2007-03-15 00:29:17 · 12 answers · asked by Anonymous in Science & Mathematics ➔ Physics
because work is like energy and is not a vector. it is simply a magnitude.
Force is a vector and the displacement is a vector but work cannot be a vector. it doesn't have DIRECTION. just like energy has no direction.
when you dot product two vectors, the direction goes away.
2007-03-15 00:34:19 · answer #1 · answered by a1tommyL 5 · 1⤊ 1⤋
Work is force through a distance so the dot product represents the portion of the force measured in the direction of movement and is a scalar quantity. A cross product will give you a vector at right angles to the other two vectors which does not fit the definition of work.
2007-03-15 00:59:58 · answer #2 · answered by Gene 7 · 0⤊ 0⤋
Dot product is used when the direction is in the same plane of the two quantities..
and Cross product is used when the quantity is perpendicular to both the quantities used..
Work is usually defined in terms of the dot product because it is only the component of the force along the direction of motionof the object - F cos(q) - which does any work and the dot product nicely expresses product in a compact form. One corollary is that the perpendicular component of the force can never do any work on object.
You can understand the fundamental of cross product by thumb rule..
2007-03-15 00:35:55 · answer #3 · answered by Anonymous · 0⤊ 0⤋
Dot Product Work
2016-12-12 09:52:11 · answer #4 · answered by vaibahv 4 · 0⤊ 0⤋
By definition, work done by an applied force is the displacement in the direction of the force applied. Dot product of force and displacement gives the magnitude of the component of displacement in the direction of the force because dot product of any two vectors is the projection of one vector on the other.It is a scalar simply because it is the magnitude of the component.
2007-03-15 02:45:55 · answer #5 · answered by vishal 1 · 0⤊ 0⤋
Work is usually defined in terms of the dot product because it is only the component of the force along the direction of motionof the object - F cos(q) - which does any work and the dot product nicely expresses product in a compact form. One corollary is that the perpendicular component of the force can never do any work on object.
For a more detailed explanation with illustrations, please refer to the source website. Hope this helps.
2007-03-15 00:39:14 · answer #6 · answered by zhoix_12 2 · 0⤊ 0⤋
Work done=Fxd is the product of magnitude of force acting on the body and its displacement.
In vector form,work done is the dot product or the scaler product of force and displacement. It has only magnitude but no direction.Cross product is the vector product.
2007-03-16 02:42:09 · answer #7 · answered by sagar k 1 · 0⤊ 0⤋
Work is a scalar quantity and the cross product of 2 vectors gives answer in vectors.
2007-03-15 01:58:19 · answer #8 · answered by manarshh_jot 2 · 0⤊ 0⤋
we know work done is the product of force and displacement....right.. as force is a vector it acts on the body in many directions, truly it will have vertical and horizontal components.... i.e fsin(theta) and f cos(theta)....of those the body moves in the direction of fcos(theta)....so the formula becomes fcos(theta)*displacement in that direction....that yields a scalar i.e work....consider this example even if u apply the same force in inclined direction the work wont be the same.....here only fcos(theta) plays the role.... so work is a scalar....
2007-03-15 04:52:47 · answer #9 · answered by naga 1 · 0⤊ 0⤋
Bcz it is energy ,a scalar quantity, hence doesnt posses any direction.Energy is expressed only in magnitude.
2007-03-16 01:11:47 · answer #10 · answered by vivek 2 · 0⤊ 0⤋