Secondary IV • 1yr.

Why do we sometimes calculate the work with the cos of the angle between the force and the displacement and sometimes without? Is this in a special case or an exception?

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Secondary IV • 1yr.

Explanation from Alloprof

This Explanation was submitted by a member of the Alloprof team.

Good morning LucidWhale7282,

Thank you for your question.

Depending on the information given, work may be calculated using two formulas (W=△E, where W= Works (J) and △E=energie variation (potential or kinetic) (J)) or W=F⋅△x, where W=work (J), F=force (N), and △x=displacement of the object (m)).

Therefore, often, problems give you a displacement, a force, and an angle, and you will need to calculate the find the force component in the same direction as the movement before calculating the work.

For example :

We pull on a suitcase with a force of 150N on 10 meters and forming a 30-degree angle with the ground. What is the work done by the suitcase?

Therefore, you will need to start by calculating the effective force to find the force component in the same direction as the movement :

Feff=F⋅cosθ⇒Feff=150N⋅cos30∘=129,9 N.

Then, you will be able to calculate the work :

W=F⋅△x⇒W=129,9 N⋅10 m=1299 J

And the answer will be 1299J.

I hope you found my answer helpful.

Do not hesitate to ask us more questions if needed!

Emilie