why is work done a scalar and not a vector.?

Question

work is said to a dot product of two vectors =s.f

Answer 1

force and distance are taken to be vector quantities, and combined using the dot product:


where φ is the angle between the force and the displacement vector. This formula holds true even when the object changes its direction of travel throughout the motion.

In mathematics, the dot product, also known as the scalar product, is a binary operation which takes two vectors over the real numbers R and returns a real-valued scalar quantity.

so u see work is scalar which is a product of two vectors

Answer 2

avobe people are wrong. distance is scalar not vector. displacement is vector. and work = force * displacement. and the dot product of two vectors is always a scalar hence work done is scalar. also scalar quantities do not have any sense of direction as work.

Answer 3

u ve the answer in the question itself. dot product means mulptiplication of two vectors which eventually gives u a scalar. in this case work done is the dot product of force and distance. both of the latter have a magnitude and direction (meaning they are scalar); whereas work done has only magnitude (it doesnt have a specific direction). and work done doesnt depend on the path followed and time taken.

Answer 4

ok. work done = force (vector) * delta (x) (direction) (which is also a vector). Here delta x is displacement with vectors in x, y, z plane. Also force is a vector in directions x, y, z.

W.D. = (F(x)+F(y)+F(z)).(D(x)+D(y)+D(z)) where D is the displacement in x, y and z directions. (.) stands for dot product. or simply WD = F(x)D(x)+F(y)D(y)+F(z)D(z) since sin 90 = 1 and sin 0= 0 with no sense direction as directions cancel themselves in dot product x.y=y.z=z.x=0.

Answer 5

because vector quantity also contains direction
for e.g. distance-scalar(any direction)
displacement-vector(in a particular direction)

i don't remember the formula if you can give that i can explain it in a better way

Answer 6

a vector can be drawn cause, apart of its scalar value, it also has a direction and a sense (that's why, speed is a vector, for instance......cause you can draw the direction and the sense of the speed.......which you can't do for work)