Forces and Motion (Vocabulary)

Net Force

• Iditarod mushers start with 16 dogs and must finish with at least 5. Dogs can be removed if they get sick or hurt and are taken care of by vets while the race continues.
• Why finish with many dogs? Each dog pulls the sled, adding up to a bigger total push (force) on the sled.
• When several pushes or pulls (forces) act on an object, the net force is the total of all those forces combined.
• Forces have two important parts: how strong they are (magnitude) and which way they are going (direction).
• If forces push or pull in the same direction, you add their strengths together.
  • Example: Three people push a van forward with forces of 100 N, 125 N, and 200 N.
  • Net force = 100\,\text{N} + 125\,\text{N} + 200\,\text{N} = 425\,\text{N}.
  • Since all are pushing forward, the total (net) force is 425 N in the forward direction.
• If forces push or pull in opposite directions, you subtract them to find the net force. The direction of the net force will be the same as the stronger force.
  • Example: A dog pulls forward with 75 N; a girl pulls backward with 50 N on a leash.
  • Net force on the leash = 75 N - 50 N = 25 N in the forward direction (because 75 N forward is stronger).
  • In math: a forward force is positive (+75\,\text{N}), a backward force is negative (-50\,\text{N}). Net force = +75\,\text{N} + (-50\,\text{N}) = 25\,\text{N} forward.
• The net force helps us guess how an object will move by looking at all forces at once.
• Sometimes, the net force is just one main force, if other forces cancel each other out or are very small.
• A negative net force means an object will speed up in the opposite direction, or slow down if it's already moving in the positive direction (like brakes slowing a train).
• Real-life example: When a train on a roller coaster track brakes, the brakes push backward. If the forward pushes are small, the total push is backward, and the train slows down (this is called negative acceleration).

Important Formulas

• Net force is the total sum of all individual forces: F_{\text{net}} = \sum F_{i} (meaning you add them, considering their directions).
• If forces are in the same direction:
  • F_{\text{net}} = F_1 + F_2 + \dots
• If forces are in opposite directions:
  • The net force is the difference between the larger and smaller force. Its direction is the same as the larger force.

Newton's First Law (Law of Inertia)

• The net force tells us if an object's motion will stay the same (net force = 0) or change (net force is not 0).
• Balanced forces: The net force is 0 N. This means all forces cancel each other out.
• Unbalanced forces: The net force is not zero. These forces will cause an object to accelerate (speed up, slow down, or change direction).
• Newton's First Law (also called the Law of Inertia) says:
  • An object that is not moving will stay not moving.
  • An object that is moving will keep moving at the same speed and in the same straight line, unless an unbalanced force pushes or pulls on it.
• This means an object's motion won't change unless an uneven force acts on it.

An Object at Rest (Not Moving)

• If all forces on a still object are balanced (net force = 0), the object will not move.
• Example: A luggage cart sitting still with balanced forces will stay still (Net force = 0 N).

An Object in Motion (Moving)

• If an object is already moving and the forces on it are balanced (net force = 0), it will keep moving at the same speed and in the same direction. It won't speed up or slow down.
• Example: A moving cart has friction pulling it backward and a hand pushing it forward. If these two forces are equal, the cart moves at a steady speed.

Unbalanced Forces and Changes in Motion

• When an unbalanced force acts on a moving object, the object will accelerate.
• If the net force pushes or pulls in the same direction the object is moving, the object speeds up.
• If the net force pushes or pulls in the opposite direction the object is moving, the object slows down.
• Example: Pushing a luggage cart with a force stronger than friction makes it speed up (forward acceleration). If you pull the cart backward, the net force is backward, and it slows down.

Quick Summary of Newton's First Law

• Balanced forces mean zero net force; an object's motion stays the same (either still or moving at a constant speed).
• Unbalanced forces cause acceleration (speeding up or slowing down) depending on which way the net force pushes compared to the object's motion.

Designing a Better Seatbelt

• Cars have changed a lot over time, but seatbelts are still super important for safety because of Newton's First Law.
• Engineers use criteria (what a design needs to do) and constraints (what limits the design) when creating new things.
• Engineer Nils Bohlin realized that in a head-on crash, your body keeps moving forward because of inertia (Newton's First Law) unless something holds it back.

What Seatbelts Need to Do (Criteria) and What Limits Them (Constraints)

• Criteria: The seatbelt must hold both your upper body and lower body safely in place during a crash. It also needs to be comfortable and easy to buckle with one hand.
• Constraints: The seatbelt can't be too expensive to make, and it needs to be easy to put into cars. Otherwise, car companies wouldn't install them.
• The three-point seatbelt was made to meet all these requirements.
• It successfully holds the upper and lower body, is comfortable, and can be buckled easily with one hand.

The Three-Point Solution (How it Works)

• How it's built: It uses two straps that are joined together and connect to the car at three different spots.
  • The top strap goes over your shoulder.
  • The bottom strap connects near one hip.
  • Both straps connect together near your other hip.
• Benefits: It's easy to use with one hand and simple to pull across your body to buckle.
• Parts and how it's made: It uses a few simple parts (one long strap, a two-part buckle, and some gears). The materials can be cheap, and it's easy to put together.
• History and impact:
  • First used in cars in 1959.
  • Became a legal requirement in American cars in 1968.
  • It's been improved over the years, but the basic design is still the same.
  • It has changed how we expect cars to be safe and led to laws requiring everyone to wear seatbelts.

Newton's Second Law

• When Iditarod mushers want their sled to go faster, they get the dogs to pull harder, which makes the sled speed up more (increase acceleration).
• Newton's Second Law connects three things: how fast an object speeds up (acceleration), the total force pushing or pulling it (net force), and how heavy it is (mass).
• The law says: An object's acceleration is equal to the net force on the object divided by its mass.
  • Formula: a = \frac{F}{m} (acceleration = net force divided by mass).
  • It's also often written as: F_{\text{net}} = m a (net force = mass times acceleration).

Acceleration and Force

• More net force means greater acceleration (if the mass stays the same).

  • Example with a sled and dogs (each pulling with 50 N):
  • 3 dogs: Total net force = 3 \times 50\,\text{N} = 150\,\text{N}.
  • 6 dogs: Total net force = 6 \times 50\,\text{N} = 300\,\text{N}.
  • If the sled's mass stays at 100 kg, doubling the number of dogs (and thus the force) doubles the acceleration. More force means more acceleration for the same weight.

• Mass effect: For the same amount of net force, heavier objects speed up less.

  • A heavier sled (more mass) will have less acceleration if the dogs pull with the same total force.
  • Sled mass example:
  • Mass = 300 kg with net force = 300 N (\rightarrow) acceleration = a = \frac{F}{m} = \frac{300}{300} = 1.0\,\text{m/s}^2
  • Mass = 150 kg with the same net force = 300 N (\rightarrow) acceleration = a = \frac{300}{150} = 2.0\,\text{m/s}^2

Key Relationships

• If the force stays the same, doubling the mass cuts the acceleration in half. Heavier objects speed up more slowly.
• If the mass stays the same, doubling the force doubles the acceleration.
• The weight of the sled changes with how many supplies are inside. Heavier sleds speed up less with the same pulling force from the dogs.

Mass-Acceleration Examples (Figures)

• Light sled with six dogs:
  • Mass = 100 kg, Net force = 300 N (\rightarrow) a = \frac{300}{100} = 3.0\,\text{m/s}^2
• Heavy sled with six dogs:
  • Mass = 200 kg, Net force = 300 N (\rightarrow) a = \frac{300}{200} = 1.5\,\text{m/s}^2
• Summary: If you double the mass from 100 kg to 200 kg, but keep the net force the same, the acceleration becomes half (from 3.0 to 1.5 m/s(^2)).

Forces Around You (Friction)

• In everyday life, many forces are happening. Friction is an important force that always tries to stop motion.
• A coin sliding on a table slows down and stops because of friction.
• Friction is a force that pushes against the motion between two surfaces that are touching.
• Friction always acts in the direction opposite to where the object is moving.
• Friction causes the sliding coin to slow down (negative acceleration).

Good Uses for Friction

• Friction helps us stand up and walk without slipping.
• In sports, friction helps athletes stop or change direction (like softball players sliding into a base to stop).
• In many situations, friction is helpful and necessary for controlling movement and staying safe.

Quick Important Points about Friction

• Friction is a contact force (requires touching) that opposes motion between surfaces.
• It can make moving objects slow down or stop, or it can help us stop safely and get good grip in daily activities.
• Understanding friction, along with net force and Newton's laws, helps explain how objects start, stop, and change speed in the real world.

Extra Notes and Simplification

• Net force idea:
  • F_{\text{net}} = \sum F_{i} means you add up all forces, remembering which direction each force is going (like using positive for one way and negative for the other).
• Direction rules:
  • You can choose a positive direction for a problem (like forward). The net force's direction will match if it's positive or be opposite if it's negative.
• Newton's laws in short:
  • First Law: Balanced forces mean no change in motion; unbalanced forces mean acceleration.
  • Second Law: The formula is \mathbf{a} = \frac{\mathbf{F}\{\text{net}}}{m} or \mathbf{F}\{\text{net}} = m\mathbf{a}.

Quick Reference Guide

• Net force in the same direction: Add their strengths together.
• Net force in opposite directions: Subtract the smaller strength from the larger strength; the direction is the same as the larger force.
• If F_{\text{net}} = 0, the object's motion doesn't change (still objects stay still; moving objects keep moving at a steady speed).
• Acceleration, Net Force, and Mass: Acceleration gets bigger if the net force gets bigger. Acceleration gets smaller if the mass gets bigger. The formula is a = \frac{F_{\text{net}}}{m}.
• If you make the mass heavier but keep the net force the same, acceleration goes down. If you make the net force stronger but keep the mass the same, acceleration goes up.
• Friction: Pushes against motion. It can either slow things down or help us control moving and stopping, and keep us from slipping.

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