Tutorial 1.1: Forces and Motion¶
Time: ~15 minutes Prerequisites: Tutorial 0: Welcome
The Shopping Cart Analogy¶
Imagine you're at a grocery store with a shopping cart.
Empty Cart Full Cart
+-------+ +-------+
| | LIGHT |███████| HEAVY
| | Easy to push |███████| Hard to push
+---+---+ +---+---+
| |
[O] [O]
Question: Which cart is easier to push? Why?
The empty cart is easier because it has less mass (weight). You need less force to move it.
This simple observation is the foundation of physics that makes robots work!
Newton's Three Laws (The Simple Version)¶
Sir Isaac Newton figured out the rules of motion about 400 years ago. Here's what they mean for your robot:
Law 1: Objects Stay Put (or Keep Moving)¶
"An object at rest stays at rest, and an object in motion stays in motion, unless a force acts on it."
For your robot: - Your robot won't move unless motors push it - Your robot won't stop unless you tell it to (or friction slows it)
flowchart LR
A["Robot at rest<br/>Stays still"] -->|"Force applied<br/>Motors push"| B["Robot moving<br/>Keeps moving!"]Law 2: Force = Mass × Acceleration (F = m × a)¶
"The force needed to move something depends on how heavy it is and how fast you want it to go."
For your robot: - Heavier robot = need more motor power - Want faster acceleration = need more motor power - This is why we choose motor gear ratios carefully!
SAME FORCE, DIFFERENT MASS:
Light Robot Heavy Robot
+--------+ +===========+
| 5kg | →→→→→→→→ | 15kg | →→
+--[O][O]+ +===[O][O]==+
Accelerates FAST Accelerates SLOW
Law 3: Every Action Has a Reaction¶
"When you push something, it pushes back."
For your robot: - When wheels push against the floor, the floor pushes your robot forward - When you push an opponent, they push back on you - This is why heavier robots are harder to push around!
Your Robot Opponent
+--------+ +--------+
| PUSH →| |← PUSHES|
| | | BACK! |
+--[O][O]+ +--[O][O]+
Action Reaction
How This Applies to Robot Motors¶
Your VEX V5 motors create force by spinning. That spinning force is called torque.
flowchart LR
A["Motor creates torque"] --> B["Spinning shaft"]
B --> C["Wheel pushes floor"]
C --> D["Floor pushes robot forward!"]The Force Equation in Practice¶
Let's say your robot weighs 5 kg and you want it to accelerate at 2 m/s²:
Your motors need to provide at least 10 Newtons of force!
Note: VEX motors are rated in torque (Newton-meters), not Newtons directly. We'll cover torque in the next tutorial!
Why Robot Weight Matters¶
In the Push Back competition, you might need to push opponents or resist being pushed:
Pushing Match:
Light Robot (5kg) Heavy Robot (15kg)
+--------+ +============+
| | →→→ | |
+--[O][O]+ +===[O][O]===+
Light robot pushes... Heavy robot barely moves!
But gets pushed back! And can push light robot around!
←←←←←←←← →→→→→→→→→→→→→→→
Trade-off: - Heavy robot = hard to push, but slower and needs more battery - Light robot = fast and agile, but easier to push around
For Push Back, you'll need to decide what's more important for your strategy!
Code Connection: Limiting Force¶
Look at src/utils.py:
def clamp(value, min_val, max_val):
"""
Clamp a value between minimum and maximum bounds.
"""
return max(min_val, min(value, max_val))
This function limits values - like limiting how much force a motor can apply!
Example:
motor_power = 150 # Someone requested 150% power
clamped_power = clamp(motor_power, -100, 100) # But max is 100%
# Result: clamped_power = 100
Why do we clamp? Because: 1. Motors have maximum power limits 2. Too much power can damage mechanisms 3. You might want to limit speed for safety
Friction: The Hidden Force¶
Friction is the force that resists motion. It happens whenever two surfaces touch.
Robot on smooth floor Robot on carpet
+--------+ +--------+
| | | |
+--[O][O]+ +--[O][O]+
═════════════ ~~~~~~~~~~~~
Low friction High friction
Easy to slide Hard to move
For your robot: - Too little friction = wheels spin but robot doesn't move (like on ice) - Too much friction = motors work hard, battery drains fast - Just right = wheels grip and robot moves efficiently
This is why we choose different wheel types: - Traction wheels = high friction for pushing - Omni wheels = can slide sideways (we'll explain why that's useful!)
Momentum: Why Heavy Things Are Hard to Stop¶
Momentum = Mass × Velocity
Slow, heavy robot Fast, light robot
+============+ +--------+
| 15kg | → (2 m/s) | 5kg | →→→→ (6 m/s)
+===[O][O]==+ +--[O][O]+
Momentum = 30 kg·m/s Momentum = 30 kg·m/s
SAME momentum, but the heavy robot is harder to dodge!
In Push Back, a heavy robot moving slowly has lots of momentum - hard to stop or redirect!
Summary¶
| Concept | What It Means | For Your Robot |
|---|---|---|
| Mass | How heavy something is | Affects speed and pushing ability |
| Force | Push or pull | Motors create force to move robot |
| Acceleration | How fast speed changes | More force = faster acceleration |
| Friction | Resistance between surfaces | Wheels need friction to grip |
| Momentum | Mass × velocity | Hard to stop heavy/fast objects |
Exercise: Force Calculations¶
Problem 1: Your robot weighs 8 kg. How much force do you need to accelerate at 3 m/s²?
Problem 2: You have two robots: - Robot A: 6 kg, moving at 4 m/s - Robot B: 12 kg, moving at 2 m/s
Which has more momentum? Which would be harder to stop?
Problem 3: Look at the clamp() function in src/utils.py. What would clamp(-150, -100, 100) return?
Answers¶
Problem 1: F = 8 × 3 = 24 Newtons
Problem 2: - Robot A momentum: 6 × 4 = 24 kg·m/s - Robot B momentum: 12 × 2 = 24 kg·m/s - Same momentum! But Robot B has more mass, so it's harder to redirect.
Problem 3: clamp(-150, -100, 100) returns -100 (the minimum allowed value)