is work a scalar quantity if yes then why doess direction of force matter in it?

Question

and if no then why do books show it a scalar quantity

Answer 1

yes work is a scalar quanitity ....

force when applied on a body causes movement(displacement) and hence work is done on the body ...

W=F.S( here we take dot product of vectors hence we get a scalar)


here mod(W)=mod(F)*mod(S)*cos(X) (Xis angle btwn force and displacement)

i.e w=0 when x is 90 degrees
w=f.s when x is 0 degrees
w= - f.s when x is 180 degrees
hence depending on direction of force w.r.t displacement the work done varies...

Answer 2

Work is a scalar quantity defined with respect to two vectors: Force and displacement. If these vectors change in any way direction or magnitude, then the value of work will change. But we never say so much work is done in any definite direction.

To decide whether a given physical quantity is scalar or vector one has to see what happens to it or its expression when the frame of reference is rotated. If there is a vector F represented by its three components Fx, Fy and Fz and the displacement vector is S with its components Sx, Sy and Sz. and now we rotate the frame of reference, then Fx, Fy and Fz and so also Sx, Sy and Sz will have respectively different values in the new reference frame, but there will be no change in W = F.S because its value depends upon magnitudes of F and S and the angle between these vectors, all these three quantities are scalar because they do not change when reference frame is rotated.

Answer 3

Work done by a force in displacing a body by x is given by
W=F.x here '.' implies vector scalar product or dot product.
If simplified this gives

W=|F||x|cos(theta) where theta is the angle made by the force vector with the displacement vector and | | indicates absolute value. Theta will change as direction of force changes, hence the result!

Answer 4

Because work is defined as a scalar product of force vector and path vector. If for instance force is perpendicular to the path the work (done by that force) is zero, although neither force nor path might be zero.

Answer 5

yes work is a scalar quantity....on the other hand...FORCE applied in doing the work is ..obviously...a vector quantity...don't confuse the two.

Answer 6

work yeah is a scalar product...or a dot product...
according to vector algebra, (identity it is)... that a vector dotted to a scalar, is scalar...
force vecter distance scalar...right
but with vector product, or cross product, when a vector is crossed to a scalar, it can not be posssible.... only cross vectors with vectors...