Co-planar forces on a crane

How to use this resource

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Below is an interactive which supports the resource. The interactive can be launched by clicking on its image, or through links in the PDF itself.

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Topic areas

Mechanical engineering

  • Direct forces
  • Concurrent co-planar forces
  • Force diagrams
  • Resultant of a set of co-planar forces
  • Conditions for equilibrium and motion
  • Newton’s second Law, F = ma


  • Vector addition
  • Resolving a vector into two perpendicular components
  • Trigonometric functions for sine and cosine
  • Trigonometric identities
  • Simultaneous equations



Problem statement

Mechanical design engineering is the basis of every engineered structure, whether static (non-moving) or dynamic (moving). One very important aspect is the calculation of the forces acting within and upon a structure and using these to ensure any design will be able to withstand the stresses and strains expected of it without failure. 

For example, in the crane image, the cables must be strong enough to lift and move the bucket, while the rigid mechanical frame must be able to support the load without buckling. Additionally, the whole crane must be stable so that it does not tip over when manoeuvring a full bucket. How can the forces acting on a structure be determined and how do they change when an object that is initially stationary starts to move?


Click the image to load vector force addition interactive. 

The above interactive can be used to demonstrate and test knowledge of the vector addition of forces that are represented as column vector and determine whether they are in equilibrium  or not.

Click the image to load resolve forces interactive. 

The above interactive can be used to demonstrate and practice the resolving of forces into horizontal and vertical components.

Click the image to load resolve forces bucket interactive. 

The above interactive can be used to demonstrate and practce solving the tension problem for user-definded angles.

Supported by

  • Royal Academy of Engineering
  • Motorola Solutions Foundation