Scalars and Vectors

what are scalars?

quantities that have magnitude but no direction.

what are vectors?

quantities that have both magnitude and direction.

what are some examples of scalars?

temperature, mass, energy, distance, speed, density, time.

what are some examples of vectors?

displacement, velocity, weight, acceleration, force, pressure, momentum, gravity,drag.

what is displacement?

the length and direction of a straight line drawn from the starting point to the finishing point.

what is velocity?

a measure of displacement of an object per unit time.

can an object have a constant speed but a changing velocity?

yes, if the speed is constant but the object is changing direction.

what are the two ways to add vectors?

calculation-if the vectors are perpendicular, scale drawing if vectors aren't perpendicular.

how do you do vector calculation?

combined vectors produce a right angled triangle and magnitude of resultant vector is found using Pythagoras' theorem. direction of resultant vector is found from angle it makes with horizontal or vertical.

how do you do a vector scale drawing?

link vectors head to tail, draw in resultant vectors, measure length with ruler and angle with protractor.

what is resolving a vector?

when a single resultant vector is represented by two vectors.

what are components?

the parts a single resultant vector is broken down into.

regarding forces on an inclined plane, what is the normal force equal to?

Fn=mgcos(theta)

regarding forces on an inclined plane, what is the x component force fg equal to?

fg=mgsin(theta) since they are parallel to eachother.

regarding forces on an inclined plane, how do you find acceleartion of an object moving down the slope with and without friction.

with friction- a=gsin(theta)- muk gcos(theta)

without friction- a=gsin(theta)

regarding forces on an inclined plane, how do you find the acceleration of an object moving backwards up an incline, with friction and also in the reverse direction?

block moving in positive x direction- a=-gsin(theta)-muk gcos(theta)

block moving in negative x direction- a=gsin(theta)+muk gcos(theta)

when is an object in equilibrium?

when it is at rest or moving at a constant velocity.

in equilibrium what are coplanar forces represented by?

a closed vector triangle

what is equilibrium?

a state where all forces acting on an object are balanced, there is no net resultant force, the sum of all moments is zero.