Projectile and Cicular motion

A. Projectile motion

  Projectile motion is a form of motion in which an object or particle (called a projectile) is thrown near the earth's surface, and it moves along a curved path under the action of gravity only. The implication here is that air resistance is negligible, or in any case is being neglected in all of these equations. The only force of significance that acts on the object is gravity, which acts downward to cause a downward acceleration. Because of the object's inertia, no external horizontal force is needed to maintain the horizontal velocity of the object.

This is an example of a projectile motion lets assume that the deegre is 30 deegre and the velocity is 60m/s

We can find to find :

1. Vox= 60.cos 30 = 52

    Voy= 60.sin30 = 30

2. Velocity at certain time at the respect of horizontal ex: 2 sec

    √Voy^2+Vox^2=√30^2+52^2= 60m/s

3. Height or the range of the projectile for example we take the Range of the bullet at 2 sec at the respect of the Horizontal

  Vox . time

  52.2= 104 m

4. Next we can find the maximum height of the projectile

  Voy^2/2g= 30^2/20= 900/20= 450

Linear Motion

Position

Posistions represent the location of an object in a coordinate system. Example of we walk 10 m to the front and 5 m back the total position is added 10+5=15

Displacement

we say an object is displaced when its position change of position. Example a guy walk 10 m to the north then 5m back back to the south the displacement only 5m because 10-5=5 and he only change postion or 5 m

Equation in Linear motion

Equation 1= relation between initial velocity final velocity, time take and the acceleration (A= V1-V0/T= Vo+at)

Equation 2= relation between distance ,initial velocity, acceleraton and time D= Vo+1/2 at^2

Equation 3= relation between initial velocity, final velocity, acceleration, distance V1^2=Vo^2 +2as

Example: An apple falls from a tree and 0.5 second later hits the ground. How fast is the apple falling when its hits the ground?

* V1=Vo+at

V1=0 + 10x0.5

V1= 5m/s

 we use the equation because it has vo and time but we need to find the acceleration between them

we can determine the positive, negative and zero
*0-5= positive
*5-10= zero
*10-15= negative
*15-20=zero
*20-25= Negative

 

 

Vector

that's the formula to find the resultant of a vector if the angle / teta is no 90 deegre

In vector we know Sin and Cos
sin = y/r
cos= x/r

hypotenus = R
opposite = Y
adjacent = X

when we want to find the X or Y of vector and it use x/r it use Cos and if it's using y/r it use Sin
This is the list of Cos and Sin that we can use to :

this is an example question :
1. There are 3 vector the first one go to north west with 15N 37 deegre the aspect of south. The secondone go to south east with 9N 37 deegre the aspect of south and the third one with 10N go to east find the resultan of the vector
we can directly minus f1 and f2 becuase they have same teta or deegre 15-9=6N
F3x+F1x=9-3.6=5.4
F3y+F1y=0+4.8=4.8

√5.4^2 +4.8^2 =7.2N
4.8/5.4= 0.8
tan^-1 0.8 =38,65

Measurement and Dimension

 Measurement usually used when we want to measure something ex: we want to calculate the Velocity of an object we can use Distance traveled.

                                                         Time taken

In measurement we know [M] ,[L],[T] this three is the basic Dimension

[M] stand for mass [L] stand for length and [T] stand for time

 we can input this three Dimension to a formula example velocity formula:

Distance/Time taken so distance means [L] and time mean [T] so we can say [M].[T]-1/ [M]/[T]

Measurement need to be learned because we know the Si for every units then we can input to the [M],[T],[L] quantity

In measurement we also learn how to use Vernier caliper 

This is the way to use Vernier Caliper

Vernier caliper is used to measure an object that's realy tiny Ex: pencil diameters, Coin, etc.

This is an example  of a measurement question

1. If an object has the shape of cube with 5cm long and have the mass of 15 kg what is the Density and the dimension of the object

Answer: Because density formula is m/V so we can make 5x5x5=1.25M so 15/1.25 =12 Kg/M3

and the dimension is [M].[L]-3 because kg / m3 so we add -3 because its kg divided by m3.

 

Significanat figure

- All non-zero digits are considered significant

- Zeros appearing anywhere between two non-zero digits are significant

- All numbers in scientific notatran are significant figure

Ex: 0,628 have 3 SF   x    2,2 have 2 sf = 1,35226 have more than 2 sf so we round off it become 1,4 so it have 2 sf