are work and power scalar or vector quantities? pls explain your answers?

Question

Further to this question, if displacement and force are given in terms of their i,j and k components, how can the power be calculated?

Answer 1

Work and power are both scalar quantities. When somebody talks about the work done there is no reference to what direction it is done in. The same goes for power: it makes no sense to speak about the direction power was delivered in.

Answer 2

Those two questions are not worded very well. It's true that "force is a vector"; and it's also true that "pounds are a unit of force"; but it is not quite true that "2 pounds" is a vector. I understand the point that the question's author (your teacher?) is trying to make; but he/she makes it poorly. Technically speaking, in Question #1, there is only one choice which IS a vector, and that is "d". And technically, in Question #2, ALL of the choices are scalars. That is because, technically, a vector is a quantity that is expressed by using TWO numbers; one number to express a "magnitude" (an amount); and the other number to express a direction. (Or, if the vector is in 3 dimensions, then you use three numbers; one to express the magnitude, and two to express the direction). "East" can be translated into a number (you could say it's "90 degrees" in some frame of reference); so "2 kilometers per hour east" counts as a vector. None of the other choices (in either question) is truly a vector, however; because the simple fact is, it's not a vector if it's described using only one number. In physics, certain concepts (such as "force" and "momentum") are not very useful unless you attach a direction to them; so they are virtually always expressed as vectors. Other concepts (such as "mass" and "time") aren't usually associated with any particular direction; so they are virtually always expressed as scalars. Still other concepts (such as "speed" and "length") are sometimes useful with a direction attached, and in other cases useful without a direction; so they may sometimes be expressed as vectors and sometimes not (to emphasize the difference, "speed" is called "velocity" when it has a direction attached; and "length" is called "displacement" when it has a direction attached). So in summary: 1) The technically correct distinction is: If a quantity is expressed in terms of both a magnitude and a direction, it's a vector; if it's expressed in terms of magnitude only, it's a scalar. 2) In physics, some kinds of quantity are virtually always associated with a direction, and other kinds virtually never are. You can use this fact to get the "right" answer in your workbook, even though (I maintain) the workbook is technically incorrect.

Answer 3

Both work and power are scalars. Both force and displacement are vectors, but work is their dot product, which makes it a scalar. Similarly for power, which is the dot product of force and velocity.