write some causes of friction
Answers
Explanation:
Equations of an Oblique Projectile Motion Without
Calculus
Uchenna Okwudili Anekwe
Department of Physics, University of Science and Technology, Aleiro, Nigeria([email protected])
Abstract This Manuscript involves the derivation of the equations of motion of a projectile round an oblique path.
Using the three equations of motion in Physics, we derived the equation for the time to reach the maximum height from the
first equation of motion in Physics, the time of flight equation from the second equation of motion in Physics, the
Maximum height equation from the third equation of Motion in Physics and lastly the horizontal range equation from the
knowledge of the definition of distance in Physics which is the product of the average velocity and the time taken during
the course of the motion.
Keywords sin, cos, eqn
1. Introduction
The motion of an object is called two dimensional, if two
of the three co-ordinates are required to specify the position
of the object in space changes w.r.t time. In such a motion,
the object moves in a plane. For example, a billiard ball
moving over the billiard table, an insect crawling over the
floor of a room, earth revolving around the sun etc. Two
special cases of motion in two dimensions are 1. Projectile
motion 2. Circular motion
A hunter aims his gun and fires a bullet directly towards a
monkey sitting on a distant tree. If the monkey remains in his
position, he will be safe but at the instant the bullet leaves the
barrel of gun, if the monkey drops from the tree, the bullet
will hit the monkey because the bullet will not follow the
linear path. The path of motion of a bullet will be parabolic
and this motion of bullet is defined as projectile motion. If
the force acting on a particle is oblique with initial velocity
then the motion of particle is called projectile motion.
A body which is in flight through the atmosphere but is not
being propelled by any fuel is called projectile.
Example: (i) A bomb released from an aeroplane in level
flight (ii) A bullet fired from a gun (iii) An arrow released
from bow (iv) A Javelin thrown by an athlete.
Assumptions of Projectile Motion
(1) There is no resistance due to air.
(2) The effect due to curvature of earth is negligible.
(3) The effect due to rotation of earth is negligible.
(4) For all points of the trajectory, the acceleration due to
gravity ‘g’ is constant in magnitude and direction.
Types of Projectile Motion
1. Oblique projectile motion
2. Horizontal projectile motion
3. Projectile motion on an inclined
Oblique Projectile
In projectile motion, horizontal component of velocity
(u cos), acceleration (g) and mechanical energy remains
constant while, speed, velocity, vertical component of
velocity (u sin ), momentum, kinetic energy and potential
energy all changes. Velocity, and KE are maximum at the
point of projection while minimum (but not zero) at highest
point.
Horizontal Projectile
A body be projected horizontally from a certain height ‘y’
vertically above the ground with initial velocity u. If friction
is considered to be absent, then there is no other horizontal
force which can affect the horizontal motion. The horizontal
velocity therefore remains constant and so the object covers
equal distance in horizontal direction in equal intervals of
time.
Projectile Motion on an Inclined Plane
The motion of a particle projected up with a speed u from
an inclined plane which makes an angle with the horizontal
velocity of projection that makes an angle with the inclined
plane is called Projectile Motion on an Inclined Plane. [1]
To be a true projectile, an object must:
1. Have negligible lift and drag from the air.
• A Frisbee would not be a projectile because of its lift.
• A wad of paper thrown through the air at a fast speed is
not a true projectile due to the amount of air friction or
“drag”.
2. Have no means of self propulsion.
• A model rocket would not be a true projectile because it
Explanation:
1. friction causes heat.
2. friction causes automobiles or machinery to heat up due to regular wear and tear.
3. friction causes moving of heavy objects difficult.
4. friction helps us to walk on road.