# Worksheet: Resultant of a Set of Coplanar Forces Acting at a Point Geometrically

In this worksheet, we will practice solving problems involving the resultant of a set of coplanar forces acting at a point geometrically using a polygon of forces.

Q1:

Dina is attempting a mechanics problem in which four coplanar forces , , , and are acting on a body. She needs to determine whether the body is in equilibrium or not. She remembers her teacher saying something about checking whether she could arrange the forces into a polygon. So, she has drawn the shown parallelogram.

Dina concludes that the forces are in equilibrium. Is she correct?

• AYes
• BNo

Which of the following best describes what she has done?

• AShe has got the right answer. However, her figure is wrong. She has not paid attention to the direction of the forces. All the forces should meet head-to-tail, whereas, in her diagram, and meet head-to-head and and meet head-to-head. However, since the forces form a parallelogram, she can swap and over and she will have a correct diagram.
• BShe has got the wrong answer because she has not arranged the forces in numerical order.
• CShe has got the wrong answer because all the forces should meet head-to-tail, whereas, in her diagram, and meet head-to-head and and meet head-to-head. So, the forces do not form a polygon and they are not in equilibrium.
• DShe has got the right answer using the right method.
• EShe has got the right answer. However, her figure is wrong; she has not paid attention to the order of the forces. She should have arranged the forces in numerical order.

Q2:

Six coplanar forces , , , , , and are acting on a body in equilibrium. Their polygon of forces is shown.

Given that , , , , and , find the magnitude of .

• A newtons
• B 19 newtons
• C newtons
• D newtons
• E 6 newtons