work is not a scalar quantity

Question

physical science 

Answer 1

Work is a scalar quantity.  It is the scalar product of two vectors (also called the dot product), a force vector and a displacement vector.  Even though both are vectors, the scalar product of the vectors is a scalar.  Mathematically, it is the projection of the force in the direction of the displacement multiplied by the magnitude of the displacement, which is the same as the projection of the displacement in the direction of the force multiplied by the magnitude of the force.

 

F = force vector

|F| = magnitude of the force vector = a scalar

d = displacement vector

|d| = magnitude of the displacement vector = a scalar

θ = angle between the force vector and the displacement vector

W = work

 

W = F·d = |F||d|cosθ = a scalar

Answer 2

It is not scalar because work is a vector quantity.  The reason for this is that to establish work, you need to apply a force to an object in a specific direction.  Since force is a vector, work must also be a vector.

 

The formula for work is

 

W = Fd

 

where:

W = work

F = force

d = distance