Which of the following is a scalar quantity?
displacement
perpendicular component of force
parallel component of force
work
DISPLACEMENT
I am inclined to disagree.
Displacement is a vector with magnitude and direction. DISTANCE is the scalar magnitude of displacement.
However Work, for example in Joules, is clearly scalar and has no direction. It is a dot product of force and displacement vectors and has no direction.
Components of vectors such as components of a force vector are also scalars. They are the dot product of the vector with the unit vector in the component direction.
For example Fx = F dot i = |F|cos of angle to x axis
To determine which of the following is a scalar quantity, let's understand what a scalar quantity is. A scalar quantity is a physical quantity that only has magnitude and no direction. In contrast, a vector quantity has both magnitude and direction.
Now, let's analyze each option:
1. Displacement: Displacement is a vector quantity as it includes both magnitude (the distance) and direction (the change in position).
2. Perpendicular component of force: Force is a vector quantity, and its perpendicular component also has both magnitude (the force) and direction (perpendicular to the force).
3. Parallel component of force: Similar to the perpendicular component, the parallel component of force is also a vector quantity as it has both magnitude (the force) and direction (parallel to the force).
4. Work: Work is the scalar quantity in this list. Work is defined as the dot product of force and displacement. While force and displacement are vector quantities, their dot product results in a scalar quantity, which represents the energy transferred or expended.
Therefore, the scalar quantity among the given options is work.