TWO DIMENSIONAL AND VARIED MOTION

Projectile Motion

The Pendulum

Projectile Motion

A projectile is an object that is thrown into the air.

A projectile moves forward due to its inertia.

It accelerates downward due to gravity.

The path a projectile makes while in the air is a curve called a trajectory.

Horizontal Motion

Roll a ball along a horizontal surface, and its velocity is constant because no component of gravity acts horizontally. There is no acceleration.

Vertical Motion

Drop the ball, and it

accelerates downward

and covers greater

vertical distances

each second. It accelerates

at 9.8 m/s2.

Projectile Motion (see example)

The horizontal component of motion for a projectile is completely independent of the vertical component of motion. The combination of both motions produce the curved path.

Velocity of a Projectile at Various Points

Projectile Fired at a Steeper Angle

Paths of Projectiles Launched at Different Angles -No Air Resistance

HEIGHT

RANGE

7560

45

30

15

With No Air Resistance….

1. The time for a projectile to reach its maximum height equals the time to fall from that height to the ground.

2. The projectile is traveling at the same speed when it returns to the ground as it had when it was released.

3. The vertical velocity of a projectile will be zero at the top of its arc.

Satellite

A projectile that is moving fast enough that its arc matches the curvature of the earth.

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The Pendulum

An object that is suspended so that it can swing back and forth about an axis is called a pendulum.

The swing of a pendulum is an example of simple harmonic motion, which means it repeats itself over and over.

The Pendulum

The time of a back-and-forth swing of a pendulum is called the period of a pendulum. It is measured in seconds.

The period of a pendulum only depends on the length of the pendulum and the acceleration of gravity. (see example)

Calculating the period of a pendulum

Use the equation:

Where

T= period of pendulum

l = length of pendulum

g = gravity

Calculating the period of a pendulum

An astronaut sets up a pendulum on the moon, where gravity is 1.6 m/s2. If the pendulum is 1 meter long, what will the period of the pendulum be?

sec97.4

)79.0(26.1

12

2

T

T

T

g

lT

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