light, inextensible strings, π΅ πΆ and π΄ πΆ . Given that π΅ πΆ = 2 . 4 c m , π΄ πΆ = 3 . 2 c m , and the strings are perpendicular, find the tensions π 1 and π 2 .

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