UNIT 1: Forces and movements

ESO 2

WHAT IS MOVEMENT?

Which of these things move?

For people on the big wheel, the

boat moves but to people on the

boat, it will be at rest.

Great example of

movement and systems

of reference

We say that an object is moving when it changes its position with respect to another one that we consider as fixed.

Don't forget that even if you appear to be standing still, the Earth is moving around the Sun, and the Sun is moving around our galaxy.

Everything in the universe moves. Movement can be slight or slow, but it still happens.

MOTION ELEMENTS

Trajectory.

Position.

Distance travelled

Time taken

Speed

Acceleration.

TRAJECTORY

Trajectory is the path that a moving object follows through space. It can be rectilinear, circular, elliptical, parabolic, etc.

POSITION

Position is where an object is located. If we want to describe the movement of a person who is running, we measure the distance from the person to a point that we have taken as reference. This distance is called position and is represented by the letter “s”.

Positions on the left of the reference system are often taken as negative and on the right as positive.

R + -

1m

s0 s1 s2 s3

s0 = - 6 m

s1 = - 4 m

s2 = + 3 m

s3 = + 8 m

The positions of the ball would be:

DISTANCE TRAVELLED

The distance travelled is equal to the subtraction between two positions, the final position minus the initial position if there is no change in the sense of the movement.

R + -

1m

s0 s1 s2 s3

The distance travelled by the ball from the initial position to

the position 3, would be:

distance travelled = s3 - s0 = 8 m – (-6 m) = 8 m + 6 m = 14 m

The position can be either a positive or a negative

number but the distance travelled is always a positive

number.

Imagine that the ball goes from the position 3 to the position 2.

The distance travelled would be: s2 - s3 = + 3 m – 8 m = - 5 m

However, we will say that the distance travelled is 5 m.

R + -

1m

s0 s1 s2 s3

Example

SPEED

Speed is how fast an object is moving. It is the ratio between the distance travelled and the time elapsed to do it. It is represented by the letter “v”.

The mathematical expression of the speed is:

Distance

Speed (v)

Time

The SI unit of speed is m/s

REMEMBER SIDOT Speed Is Distance Over Time

A sheep is running down a farmer’s track. It takes exactly 10 seconds

to move between two fence posts, 10 meters apart. What’s the sheep`s speed?

Step 1) Write down what you know:

Distance: 10m Time: 10 seconds

Step2) We want to find speed:

Speed (v) = Distance (e) / Time (t)

v= 10/10= 1m/s

Example

• A car is moving on a straight road at an average speed of 72km/h. Calculate the distance covered in one and a half hours. Use SI units.

Distance= Speed*Time

e= 72km/h*1,5h=108h 108.000m

Distance

Speed (v)

Time

An athlete can run long distances at 4 metres per

second. How far can she run in?

a) 50 seconds --------------------------200m

b) 3 minutes---------------------------- 720m

c) 1 hour--------------------------------- 14400m

d) 2 hours and a half----------------- 36000m

A dog can run long distances at 3 metres per second.

How long can it run in?

a) 120 meters ------------------------ 40 s

b) 1200 meters-------------------------400s

c) 2100 meters ----------------------- 700s

d) 5400 meters------------------------ 1800s

An athlete can run long distances at 8 meters per

second. How far can he run in?

a) 10 seconds --------------------------80m

b) 12 minutes----------------------------5.760m

c) 1 hour and a half -------------------43.200m

d) 2 hours -------------------------------57.600m

a)How long does he take him to row:

• 70 m---------------------------------------35s

• 800 m ------------------------------------400s

• 1 km and a half ------------------------750s

b) How far can Andrew row in:

• 12 seconds-----------------------------24m

• 3 minutes and a half-----------------420m

• 4 hours-----------------------------------28800m

Andrew rows at an average speed of 2 meters per

second.

Use common sense with speed

• Although it is very important use SI unit sometime has no sense use it. For instance:

Average speed of the Continental

Plates is 2cm per year

6,34*10-10 m/s

Average speed of halley’s comet

is 100km/s

10*104m/s

A snail moves 5 m in 2 hours. If it moves at the same

speed all the time, calculate:

a) The time it takes to move 20 m------------------------------- 8h or 28000s

b) The time it takes to move 1 m --------------------- 0,4h ó 24min ó 1440s

c) The distance it would move in 3 hours and a half ------------ 8,75m

d) The distance it moves in 15 minutes -----------------------------0,625m

GRAPHS OF THE UNIFORM MOTION (I)

Distance versus Time

In the uniform motion the speed is always the same.

The distance-time graph for constant speed is a straight line.

DO NOT FORGET

• The graph s/t doesn’t say to us

anything about the trajectory

GRAPHS OF THE UNIFORM MOTION (III)

(example)

The steeper the

straight line is,

the faster the

movement is

vA 4 m/s vB 2 m/s

VB =4m/s

VA =2 m/s

Draw the distance-time graph for 6 m/s and 8 m/s constant speed

.

Draw the distance-time graph for 3 m/s and 10 m/s constant speed

.

v (m/s)

t (s)

GRAPHS OF THE UNIFORM MOTION (II)

Speed versus Time

In the uniform motion the speed is constant.

The velocity-time graph for constant velocity is a horizontal line.

Speed (m/s)

Distance (m)

Time (s)

20m/s 20m 1s

20m/s 40m 2s

20m/s 60m 3s

20m/s 80m 4s

20m/s 100m 5s

ACCELERATION

If speed does not change in a movement, it is an uniform motion and if it changes in a movement, it is an accelerated motion The acceleration is defined as the ratio between what the speed has changed and the time elapsed to occur that change. In other words Acceleration is defined as the rate at which an object changes its speed. An object is accelerating if it is changing its speed. It is represented by the letter “a”. The mathematical expression of the acceleration is:

vfinal - vinitial

a

tfinal - tinitial

The SI unit of acceleration is m/s2

A cyclist accelerates from 0 m/s to 8 m/s in 3 seconds. What is his acceleration ?

A car accelerates from 0 to 30 m/s in 8 seconds. What is its acceleration?

vfinal - vinitial

a cyclist

tfinal - tinitial

8 m/s – 0 m/s

3 s – 0 s

2,6 m/s2

vfinal - vinitial

a car

tfinal - tinitial

30 m/s – 0 m/s

8 s – 0 s

3,7 m/s2

Example

A race car accelerates uniformly from 18.5 m/s to 46.1 m/s in 2.47 seconds.

Determine the acceleration of the car

a = 11.2 m/s2

FORCES

• A FORCE IS ANYTHING

THAT CAN DEFORM A

BODY OR CHANGE ITS

STATE OF MOVEMENT OR REST

FORCES (II) • Forces are nearly always pushes and pulls.

• We need to use a force to get something moving.

• Small forces can be measured with a force meter in

units called Newton (N).

• Forces have direction and we use arrows

to show the direction of a force

.

FORCES (III)

• A force can

• Change the direction

• Speed something up

• Slow something down

• Change shape

MASS versus WEIGHT

MASS WEIGHT

It measures the amount of matter.

It measures the gravitational force acting on an object.

Mass is measured in kilograms, kg, or grams, g. Weight is a force and forces are measured in Newton, N.

The mass of an object doesn’t depend on its location.

The weight of an object weight depends on its location, because the gravitational force varies with the location. gEarth: 9,8 m/s2

gMoon: 1,67 m/s2; gMars: 9,8 m/s2;gMercury: 2,6 m/s2

We can measure it with balances. We can measure it with force meter or dynamometers.

Weight and mass are linked to gravity, g, through the equation W=m.g

Exercise

• Complete the following chart:

Mass in the Earth

Weight in the Earth

gEarth: 9,8 m/s2

Weight in the Moon

gMoon:1,67 m/s2

Weight in Mars

gMars: 3,71 m/s2

Weight in Mercury

gMercury: 2,6 m/s2

10Kg

19,6N

66,8N

40,81N

52N

Archimedes´ Principle

An immersed body is buoyed up by a force that is equal to the weight of the fluid that it displaces.