UPCAT Physics — Work, Energy & ImpulseCheat Sheet
Cheat sheet for UPCAT Physics — Work, Energy & Impulse. Compact, printable, and organised around the concepts University of the Philippines tests most frequently in the UPCAT 2026. Perfect for the week before exam day.
Exam context
On the UPCAT 2026, the Physics subtest carries a "Core" weight in University of the Philippines's pattern. Work, Energy & Impulse lands at position 4th out of 6 in the standard review order. Target score is UPG ≤ 2.2 typical, and roughly 20 items come from Physics on a typical UPCAT paper.
Work, Energy & Impulse - Cheat sheet
Your last-minute revision companion for Work, Energy & Impulse - all formulas, definitions, and key concepts for UPCAT success
Sections
Formulas
Formula
W = F × d × cos θ
Meaning
W = work (J), F = force (N), d = displacement (m), θ = angle between F and d
Watch Out
Don't forget the cosine factor - work is zero when θ = 90°
When To Use
When force is applied at an angle to displacement direction
Formula
W = F × d (when θ = 0°)
Meaning
W = work (J), F = force (N), d = displacement (m)
Watch Out
Only use when force is parallel to displacement
When To Use
When force and displacement are in the same direction
Section Title
Work
Important Facts
- Work is a scalar quantity
- SI unit: Joule (J) = N·m = kg·m²/s²
- Work done by gravity depends only on vertical displacement
- Work done by conservative forces is path-independent
- Net work equals change in kinetic energy (Work-Energy Theorem)
Key Definitions
Term
Work
Example
Lifting a book against gravity
Definition
Energy transferred when a force acts through a displacement
Term
Positive Work
Example
Pushing a cart forward
Definition
Force component is in same direction as displacement (0° ≤ θ < 90°)
Term
Negative Work
Example
Friction opposing motion
Definition
Force component opposes displacement (90° < θ ≤ 180°)
Term
Zero Work
Example
Carrying books while walking horizontally
Definition
Force is perpendicular to displacement (θ = 90°)
Diagrams To Know
- Force-displacement diagram with angle θ
- Work done by gravity on inclined plane
- Work-energy bar charts
Formulas
Formula
KE = ½mv²
Meaning
KE = kinetic energy (J), m = mass (kg), v = velocity (m/s)
Watch Out
Velocity is squared - doubling speed quadruples kinetic energy
When To Use
For any moving object
Section Title
Kinetic Energy
Important Facts
- Kinetic energy is always positive
- Depends on reference frame
- Maximum when object moves fastest
- Zero when object is at rest
Key Definitions
Term
Kinetic Energy
Example
Moving car, flying ball, flowing water
Definition
Energy possessed by an object due to its motion
Diagrams To Know
- KE vs velocity graph (parabolic)
- Energy bar charts showing KE changes
Formulas
Formula
PE = mgh
Meaning
PE = gravitational potential energy (J), m = mass (kg), g = 9.8 m/s², h = height (m)
Watch Out
Height is measured from chosen reference point - PE can be negative
When To Use
For objects in gravitational field at different heights
Formula
PE = ½kx²
Meaning
PE = elastic potential energy (J), k = spring constant (N/m), x = displacement (m)
Watch Out
Displacement is from equilibrium position, not total length
When To Use
For compressed or stretched springs
Common Values
Value
9.8 m/s²
Symbol
g
Quantity
Gravitational acceleration
Section Title
Potential Energy
Important Facts
- PE depends on reference point chosen
- Gravitational PE increases with height
- Elastic PE is always positive
- Conservative forces have associated PE
Key Definitions
Term
Potential Energy
Example
Water behind dam, compressed spring, lifted object
Definition
Stored energy due to position or configuration
Term
Gravitational PE
Example
Book on shelf, water at height
Definition
Energy stored due to position in gravitational field
Term
Elastic PE
Example
Compressed spring, stretched rubber band
Definition
Energy stored in deformed elastic materials
Diagrams To Know
- PE vs height graph (linear)
- PE vs spring displacement graph (parabolic)
- Energy transformation diagrams
Formulas
Formula
E = KE + PE = constant
Meaning
E = total mechanical energy (J), KE = kinetic energy (J), PE = potential energy (J)
Watch Out
Only applies when non-conservative forces are absent or do zero work
When To Use
When only conservative forces act (no friction, air resistance)
Formula
½mv₁² + mgh₁ = ½mv₂² + mgh₂
Meaning
Initial KE + initial PE = final KE + final PE
Watch Out
Make sure to use consistent reference point for height
When To Use
Comparing two states in conservative system
Section Title
Mechanical Energy Conservation
Important Facts
- At highest point: maximum PE, minimum KE
- At lowest point: minimum PE, maximum KE
- Total mechanical energy constant in conservative systems
- Energy transforms between kinetic and potential
- Non-conservative forces cause energy loss
Key Definitions
Term
Mechanical Energy
Example
Pendulum swinging, roller coaster motion
Definition
Sum of kinetic and potential energies
Term
Conservative Force
Example
Gravity, spring force, electrostatic force
Definition
Force whose work is path-independent
Term
Non-conservative Force
Example
Friction, air resistance, applied force
Definition
Force whose work depends on path taken
Diagrams To Know
- Energy transformation in pendulum motion
- Energy bar charts at different positions
- PE vs position graphs with turning points
Formulas
Formula
W_net = ΔKE = KE_f - KE_i
Meaning
W_net = net work (J), ΔKE = change in kinetic energy (J)
Watch Out
Must use NET work (sum of all forces), not individual forces
When To Use
Relating net work done to change in kinetic energy
Formula
W_net = ½mv_f² - ½mv_i²
Meaning
Net work equals final KE minus initial KE
Watch Out
Final and initial refer to the same object
When To Use
When you know initial and final velocities
Section Title
Work-Energy Theorem
Important Facts
- Applies to any system regardless of forces involved
- Links force and motion concepts
- Useful when acceleration is not constant
- Can solve problems without knowing time
Key Definitions
Term
Work-Energy Theorem
Example
Braking car, accelerating rocket
Definition
Net work done equals change in kinetic energy
Diagrams To Know
- Free body diagram with work calculation
- Before and after velocity diagrams
Formulas
Formula
p = mv
Meaning
p = momentum (kg·m/s), m = mass (kg), v = velocity (m/s)
Watch Out
Momentum is a vector - direction matters
When To Use
For any moving object
Formula
J = Ft = Δp
Meaning
J = impulse (N·s), F = average force (N), t = time interval (s), Δp = change in momentum
Watch Out
Use average force, not instantaneous force
When To Use
When force acts for a specific time interval
Formula
J = p_f - p_i
Meaning
Impulse equals final momentum minus initial momentum
Watch Out
Must consider direction (+ and - signs)
When To Use
When comparing before and after states
Section Title
Impulse and Momentum
Important Facts
- Momentum is conserved in isolated systems
- Large force for short time = small force for long time (same impulse)
- Impulse = area under F vs t graph
- Units: momentum (kg·m/s), impulse (N·s = kg·m/s)
Key Definitions
Term
Momentum
Example
Moving truck has more momentum than moving bicycle
Definition
Product of mass and velocity; quantity of motion
Term
Impulse
Example
Kicking a ball, catching an egg gently
Definition
Product of force and time; change in momentum
Diagrams To Know
- Force vs time graph (impulse as area)
- Before and after collision diagrams
- Vector diagram for momentum conservation
Must Remember
- Work = F × d × cos θ (don't forget the cosine!)
- KE = ½mv² (velocity is squared)
- PE = mgh (gravitational) or ½kx² (elastic)
- Conservation of energy: KE + PE = constant (no friction)
- Work-Energy Theorem: W_net = ΔKE
- Momentum p = mv (vector quantity)
- Impulse J = Ft = Δp
- Work is zero when force is perpendicular to displacement
- Doubling speed quadruples kinetic energy
- g = 9.8 m/s² in all gravitational PE problems
Last Minute Tips
- Always check if cos θ is needed in work problems - if force and displacement aren't parallel, you need it
- In energy conservation problems, choose your reference point for PE carefully and stick with it
- For collision problems, draw before and after diagrams with momentum vectors
- Remember that negative work means the force opposes motion (like friction)
- When using work-energy theorem, count ALL forces to get net work - don't forget friction or normal force if they do work
Comparison Tables
Rows
Values
- No
- Yes
Property
Work depends on path
Values
- Yes
- No
Property
Associated with PE
Values
- Conserves mechanical energy
- Dissipates mechanical energy
Property
Energy conservation
Values
- Gravity, spring force
- Friction, air resistance
Property
Examples
Columns
- Property
- Conservative
- Non-conservative
Table Title
Conservative vs Non-conservative Forces
Rows
Values
- F × d × cos θ
- F × t
Property
Definition
Values
- Joule (N·m)
- N·s
Property
Units
Values
- Kinetic Energy
- Momentum
Property
Changes
Values
- Displacement
- Time
Property
Related to
Columns
- Quantity
- Work
- Impulse
Table Title
Work vs Impulse
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