Mechanics and kinematics Unit Two Mechanics and kinematics Describing motion

How far did the object travel?” In science, Motion is defined as The change in position for a particular time interval. You can then start describing motion with the question, “ How far did the object travel?”

Distance and displacement HOW FAR? Distance and displacement

How far did the object travel? There are actually two ways to answer this question. First is by getting the total length of the path travelled by the object.

Example: Ali ran 10m to the east, then 5m to the south, and another 10m to the west. So it has travelled a total of 25 meters. (DRAW) The other way is by measuring the distance between the initial position and final position of the object. Ali has travelled 5 meters to the south.

In science, the first measurement gives the distance travelled by the object while the second measurement gives its displacement.

Adobe file: Here are more illustrations showing the difference between distance travelled (represented by broken lines) by an object and its displacement (represented by continuous lines).

P.O. C Distance Displacement Can you give one difference between distance and displacement base on the given examples? P.O. C Distance Displacement Definition It is the actual path that the body covered It is the distance covered in a certain direction It is the shortest distance between final and initial points Type of quantity Scalar Vector

1-Calculate the distance and displacement when an object moves from (A) to (B). 2-Calculate the distance and displacement when an object moves from (A) to (A) again .

1-Calculate the distance and displacement when an object moves from (A) to (C). 2-Calculate the distance and displacement when an object moves from (A) to (A) Again.

In which case can displacement be equal to zero? Is it possible to get zero displacement?

Speed velocity and acceleration

Speed is the term used to describe the distance traveled in a unit of time The distance can be in a straight line or around a corner

Speed 1-

Speed speedometer 2-Instantaneous Speed : the speed at any given instant in time=actual speed speedometer

average velocity. Example1 The physics teacher walks 4 meters East, 2 meters South, 4 meters West, and finally 2 meters North. The entire motion lasted for 24 seconds. Determine the average speed.

Answer The physics teacher walked a distance of 12 meters in 24 seconds; thus, her average speed was 0.50 m/s.

Velocity Velocity is the term used to describe the displacement traveled in a unit of time It describes how fast and in what direction a body is moving

Now the formula : V = displacement/time

For motion in straight line you can use + or – to indicate the direction V=+ 10 m/s V= -10 m/s

P.O. C Speed Velocity Vector Scalar Type of quantity DEFINATION It is the distance traveled in a unit of time It is the displacement traveled in a unit of time Type of quantity Scalar 𝒗= 𝒔 𝒕 Vector 𝐕𝐞𝐥𝐨𝐜𝐢𝐭𝐲= Displacement Time

Acceleration is the rate of change of velocity Acceleration has direction and magnitude. Thus, acceleration is a vector quantity. http://www.youtube.com/watch?v=_BM89yVZoBg&mode=related&search=

Now the formula of accelerstion is : 𝒂= ∆𝒗 ∆𝒕 𝒂= 𝒗−𝒖 𝒕 𝒇 − 𝒕 𝒊   𝒂: Acceleration (m/ s 2 ) (𝒗: ( 𝐟𝐢𝐧𝐚𝐥 𝐯𝐞𝐥𝐨𝐜𝐢𝐭𝐲 (m/s). 𝒖: initial velocity (m/s ) 𝒕 𝒇 : time of the end of motion( Sec ) : 𝒕 𝒊 : time of the beginning of motion  ∆v = change in velocity ( subtract, final – initial) a = v-u

GRAPHS

Motion graphs

Higher the speed more the gradient Low speed means less slope or gradient High speed means more slope or gradient

2. Speed or (velocity) Vs time graphs 1. On a speed or (velocity) -time graph the gradient of the line is the acceleration 2. On a speed or (velocity ) - time graph the area under the the line is equal to the distance or displacement traveled

Example1 In the graph below describe the motion of the object? average velocity. Example1 In the graph below describe the motion of the object?

In region A the object is moving with constant acceleration. In region B the object is moving with constant velocity. In region C the object is again  moving  with  constant  acceleration, but when compared with region A: 1. the acceleration is slower because the slope is less steep 2. the acceleration is negative because the slope is downwards. The total distance travelled by the object can be calculated by measuring the area under the graph.

This area can be divided into two triangles and one rectangle. The area of triangle A = ½ base x height             = 0·5 x 10 x 20 = 100. The area of triangle C= ½  x (70 - 30) x 20 = 400. The area of rectangle B = (30 - 10) x 20 = 400. The distance travelled is the total area = A + B + C               = 100 + 400 + 400 = 900 m.

Equation Of Motion

What are equation of motion? Whenever object moves and you want to describe its motion… There are four equations of motion to find The relationships between displacement, time, velocity, and constant acceleration They apply if the motion is in a straight line And acceleration is uniform

Five Quantities Or Variables

Equation of motion 𝒗=𝒖+𝒂∆𝒕 ∆𝒔=𝒖∆𝒕+ 1 2 𝒂 ∆𝒕 2 ∆𝒔= 1 2 (𝒖+𝒗)∆𝒕 Does not include s ∆𝒔=𝒖∆𝒕+ 1 2 𝒂 ∆𝒕 2 Does not include v ∆𝒔= 1 2 (𝒖+𝒗)∆𝒕 Does not include a 𝒗 2 = 𝒖 2 +2𝒂∆𝒔 Does not include t

Derive the first equation of motion 𝑎= 𝑣−𝑢 ∆𝑡 𝑣−𝑢=𝑎∆𝑡 𝒗=𝒖+𝒂∆𝒕

Example 1 A car accelerate form rest at 3ms -2 A car accelerate form rest at 3ms Along a straight road. How far does the car travelled after 4 s?? S= 24 m

Example 2 A car is travelling 20 m/s along a straight road, The driver puts the brakes on for 5 s. If this causes a deceleration of 3ms What is the car’s final velocity? -2 -1

A racing car reaches a speed of 42 m/s A racing car reaches a speed of 42 m/s. It then begins a uniform negative acceleration, using its parachute and braking system, and comes to rest 5.0 s later. Find the distance that the car travels during braking. حساب المسافة اللازمة لتوقف سيارة ، بمعرفة سرعتها الابتدائية وزمن التوقف.

What is free fall . Free falling is a motion under force of gravity as the only force acting on the moving object. The acceleration on an object in free fall is called the acceleration due to gravity, or free-fall acceleration Practically, free falling can only take place in vacuum

Air Resistance In air… A stone falls faster than a feather Air resistance affects stone less In a vacuum A stone and a feather will fall at the same speed. When air resistance is negligible, mass has no effect on the downward motion on an object.

. Free Fall The acceleration of gravity (g) for objects in free fall at the earth's surface is 9.8 m/s2. Galileo found that all things fall at the same rate.

. Free Fall The rate of falling increases by 9.8 m/s every second. Height = ½ gt2 For example: ½ (9.8 )12 = 4.9 m ½(9.8)22 = 19.6 m ½ (9.8)32 = 44.1 m ½ (9.8)42 = 78.4 m

. Free Fall Acceleration due to gravity is constant during upward and downward motion. Free-fall acceleration on Earth’s surface is (9.8 𝑚/ 𝑠 2 ≈ 10 𝑚/ 𝑠 2 ) at all points in the object’s motion. When the body fall down the velocity increases by rate = 9.8 m/s for each second g = +9.8𝑚/ 𝑠 2 When the body thrown up the velocity decreases by rate = 9.8 m/s for each second g = -9.8𝑚/ 𝑠 2

. Equation of Motion for Free Fall 𝒗 =𝒖+𝒈∆𝒕 ∆𝒅=𝒖∆𝒕+ 𝟏 𝟐 𝒈 ∆𝒕 𝟐 𝒗 𝟐 = 𝒖 𝟐 +𝟐𝒈∆𝒅 

Free Fall - example 1) A coin is dropped in a vacuum tube, Find the coin's velocity after.30 seconds. Vf = ? t = .30 seconds a = g = - 9.8 m/s2 (falling) Vi = 0 m/s vf = vi +at Vf = vi +gt Vf = 0 -10 m/s2 x .30 s Vf = -3 m/s

Free Fall - example 2) If a rock is dropped from a building, and it takes 18 seconds to reach the ground, how tall is the building? 56

Sample Problem 1. A worker drops a wrench from the top of a tower 80.0 m tall. What is the velocity when the wrench strikes the ground? 2. How far above the floor would you need to drop a pencil to have it land in 1 s? H.B solving problem numbers 1 and 2 page 27 ٚ

Force There are forces all around us. We make use of forces to do a lot of things in our everyday life. Force is a push or a pull acting upon an object. Whenever we push or pull an object, we exert a force. We cannot see a force, but we can see and feel its effects.

The following diagrams shows activities that involve ………….forces. These diagrams shows activities that involve Pushing forces

The following diagrams show activities that involve ………….. forces. The following diagrams show activities that involve pulling forces.

Force Non Touch Force Touch Force Air Resistance Force acts on an object only by touching it. Normal force Air Resistance Force acts at a distance (long-range force). Gravitational Force Magnetic force

The effects of forces The effects of a force include (a) force changes the shape of an object (b) force changes the position of an object (c) force changes the speed of a moving object (d) force changes the direction of a moving object

Force can change the shape of an object Pressing, bending and stretching can change the shape of an object. (a) Bending (b) Stretching (c) Pressing

Force changes the speed of a moving object such as: Move it Stop it Increase or decrease its speed

force changes the position of an object Hit a ball move move

Force changes the direction of a moving object. A force can change the direction of an object's movement.

The unit of force We measure force in units called Newton (N). (1N resultant force acting on 1kg produces an acceleration of 1m/s2). We can measure a force using a spring balance or Newton meter.

Equal forced Two forces are equal when the two forces (magnitude) and direction are the same.

Balanced forces When the forces acting on an object are balanced, they cancel each other out. The net force (RESULTANT) is zero. Effect : the object at is at rest [ velocity = 0]

Question 1 Forces of 12 N and 5 N both act at the same point, but their directions can be varied. a) What is their greatest possible resultant? b) What is their least possible resultant? c) If the two forces are at right angles, find the resultant.

Question 2 Which one of the following effect of force on an object is not true ? Change its shape Change its position or direction Change its colour Change its speed