Newton’s Laws of Motion
- You’re riding a skateboard.
- As you push off the ground, you accelerate forward.
- But what if you stop pushing? You gradually slow down and eventually come to a halt. Why does this happen?
This simple scenario illustrates the core principles of Newton’s laws of motion, which describe how objects move and interact with forces.
First Law of Motion: Inertia
Understanding Inertia and Its Implications
Newton's first law of motion
Newton’s first law of motion states:
An object at rest stays at rest, and an object in motion stays in motion at a constant velocity, unless acted upon by a net external force.
This principle is known as inertia.
Inertia
Inertia is the tendency of an object to resist changes in its state of motion.
- Objects at Rest: A book on a table remains stationary unless a force (like a push) moves it.
- Objects in Motion: A rolling ball continues to move in a straight line at constant speed unless friction or another force slows it down.
- Inertia depends on mass: the greater the mass, the greater the inertia.
- This is why it’s harder to push a car than a bicycle.
- Imagine sliding a hockey puck on ice.
- It glides smoothly because the ice reduces friction, allowing the puck’s inertia to keep it moving.
Second Law of Motion: $F = ma$
Deriving and Applying $F = ma$ to Linear Motion Scenarios
Newton’s second law of motion provides a quantitative description of how forces affect motion:
Newton's second law of motion
Newton's second law of motion states:
The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
Mathematically, this is expressed as:
$$
\vec{F}_{\text{net}} = m \vec{a}
$$
where:
- $F$ is the net force acting on the object (in newtons, N).
- $m$ is the mass of the object (in kilograms, kg).
- $a$ is the acceleration of the object (in meters per second squared, m/s²).
If a 5 kg object experiences a net force of 20 N, its acceleration is:
$$
a = \frac{F_{\text{net}}}{m} = \frac{20 \text{ N}}{5 \text{ kg}} = 4 \text{ m/s}^2
$$
This means the object accelerates at 4 m/s² in the direction of the net force.
Why $F = ma$ Matters
- Predicting Motion: By knowing the forces acting on an object, you can predict how it will move.
- Designing Systems: Engineers use $F = ma$ to design everything from cars to rockets, ensuring they perform as expected under various forces.
Confusing mass and weight is a common error.
Mass is the amount of matter in an object (measured in kg), while weight is the gravitational force acting on it (measured in N).
Third Law of Motion: Action-Reaction Pairs
Analyzing Examples Such as Propulsion and Collisions
Newton's third law of motion
Newton’s third law of motion states:
For every action, there is an equal and opposite reaction.
This means that forces always occur in pairs, known as action-reaction pairs.
- Propulsion:
- When a rocket expels gas backward, the gas pushes the rocket forward with an equal and opposite force.
- This is how rockets move in space.
- Collisions:
- When a car crashes into a wall, the car exerts a force on the wall, and the wall exerts an equal and opposite force on the car.
- This is why both the car and the wall experience damage.
- Think of action-reaction pairs like a tug-of-war.
- If two people pull on a rope with equal force, the rope doesn’t move.
- The forces are equal and opposite, cancelling each other out.
- How do Newton’s laws of motion illustrate the interconnectedness of forces and motion in the universe?
- Can you think of examples where these laws apply on a cosmic scale?
Remember, Newton's third law describes forces that two different objects exert on each other, not forces acting in opposite directions on the same object.
Contact Forces and Field Forces
Contact Forces
Contact forces
Contact forces are forces that arise due to direct physical interaction between two objects.
These forces play a crucial role in the motion and equilibrium of bodies and are fundamental in understanding the behavior of objects in various scenarios.
- Normal Force ($F_N$):
- The normal force acts perpendicular to a surface, supporting an object resting on it.
- For objects on a horizontal surface, $F_N = mg$, where $m$ is mass and $g$ is gravitational acceleration.
