【Physics: Force and Motion】A Thorough Guide to Cracking the Common Test
Hello everyone! When you hear the word "Physics," you might feel like it's "full of tricky calculations" or "too many formulas to memorize." But don't worry! This unit on "Force and Motion" is actually very simple—it’s just about learning the rules that describe the movement of things all around us.
It might feel tough at first, but if you master the key points one by one, you’ll definitely have that "Aha!" moment. Let’s learn and have fun together!
1. Velocity and Acceleration: Describing Motion with Numbers
To understand how an object moves, let’s first clarify the difference between "velocity" and "acceleration."
What is Velocity?
Velocity represents "how far and in what direction an object moves per second."
\( v = \frac{\Delta x}{\Delta t} \) (Velocity = Displacement ÷ Time taken)
*Note: While "speed" only considers magnitude, "velocity" always includes the direction as part of the package.
What is Acceleration?
Acceleration represents "how much the velocity changes per second." Think of it as how quickly your speed increases when you step on the gas pedal in a car.
\( a = \frac{\Delta v}{\Delta t} \) (Acceleration = Change in velocity ÷ Time taken)
【Key Point】The 3 Equations of Uniformly Accelerated Motion
These are your most important tools for the Common Test. Instead of just memorizing them blindly, focus on "which equation to use based on what information is provided."
1. \( v = v_0 + at \) (Use when you know the time)
2. \( x = v_0 t + \frac{1}{2} at^2 \) (Use when you want to find the distance)
3. \( v^2 - v_0^2 = 2ax \) (Use when you don't know the time)
Fun Fact: According to Galileo’s experiments, if you ignore air resistance, a heavy iron ball and a light feather will fall with the exact same acceleration (gravitational acceleration \( g \approx 9.8 m/s^2 \))! Pretty amazing, right?
★ Summary of this section:
・Velocity is "current motion," and acceleration is "change in motion."
・Choose your equation based on what is given in the problem statement!
2. Understanding the Nature of "Forces"
The world of physics is full of invisible "forces." Let’s introduce the main characters.
① Gravity (\( mg \))
This is the force with which the Earth pulls an object. An object with mass \( m \) [kg] is always acted upon by a downward force of \( mg \).
② Normal Force (\( N \))
This is the force exerted by a surface pushing back against an object. Think of it like this: the reason a book placed on a desk doesn't sink through is because the desk is pushing back up on it.
③ Friction
This is the force that opposes motion.
・Static friction: The force that resists an object when it's trying to start moving.
・Kinetic friction: The force that acts like a brake while an object is already moving. \( F = \mu' N \)
④ Elastic Force (Hooke’s Law)
This is the force a spring exerts to return to its original state.
\( F = kx \) (\( k \): spring constant, \( x \): stretch or compression from the natural length)
【Common Mistake】
Some people draw "centrifugal force" or "inertial force" into their diagrams from the start, but these are special forces that only appear when viewed from a "moving reference frame." For now, make it a habit to draw only the "forces from things the object is touching" + "gravity"!
★ Summary of this section:
・The golden rule is to draw forces as "arrows" in your diagrams!
・Start by drawing gravity, then check "what is it touching?"
3. Newton’s Laws of Motion: The Rules of the Universe
These are the three crucial rules regarding motion discovered by Isaac Newton.
First Law: Law of Inertia
The property where "an object at rest stays at rest, and an object in motion stays in motion with the same speed."
Example: That feeling in a bus when it brakes suddenly and your body feels like it's being thrown forward.
Second Law: Equation of Motion (\( ma = F \))
This is the most important formula in all of physics!
(Mass \( m \)) × (Acceleration \( a \)) = (Net Force \( F \))
・The greater the force, the greater the acceleration (pushing harder makes it accelerate faster).
・The greater the mass (heavier), the smaller the acceleration (heavy things are harder to move).
Third Law: Law of Action and Reaction
The rule stating, "If object A pushes object B, then object B always pushes object A back with the same amount of force."
Example: If you push a wall hard, your hand hurts, right? That’s because the wall is pushing you back!
【Key Point】Difference between "Equilibrium" and "Action-Reaction"
This is a common point of confusion!
・Equilibrium: A state where the forces acting on "a single object" cancel each other out.
・Action-Reaction: Forces acting between "two different objects" that they exert on each other.
*If the subject is just "The book is..." it’s likely equilibrium. If it’s "The book pushes the desk, and the desk pushes the book," it’s action-reaction.
★ Summary of this section:
・\( ma = F \) is the king of physics. Make sure you master it!
・Action-Reaction forces always exist in "pairs."
4. Steps to Solve Problems (The Strategy)
Even if you run into a difficult problem, you can always solve it by following these steps:
Step 1: Draw a Diagram
Draw it big. Just doing this will eliminate half of your potential mistakes.
Step 2: Draw the forces as arrows
Draw "gravity" first, then draw the forces from "contact points" (normal force, friction, tension, etc.).
Step 3: Define your axes
It’s recommended to set the direction of movement as the \( x \)-axis and the direction perpendicular to it as the \( y \)-axis.
Step 4: Set up the equation of motion \( ma = F \)
Create an equation for each axis. If the object is stationary (or moving at a constant velocity), \( a = 0 \), so it becomes an "equilibrium of forces" equation.
Step 5: Calculate and find the answer
Solve for the unknown variables (like \( a \) or \( T \)).
【A Word of Encouragement】
Many students say, "I can set up the equations, but I make mistakes in the calculation..." Physics calculations just take practice! It’s okay to be slow at first; try to set up the equations yourself and practice solving them all the way to the end. Even the Common Test problems are, at their core, just combinations of these steps.
★ Overall Summary:
・Force and motion is like a game of "making invisible forces visible with arrows"!
・With \( ma = F \) and the 3 equations of motion, you can tackle almost any problem!
・Start by applying these to everyday phenomena (cars, springs, elevators) to build your mental image!