Vectors

Question 1

How should vectors be connected?

Answer 1

From head to tail

Question 2

How can vectors be subtracted from one another?

Answer 2

By adding the negative of the 2nd vector.

Question 3

What are the perpendicular parts of the vector called.

Answer 3

They are called component vectors, specifically the horizontal and vertical components of a vector.

Question 4

Express mathematically how to find the horizontal component of a vector.

Answer 4

|𝐹⃗_h|=|𝐹⃗ |cos⁡𝜃

Question 5

Express mathematically how to find the vertical component of a vector.

Answer 5

|𝐹⃗_v|=|𝐹⃗ | sin⁡𝜃

Question 6

A cannon tilted 30° from the horizontal fires a cannonball at 40 m s-1. Determine the horizontal and vertical components of its initial velocity.

Answer 6

Express mathematically the horizontal and vertical components.

Question 7

State the sine and cosine rules and when you use them to solve the resultant vector

Answer 7

You use the sine or cosine rules to solve vectors when the angle between the resultant vectors is not a right angle. The sine rule is 𝑎/sin⁡𝐴 =𝑏/sin⁡𝐵 =𝑐/sin⁡𝐶 and the cosine rule is 𝑎=√(𝑏^2+𝑐^2−2𝑏𝑐 cos⁡𝐴).

Question 8

What is translational equillibrium?

Answer 8

Translational equilibrium is when the forces acting on an object is balanced. This happens when the object is not accelerating. Translational equilibrium is when the mathematical sum of forces equal 0.

Question 9

When can the forces on an object in translational equilibrium can be considered and provide an example.

Answer 9

The forces on an object in translational equilibrium can be considered along any straight line. For example, Σ𝑭_up =Σ𝑭_down and Σ𝑭_left = Σ𝑭_right.