1.1 vectors

1.1 Forces and Vectors

Forces

• What is a force?• A force is a PUSH or PULL experienced by an

object.• The ‘F’ in F=ma represents ‘Force’• What different types of forces are there?

The Earth PULLS the moonThe moon PULLS the Earth

The shoe PUSHES the groundThe ground PUSHES the shoe

The man PUSHES down on the chairThe chair PUSHES up on the man

Vectors

• To understand a force’s influence on the world, you need to know two qualities about the force …

• 1. Its magnitude (or size)• 2. Its direction• Quantities whose magnitude and direction are

important are called VECTORS• Quantities whose magnitude only is important

are called SCALARS

Vectors and Scalars

Vectors• Force• Velocity• Acceleration• Displacement• Field Strength

Scalars• Mass• Speed• Length• Distance• Energy

Velocity and speed

• Bill runs at a speed of 4m/s• Brian runs at a speed of 6m/s• Who will win the race?• It depends which direction each is running in.• VELOCITY is important• While running, both athletes run into a tree.• Who feels the most pain?• Brian• Here, only SPEED is important.

More on Vectors

• For objects moving in opposite directions …• One direction will be seen as POSITIVE• The opposite direction will be see as …

– NEGATIVE

• Quantities acting neither in the same direction nor the opposite direction will require the help of SINE and COSINE.

Question

• Tony lives 2km away from his work. In the morning, he leaves home at 8.30am and arrives at work at 9am. In the evening, he leaves work at 5pm and returns home at 5.30pm.

• Over the course of the day, what is Tony’s:– Total distance? (Scalar)– Total displacement? (Vector)– Average speed? (Scalar)– Average velocity? (Vector)

• Draw a graph showing how each of these 4 quantities change with time.

Distance

Time

Displacement

TimeSpeed

Time

Velocity

Time

Adding Scalars

A man drives from his home 3km to the nearest KFC. After collecting his meal, he then drives another 2km. How far has he driven in total?5km

• Adding scalars is very easy• You just need the normal rules of arithmetic• (ie: ‘+’).

Adding Vectors

• A man drives from his home 3km to the nearest KFC. After collecting his meal, he then drives another 2km. How far is he from his home?

• Assuming that he drives in a straight line before and after KFC …

• His displacement depends on which direction he drives after KFC

• The solution could be anything between …• 1 and 5km

• The sum of two or more vectors …• Is the SINGLE vector …• Which would have the same effect as the two or more

original vectors.• Draw arrows to represent each vector• Align arrows into a ‘snake so that one tail starts where

another head finishes• Join the head and tail of the snake• This is the SUM of your vectors, or RESULTANT

vector.

Home KFC

New positionMagnitude

angle

Question

• What is the SUM of the forces, or RESULTANT force on this crate?

• Move the arrows and draw in the RESULTANT vector.

70 N

50 N

Answer

70 N

50 N

m

a

m =

(70^2 + 50^2)^0.5

=86 N

a =

inv. tan (50/70)

=35.5 deg.

Question 2

• What is the SUM of the forces, or RESULTANT force on this crate?60 60

• In a closed loop, the RESULTANT vector is zero.

Resolving Vectors

In the same way that two vectors can be combined into one

It can also be useful to …

Divide one vector into two COMPONENTS

This is called RESOLVING

aV S

ine

aV Cos a

The component next to the angle

is ‘Cosine (a)’

The component far from the angle

is ‘sine (a)’

V

Resolving Vectors





aV S

ine

aV Cos a


is ‘Cosine (a)’


is ‘sine (a)’

Resolving Vectors





aSin

e a

Cos a


is ‘Cosine (a)’


is ‘sine (a)’

Question

• A boat intends to take the shortest route across a river (AB)

• However, it is pushed sideways by the current at an angle of 15 degrees

• If the boat’s actual velocity is 10 m/s…

• What velocity is due to:

– The boat’s engine?

– The current?

A

B

1510m/s

Homework

AS & A2 Success PhysicsPage 29Questions 1 & 2

1.1 vectors

Science