Vectors in two dimensions

Question 1

What is the difference between a vector and a scalar?

Answer 1

A scalar has magnitude only while a vector has magnitude and direction

Question 2

How do you determine the resultant of two forces using the tail-to-head method?

Answer 2

Step 1: Draw the first force vector, then draw the second vector, with its tail from the head of the first vector.
Step 2: Draw the resultant from the tail of the first vector to the head of the second vector.

Question 3

How do you determine the resultant force value of two forces that are perpendicular to each other?

Answer 3

Use the theorem of pythagoras

Question 4

How do you determine the resultant of two or more force vectors in two dimensions?

Answer 4

Step 1: Add all forces in the x-direction.
Step 2: Add all forces in the y-direction.
Step 3: Use theorem of pythagoras

Question 5

How do you determine the direction of a resultant force?

Answer 5

Use the equation tan @ = Ry/Rx

Question 6

What equations are used to resolve a force vector into its components?

Answer 6

Rx = Rcos @
Ry = Rsin @

Question 7

How do you determine algebraically the resultant of two or more force vectors using their components?

Answer 7

Step 1: Determine the x and y components of each force.
Step 2: Add all the x-components separately (to get Rx) and add all the y-components separately (to get Ry).
Step 3: Use equation R^2 = (Ry)^2 + (Rx)^2 to solve for R.

Question 8

How do you determine the resultant of two forces at 90 degrees to each other using the tail-to-tail method?

Answer 8

Step 1: Draw the two force vectors joined at their tails.
Step 2: Draw a dotted line parallel to the first vector that touches the head of the second vector
Step 3: Repeat step 2 with the other vector
Step 4: Draw the resultant from the tails of the two vectors to the intersection of the two dotted lines.