GRADE 9: MOTION IN TWO DIMESION
GRADE 9: MOTION IN TWO DIMESION
Much motion is not constrained to one dimension but rather occurs in two, or even three, dimensions. Two-dimensional (2D) motion means motion that takes place in two different directions (or coordinates) at the same time. Take, for example, Mark McGwire's 70th home run of the 1998 season. The flight of the baseball (neglecting crosswinds) can be represented in two dimensions. This home run is a much more interesting situation than the one-dimensional motion of a ball popped straight up. The rest of this lesson will examine how to analyze two-dimensional motion.
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Projectile Motion
WHAT IS PROJECTILE MOTION?
A projectile is any object thrown into space on which the only acting force is gravity. The primary force acting on a projectile is gravity. This doesn’t necessarily mean that other forces do not act on it, just that their effect is minimal compared to gravity. The path followed by a projectile is known as its trajectory.
When a particle is thrown obliquely near the earth’s surface, it moves along a curved path under constant acceleration directed towards the center of the earth (we assume that the particle remains close to the earth’s surface). The path of such a particle is called a projectile, and the motion is called projectile motion.
In a projectile motion, there are two simultaneous independent rectilinear motions:
Along the x-axis: uniform velocity, responsible for the horizontal (forward) motion of the particle.
Along the y-axis: uniform acceleration, responsible for the vertical (downward) motion of the particle.
Acceleration in the horizontal projectile motion and vertical projectile motion of a particle: When a particle is projected in the air with some speed, the only force acting on it during its time in the air is the acceleration due to gravity (g). This acceleration acts vertically downward. There is no acceleration in the horizontal direction, which means that the velocity of the particle in the horizontal direction remains constant.
Examples
Throwing a ball
The motion of a cannonball.
Formula
Impulse and Momentum
WHAT IS IMPULSE AND MOMENTUM?
The term "momentum" is commonly used in sports. When a commentator says that a player has momentum, it means that the player is actually on the move and it is very difficult for him/her to stop. A body that has momentum cannot be stopped, so it is mandatory to apply a force against its direction of motion for a particular period of time. The greater the momentum, the harder it is to stop. Hence, a higher amount of force is required, and considerable time should be spent to bring the body to a halt. As the force acts on the body for a given time, the body’s velocity changes, and hence its momentum changes. A force changes the velocity of an object either way. Also, if the object’s velocity changes, the momentum also changes.
Impulse is defined as the change in momentum, calculated by multiplying force with time. Since momentum is mass multiplied by velocity, the quantity m•? v equals to change in momentum.
Examples
Dropping a ball
Car crash
Egg in a carton
Formula
Conservation of Linear Momentum
WHAT IS LAW OF CONSERVATION OF MOMENTUM?
Newton’s Third law of motion states that if an object exerts a force on another, the other object also exerts a force towards it with equal magnitude. In all collisions, momentum is conserved. This is because of the law of conservation of momentum. The law of conservation of momentum states that: when two objects in an isolated system collide, the total momentum of the objects before the collision is equal to the total momentum of the objects after the collision.
WHAT IS LAW OF CONSERVATION OF MOMENTUM?
Newton’s Third law of Motion states that if an object exerts a force on another, the other object also exerts a force towards it with equal magnitude. In all collisions, momentum is conserved. This is because of the law of conservation of momentum. The law of conservation of momentum states that: when two objects in an isolated system collide, the total momentum of the objects before the collision is equal to the total momentum of the objects after the collision.
Examples
Consider this example of a balloon, the particles of gas move rapidly, colliding with each other and the walls of the balloon. Even though the particles themselves move faster and slower when they lose or gain momentum when they collide, the total momentum of the system remains the same.
Formula
SYNTHESIS 1
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SYNTHESIS 2
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REFINING 1
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REFINING 2
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