Comprehensive Notes on Motion and Forces

X-10: Motion and Forces

Motion - Frame of Reference

Motion is defined as the change of position relative to a frame of reference.
A book on a table can be considered both at rest (relative to the table) and in motion (relative to the Earth's rotation, revolution, and the universe's expansion).
Earth rotates and revolves, and the universe expands, indicating that all motion is relative.
Galaxy Spinning implies that all motion is relative.

Simplified Motion for 7th Grade

For 7th grade, motion is typically determined relative to a stationary frame of reference.
A Frame of Reference (or Reference Point) is the background that motion happens in front of, or the stationary point that motion is relative to.
In essence, background motion is ignored in 7th-grade context, focusing on changes in position relative to a stationary background.

Speed

Speed is the amount of distance traveled in a certain amount of time.
Formula: $Speed = \frac{Distance}{Time}$ , or $S = \frac{D}{T}$
Speed measures how fast an object moves.
Units: Any distance divided by any time (e.g., mi/hr, m/s, cm/hr, in/yr).
Units are crucial for determining the movement of the object.

Types of Speed

Instantaneous Speed: The exact speed at a specific time (e.g., how fast a car is traveling right now).
Constant Speed: Speed that does not change over the course of the motion.
Average Speed: Speed that changes over the course of motion.
- Formula: $Average Speed = \frac{Total Distance}{Total Time}$

Speed Graph

A straight line on a distance vs. time graph indicates constant speed.
A steeper slope indicates a faster speed.

Velocity

Velocity is speed in a given direction.
Formula: $Velocity = \frac{Distance}{Time}$ with direction, or $V = \frac{D}{T}$ + direction.
Units: Any distance divided by any time in a direction (e.g., m/s North, mi/hr West, km/s Towards the Moon).
Velocity can change without the object changing speed, simply by changing direction (e.g., 5 mi/hr East vs. 5 mi/hr North).
Velocity word problems and graph problems are the same as speed, but direction must be included.

Combining Velocities

When an object is moving with or against something that is also moving (e.g., a boat on a river, a person on a movable sidewalk).
Same Direction: If velocities are in the same direction, add them.
- Example: A boat traveling 16 km/hr east on a river flowing 10 km/hr east has a combined velocity of 26 km/hr East.
Opposite Direction: If velocities are in the opposite direction, subtract them.
- Example: Walking 3 mi/hr north on a sidewalk moving 4 mi/hr south results in a combined velocity of 1 mi/hr South.

Acceleration

Acceleration is the rate at which velocity changes.
It's the amount that velocity changes over a certain amount of time.
Velocity changes when speeding up, slowing down, or changing direction.
Formula: $Acceleration = \frac{Final Velocity - Original Velocity}{Time}$ , or $A = \frac{V<em>f - V</em>i}{T}$
Units: Any distance over time over time (e.g., cm/s/year, km/hr/s, m/s/s (or m/s²), mi/hr/hr).

Acceleration Graph - Curving Speed Graph

Slope indicates speed; a steeper slope means faster speed.
If speed changes (speeding up or slowing down), the object has accelerated.
Therefore, if the slope changes on a distance vs. time graph, the object is accelerating.
Interpreting the Shape of the Curve:
- Line A (Slowing Down/Deceleration): Starts with a steep slope (fast) and curves towards the horizontal (slow/stop).
- Line B (Speeding Up/Positive Acceleration): Starts with a shallow/gentle slope (slow) and curves towards vertical (fast).

Acceleration Graph - Speed vs. Time

A: Constant acceleration throughout the motion (slope doesn't change).
B¹, B², B³: Acceleration changes throughout the course of motion (slope changes).
- B¹: Positive slope = positive acceleration (speeding up).
- B²: Zero slope (horizontal) = zero acceleration (constant speed).
- B³: Negative slope = negative acceleration (slowing down/deceleration).

Momentum

Momentum is the influence that mass and velocity have on an object's motion.
All moving objects have momentum.
The magnitude of momentum is the product of mass and velocity.
To change momentum, a force must be applied over a certain time interval (impulse).

Newton's Laws of Motion

Sir Isaac Newton (1642-1727) formulated these laws.

Newton's First Law of Motion (Law of Inertia)

Objects at rest remain at rest, and objects in motion remain in motion at constant velocity unless acted on by an unbalanced force.
Basic Idea: Objects do what they are already doing.
- Stopped objects stay stopped.
- Moving objects continue moving.
Inertia is the resistance to changes in motion.
Larger mass = more inertia.

Newton's Second Law of Motion

Acceleration relates to force and mass.
Objects accelerate in direct proportion to the net force applied and in inverse proportion to the mass of the object.
- Direct Proportion: More Force = More Acceleration
- Inverse Proportion: More Mass = Less Acceleration

Newton's Third Law of Motion

Whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first object.
For every action (force), there is an equal and opposite reaction (force).
Forces come in pairs.

Net Force

Net Force: The combination of all forces acting on an object.
Force: A push or a pull.
- Required to cause a change in motion (acceleration).
- Speeds up, slows down, or changes direction.
- Acts in a specific direction.
Combining Forces:
- Same direction: Add Forces
- Opposite direction: Subtract Forces

Balanced vs. Unbalanced Forces

Balanced Forces: When the net force equals zero.
- Does not influence motion.
Unbalanced Forces: Whenever the net force is not zero.
- Always changes motion.
- (Speed up, Slow Down. Change Direction)

Gravity and Weight

Gravity: Everything in the universe exerts an attractive force on everything else.
Newton's Law of Universal Gravitation: $F = G \frac{m<em>1 m</em>2}{d^2}$
- $G = 6.67 x 10^{-11} \frac{Nm^2}{kg^2}$ (Gravitational Constant)
The size of the attractive force depends on the mass of the objects and the distance between them.
- Force is directly proportional to the product of masses.
- Force is inversely proportional to the square of the distance.

Mass vs. Weight

Mass is the amount of matter in an object.
Weight is how mass is influenced by the force of gravity.
Formula: $Weight = (mass)(gravity)$ , or $W = mg$
$g$ is the acceleration due to gravity.
- $g$ on Earth is approximately $9.8 m/s^2$
Weight is a specific force.
Newton is a standardized unit: Kilograms * Meters / Seconds^2
Mass doesn't change with location, while weight can.

Friction

Friction: Force exerted when two objects are in contact.
Acts opposite to the direction of motion (or attempted motion).
Slows or stops motion.
Amount of Frictional Force Depends On:
- Material of Surfaces
  - Smoother Surfaces = Less Friction
  - Rougher Surfaces = More Friction
- How hard the surfaces are pressed together (weight)
  - Less "press" (weight) = Less Friction
  - More "press" (weight) = More Friction
Increasing or Decreasing Friction:
- Decrease Friction:
  - Reduce weight (or "press")
  - Make surfaces smoother
  - Add wheels or ball bearings
  - Add fluid lubricant
- Increase Friction:
  - Add weight (or "press")
  - Make surfaces rougher
  - Make surfaces slide
  - Increase contact surface area

Air Resistance

Air Resistance: The frictional force that works against an object moving through the air.
Falling and Air Resistance:
- When an object falls on Earth, it falls through the air.
- The air exerts a frictional force which works against the fall.
Free Falling:
- When an object moves under the influence of gravity ONLY.

Terminal Velocity

The point at which the force of gravity is balanced by the force of air resistance.
When Gravity = Air Resistance
Object stops accelerating and travels at a constant velocity.
Parachute: Increase Surface Area = More Air Resistance = Lower Terminal Velocity