the 3 equations of motion show relation b/w?
what assumption are made to simplify the derivation
vf vi a, displacement & time
Object is moving along the straight line.
Acceleration is constant.
Only magnitudes of vectors such as displacement, velocity and acceleration are considered.
Direction of vi & all the quantities which are in the direction of vi are taken as +ve.
derive first equation of motion
what is the purpose of equation of motion?
These equations describe and predict the motion of objects under constant acceleration.
derive 2nd equation of motion
derive 3rd equation of motion
free-fall motion? g? value?
how do the eqn. of motion change?
projectile motion? projectile? trajectory? example?
- a two-dimensional motion of an object thrown in the air under the action of gravitational force only.
- The object that is thrown is called projectile and its path is called its trajectory.
- A football, cricket ball, a baseball or an arrow are the examples of projectile.
in the green ball example, what is Vix
Viy
ax
ay
horizontal component of velocity
vertical component of velocity
in projectile motion what happens to the acceleration?
Vi 0
There is no horizontal acceleration, while the vertical acceleration is the acceleration due to gravity
0 g
Acceleration due to gravity g is taken +ve when the ball is coming downward & -ve for the ball going upward.
The horizontal component of velocity remains constant, while the vertical component of velocity increases.
Vfx= Vix = V cos theta
Vfy= Viy+ ay t
Vfy=0+gt
Vfy=gt
magnitude of instantaneou velocity
direction of velocity?
horizontal & vertical displacement? direction?
At instant t, the horizontal displacement X covered by the ball is given by:
And the vertical displacement the body moves downward from the height is given by:
vf
Projectile Motion for an Object Launched at Some Angle with Horizontal?
x and y acceleration
Horizontal component of velocity is:
Vertical component of velocity is:
draw graph too
at any instant t, its velocity
components???
Projectile Motion for an Object Launched at Some Angle with Horizontal?
magnitude of instantenous velocity?
The direction of velocity v, is determined as:
At instant t, the horizontal displacement x covered by the ball is given by:
And the vertical displacement the body moves in going up is given by:
what is the height of the projectile? denoted by? how to find it? formula?
we can find the height of projectile if _____ is known.
what is the velocity of the body at max. height?
the max. vertical distance attained by it during the projectile motion. It is denoted by H.
To determine H, we use the third
equation of motion as
magnitude & direction of initial
velocity
0
time of flight? denoted by? how to find T?
time of summit? formula?
The time taken by the projectile from the point of projection to the point where it hits the ground at same level .denoted by T.
To determine T, we use the second equation of motion
The time taken by the projectile to reach the highest point is called the time of summit. It is
denoted by T’
Range of the Projectile? derive the formula?
only knowing two quantities; _____, we can find ________
The horizontal distance travelled by a projectile is called range. It is denoted by R.
magnitude and direction of initial
velocity
height, range and time of flight for projectile.
how to have maximum range? formula?
The greater the initial speed, the greater is the range.
For a given
value of v; the range of the projectile is maximum if sin 20 = 1, which occurs when 20 = 90°
H T & R
height, time & range
same range? how can it be acheived? examples?
If the speed of projectile vi & g remains constant, then there are always 2 such angles for which the projectile has same range. These angles are complementary angles of one another i.e., e and 90° - 0.
Hence a projectile has same range for
pairs of angles (75°, 15°), (60°, 30°) and (70°, 20°) etc.
2 angles whose sum is 90°.
Effect of air resistance on projectile motion?
effect on velocity?
range?
height?
visualize or draw the effect?
Generally, air resistance decreases the velocity of projectile. So as a result of air resistance both the horizontal component & vertical component of velocity decreases.
Air resistance affects the parabolic motion of a projectile by reducing its range & maximum height. Hence air resistance can significantly alter the trajectory of the motion
what is an isolated system?
how can we make one?
A system is said to be isolated if and only if the total external force, such as the gravitational force or friction,
acting on the system is 0.
There is no any ideally isolated system in the universe, but we consider an isolated system that does not interact with its environment.
law of conservation of momentum? mathematically?
useful in?
The total momentum of an isolated system of interacting particles is conserved.
If pi and pf, are initial & final momentums of an isolated system then according to law of conservation of momentum:
Pf=Pi
Pf-Pi=0
Ap = 0
useful in collision and explosion problems
In an explosion, what causes the kinetic energy of fragments?
in an explosion, the intial momentum is zero as it is at rest so the final momentum must be 0 too. how?
chemical energy (stored in the bonds of the atoms) is transformed into the K.E of the fragments.
the fragments must move in opposite directions with equal speed for their momentum to be conserved.
how canon obeys law of conservation of momentum?
The initial momentum is zero, cz nothing is moving. After explosion inside the cannon, the cannon ball will be shot forward at very fast speed, while the cannon itself recoils in a
much slower speed due to its heavy mass.
Sum of the final momentum will also end up to zero, this makes the initial momentum and the final momentum the same.
how rockets and jet engines work on the law of COM?
In these machines hot gases produced by burning of fuel rush out with large momentum. The machines gain an equal & opposite momentum. This enables them to move with very high velocity.
how can a karate player break a pile of tiles in one blow?
because he strikes the pile with his
hand very fast.
In doing so, the large momentum of his hand is reduced to zero in a very short time interval.
This exerts a large force on the pile of tiles which is sufficient to break them apart.
collision? types? define
- A collision occurs when two bodies come in physical contact with each other for a short interval of time & then separate.
- 2 types elastic and inelastic
- Inelastic collision is such a collision in which the momentum is conserved but kinetic energy is not conserved.
- Elastic collision is such a collision in which both the momentum and the kinetic energy of the system are conserved.
