Momentum Mission Worksheet Momentum Equation
Investigation File: 01-A
Name: __________________________
Date: __________________________
The Core Concept
Momentum is "mass in motion." Every moving object has it. It is a vector quantity (magnitude + direction).
p = m · v
p: Momentum
m: Mass
v: Velocity
Part 1: Conceptual Check
1. Which has more momentum: a 1,500 kg car parked at a stoplight or a 0.05 kg bumblebee flying at 2 m/s? Explain your reasoning.
2. A bowling ball and a tennis ball roll at the exact same speed . Which is harder to stop? Use "momentum" in your explanation.
Part 2: Vector Diagrams
Draw a vector arrow for momentum. Length = relative magnitude.
A: 10kg Cart @ 2 m/s East
B: 5kg Cart @ 4 m/s East
Comparison: What do you notice about the sizes of arrows A and B?
Part 3: Calculations
3. A heavy semi-truck has a mass of 30,000 kg and travels at 25 m/s. Calculate its total momentum. Show units.
Given Values
Math Work
4. A car with a mass of 1,200 kg is recorded having a momentum of 18,000 kg·m/s. How fast is the car moving?
Given Values
Math Work
Part 4: Road Safety Analysis
5. Explain why highway speed limits are often lower for heavy trucks than for passenger cars, using the physics of momentum.
6. A billiard ball hitting a second ball stops completely. Physics says momentum must be conserved. Where did the momentum go?
p = m · v
Momentum Investigation 01-A
Momentum Mission Answer Key Momentum Equation
TEACHER ANSWER KEY
Key
Part 1 Solutions
1. The bumblebee. The car's velocity is 0, so its momentum is 0 kg·m/s. The bee has mass and velocity, resulting in p = 0.1 kg·m/s.
2. The bowling ball. Because it has significantly more mass, it has much more momentum at the same speed. Momentum measures an object's "inertia in motion," making it harder to stop.
Part 2 Solutions
A: p = 10 * 2 = 20 kg·m/s. (Vector arrow 4cm long East)
B: p = 5 * 4 = 20 kg·m/s. (Vector arrow 4cm long East)
The arrows are identical. Both carts have the same total momentum.
Part 3 Calculations
3. m = 30,000 kg, v = 25 m/s.750,000 kg·m/s .
4. m = 1,200 kg, p = 18,000 kg·m/s.15 m/s .
Part 4 Analysis
5. Trucks have huge mass, so they generate huge momentum even at car speeds. Lowering speed limits brings truck momentum down to a level where brakes can safely stop them in similar distances to cars.
6. The momentum was transferred entirely to the second ball. Total momentum in the system (Ball 1 + Ball 2) remains constant.
Collision Categories Worksheet Collision Categories
Investigation File: 02-B
Name: __________________________
Date: __________________________
Elastic Collisions
• Objects "bounce" away cleanly.
• Momentum is conserved.
• Kinetic Energy is conserved.
Inelastic Collisions
• Objects stick or break permanently.
• Momentum is conserved.
• Kinetic Energy is LOST (heat/sound).
Part 1: Identify the Collision
A high-speed car crash where bumpers and frames crumple.
Type: ____________________
Reason:
Two steel ball bearings bouncing off each other on a hard table.
Type: ____________________
Reason:
A football player tackles another; they fall and slide together.
Type: ____________________
Reason:
Part 2: Energy Transformations
In an inelastic collision, "lost" kinetic energy turns into other forms. List three specific forms of energy that KE might turn into during a car crash.
Part 3: Drawing Collision Data
A: Elastic (Bounce)
Before
Cart 1 (1kg) @ 5 m/s
Draw Result After Impact
B: Inelastic (Stick)
Before
Cart 1 (1kg) @ 5 m/s
Draw Result After Impact
Part 4: The Crumple Zone
Automobile engineers design cars to "crumple" in a crash. This makes the collision highly inelastic instead of an elastic bounce.
Why is an inelastic "crumple" safer than a "bounce" for the people inside? (Explain using Force and Time).
Collision Safety • Investigation 02-B
Collision Categories Answer Key Collision Categories
Teacher Answer Key
Key
Part 1 Identification
A. INELASTIC . Why: Energy is lost to the work of crumpling and bending the car's frame.
B. ELASTIC . Why: They bounce cleanly with almost all energy kept as motion.
C. INELASTIC . Why: The masses combine/stick and move as one after the hit.
Part 2 Energy Transformations
HEAT
SOUND
DAMAGE
Part 3 Drawing Results
A. Cart 1 stops (v=0). Cart 2 moves RIGHT at 5 m/s. (Full transfer).
B. Carts stick together. Combined mass (2kg) moves RIGHT at 2.5 m/s.
Part 4 Reflection Answer
Crumpling increases the collision TIME . Since Force = Change in Momentum / Time, a longer time reduces the peak force felt by the passengers. A "bounce" (elastic) requires twice the momentum change, doubling the force needed!
Momentum Masterclass Slides Physics Engineering Lab
MOMENTUM
MECHANICS
Whole-Group Masterclass & Workshop
Workshop Goals
01
Master p = mv .
02
Identify Collisions .
03
Apply Conservation .
04
Analyze Impulse .
Phase 01
Defining Momentum
p = m • v
p: Momentum (kg•m/s)m: Mass (kg)v: Velocity (m/s)
Insight
Momentum is a vector . Direction matters! Right is (+), Left is (-).
On Your Own
Calculation: The Truck
A 2,500 kg truck travels north at 20 m/s.
What is its momentum?
If the truck doubles its speed, what happens to "p"?
Answer: Scaling Momentum
1. p = 2,500 kg × 20 m/s = 50,000 kg•m/s
2. Double Speed: Since p ∝ v, doubling velocity doubles momentum to 100,000 kg•m/s .
Turn & Talk
Challenge: Fast vs Massive
Elephant
6,000 kg
At 0.1 m/s
Bullet
0.02 kg
At 500 m/s
Who has more momentum?
Answer: Mass Wins
Elephant:
6,000 × 0.1 = 600 kg•m/s
Bullet:
0.02 × 500 = 10 kg•m/s
The Verdict: The Elephant! Its huge mass creates 60x more momentum than the bullet's high speed.
Phase 02
Collision Science
Elastic
Objects bounce off each other. Kinetic energy is conserved.
Inelastic
Objects stick together or deform. Kinetic energy is lost to heat.
Group Share
Workshop Test: Classify
Billiards
"Clack!" They bounce off perfectly.
Car Crash
Metal crumples and sticks.
Velcro Ball
Ball sticks to the target.
Answer Key: Collisions
Momentum Matchup Worksheet Momentum Matchup
Investigation File: 03-C
Name: __________________________
Date: __________________________
The Conservation Law
"In a closed system, the total momentum before a collision equals the total momentum after."
p_initial = p_final
Part 1: The Billiard Break
A cue ball (0.17 kg) moving at 10 m/s hits a stationary 8-ball (0.17 kg) in an elastic collision.
1. Calculate Total Initial Momentum (p)
2. Energy Prediction
Since this is ELASTIC, how will the KE after the hit compare to before?
Sketch Momentum Vectors
Part 2: Lab Data (Hit & Stick)
Two carts collide and stick (inelastic). Use conservation to find the final velocity (V).
Object Phase Mass Velocity Momentum Cart 1 (Before) 2 kg 6 m/s __________ Cart 2 (Before) 1 kg 0 m/s __________ TOTAL After 3 kg V = ? p = ________
Connecting N3rd Law: How does the fact that Cart 1 pushes Cart 2 with an equal force explain why the momentum lost by one is gained by the other?
Kinetic Energy Audit
Elastic Collisions
Total KE is conserved . The objects bounce without generating heat.
Inelastic Collisions
Kinetic Energy is lost . It transforms into internal damage or heat.
Part 3: The Skater "Explosion"
Scenario: Student A (50 kg) and Student B (100 kg) are facing each other at rest. They push off from one another.
If Student A moves LEFT at 4 m/s after the push, calculate the final velocity (speed and direction) of Student B.
Math (p_initial = p_final):
Draw Skaters AFTER the push
Student A (50kg) Student B (100kg)
Part 4: Scientific Synthesis
Case Study: A rocket in deep space accelerates forward by firing gas out the back. Explain why momentum is still conserved if you look at the entire system (Ship + Exhaust Gas).
Investigation File 03-C • Unit Record complete
Momentum Matchup Answer Key Momentum Matchup
Teacher Answer Key
Key
Part 1 Solutions
1. p = (0.17 * 10) + 0 = 1.7 kg·m/s .
2. KE is conserved (100%). Total KE after = total KE before.
Drawing: Cue ball stops. 8-ball moves Right at 10 m/s.
Part 2 Lab Table Key
Phase Mass Velocity Momentum Cart 1 2 kg 6 m/s 12.0 Cart 2 1 kg 0 m/s 0.0 TOTAL 3 kg 4.0 m/s 12.0
N3L Answer: Newton's 3rd Law says Cart 1 and Cart 2 feel equal and opposite forces for the same amount of time. This guarantees they trade equal amounts of momentum.
Part 3 Skater Explosion Solution
p_initial = 0vB = +2 m/s (RIGHT)
Drawing: Student A moves Left (v=4). Student B moves Right (v=2, half-length arrow).
Part 4 Synthesis Answer
The exhaust gas has momentum equal and opposite to the ship. Forward momentum (+) and Backward momentum (-) cancel out. The system total was 0 at the start and remains 0 at the end.
Newtonian Impacts Worksheet Newtonian Impacts
Investigation File: 04-D
Name: __________________________
Date: __________________________
Newton's Third Law
"For every interaction, there is an equal and opposite reaction force."
F_A = -F_B
Part 1: The Bug & The Windshield
A tiny bug (0.001 kg) hits the windshield of a massive speeding truck (20,000 kg).
1. Which object experiences a GREATER force during the impact?
O The Bug
O The Truck
O Exactly Equal
Explain reasoning:
2. If forces are equal, why does the bug go "splat"? (Think F = m · a)
Draw Force Vectors for BOTH below
TRUCK
BUG
Label arrows F_bug and F_truck
Part 2: Action-Reaction Pairs
A. Football Kick
Action: Foot pushes ball North.
Reaction: _____________________________________________
B. Lineman Tackle
Action: Player A pushes Player B.
Reaction: _____________________________________________
Part 3: Momentum Change Equality
Interaction forces come in pairs. If Force is equal and Time is the same, then the Impulse (F · t) is equal for both objects. This means the Change in Momentum is also equal and opposite.
Object 1 Change
+25 kg·m/s
↔
Object 2 Change
____ kg·m/s
Part 4: Lab Insight: Repelling Magnets
Setup: You push Magnetic Cart A toward Magnetic Cart B. They repel and bounce away without ever physically touching one another.
1. Application of the Law
Does Newton's 3rd Law still apply here even though they never touch? Why?
2. Force Comparison
If Cart A is twice as massive as Cart B, how do the repulsive forces compare in strength?
Newtonian Impacts • Investigation 04-D
Newtonian Impacts Answer Key Newtonian Impacts
Teacher Answer Key
Key
Part 1 Bug & Truck Key
1. Answer: Exactly Equal .
Reasoning:interaction forces always come in pairs. The force the truck puts on the bug is identical to the force the bug puts on the truck.
2. Splat Answer: Acceleration = Force / Mass. The same force causes massive acceleration for the bug's tiny mass, but negligible acceleration for the truck's huge mass.
Force arrows for both objects must be the EXACT same length and point in opposite directions.
Part 2 Action-Reaction Pairs Key
A. Reaction: The ball pushes BACK on the foot with an equal force South.
B. Reaction: Player B pushes BACK on Player A with an equal force Backward.
Part 3 Momentum Answer
-25 kg·m/s
Part 4 Lab Insight Answers
1. Yes . Contact is not required. Interaction forces are generated by the magnetic fields of the carts.
2. The repulsive forces are exactly equal in strength. Mass does not change the magnitude of the action-reaction force pair.
