Doubt in the basics definition of work

[ehabmozart]

Hello!

In my studying of work I've always been told that work done (by what? ) = Force (component along its path) times the distance it moves. Mathematically, W=F.s ... My question here is what is the geometrical presentation of saying Force x Distance ... In other words, when we multiply force vector times the displacement vector, what does it mean. If for example dot product the force vector by the unit vector of say the x-axis < 1, 0 ,0 > we will get the x component of the force. What is the case for work??

Thanks a lot for bearing my lengthy piece. And thanks in advance to whoever gives me a kind hand

 

[Doc Al]

If for example dot product the force vector by the unit vector of say the x-axis < 1, 0 ,0 > we will get the x component of the force. What is the case for work??

Take the dot product of the force and the displacement vectors. You are essentially taking the component of the force parallel to the displacement and multiplying it by the displacement.

 

[Chestermiller]

The idea is that, if an object is moving to the east, and you apply a force on the object directed to the north, the object continues moving to the east at the same speed; so no work is done by the force as far as the movement to the east is concerned. But, the object is accelerating to the north, so the force is doing work on the object in that direction. So the conclusion is that only the component of movement parallel to the direction of the force results in work being done.

Chet

 

[A.T.]

My question here is what is the geometrical presentation of saying Force x Distance

That would be the cross product. But work is the dot product.

If for example dot product the force vector by the unit vector of say the x-axis < 1, 0 ,0 > we will get the x component of the force.

Yes, that is the geometrical presentation of a dot product.

 

[PJC01]

.

Hello! It's great that you are questioning the basics of work and trying to understand it better. It shows that you have a curious and analytical mind, which are important qualities for a scientist.

To answer your question, the geometric representation of work is the product of the force vector and the displacement vector. This means that the force and displacement vectors are multiplied together to get the result of work. The result of this multiplication is a scalar quantity, which means it only has magnitude and no direction. This scalar quantity represents the amount of work done.

Similarly, when you take the dot product of the force vector and the unit vector of the x-axis, you are essentially projecting the force vector onto the x-axis. This gives you the x-component of the force, which is a scalar quantity.

In summary, the dot product of the force vector and the displacement vector in the definition of work represents the scalar quantity of work done. It is similar to taking the dot product of the force vector and the unit vector of the x-axis, which gives you the x-component of the force. I hope this helps clarify your doubt. Keep up the good work in your studies!