UPCAT Physics — Work, Energy & ImpulseRevision Notes
Final-week revision notes for Work, Energy & Impulse. If you have already studied the full chapter, this page is your go-to refresher before sitting the UPCAT. Compact, high-yield, and aligned with what University of the Philippines tests in the Physics subtest.
Exam context
The University of the Philippines College Admission Test is conducted by University of the Philippines and is scheduled for Mid-2026 (announced by UP Admissions). The Physics subtest is marked as "Core" in the official pattern, and Work, Energy & Impulse appears in position 4th of 6 in the UPCAT Physics review rotation. Passing mark: UPG ≤ 2.2 typical. Recent UPCAT 2026 papers have drawn roughly 20 questions from this subject.
Work, Energy & Impulse - Revision notes
Work, Energy, and Impulse are fundamental concepts in Physics that explain how forces affect motion and energy transfer. This chapter covers the mathematical relationships between work done by forces, different forms of energy, and momentum changes in collisions. Understanding these concepts is crucial for solving problems in mechanics and analyzing real-world situations like sports, transportation, and machinery.
Sections
Formulas
Example
A person pulls a box with 50 N force at 30° angle, moving it 10 m. W = 50 × 10 × cos(30°) = 433 J
Formula
W = F × d × cos θ
Variables
W = work (J), F = force (N), d = displacement (m), θ = angle between force and displacement
Application
Calculate work done by any force acting at an angle to the direction of motion
Example
A motor does 1000 J of work in 5 seconds. P = 1000/5 = 200 W
Formula
P = W/t or P = F × v
Variables
P = power (W), W = work (J), t = time (s), F = force (N), v = velocity (m/s)
Application
Calculate power output of engines, motors, or human activities
Exam Tips
- Always identify the force, displacement, and angle between them before calculating work
- Remember: no displacement = no work, even with large forces
- For power problems, check if you need W/t or F×v formula
- Draw free body diagrams to visualize force directions clearly
Key Points
- Work is done when a force acts on an object and causes displacement in the direction of the force
- Work is a scalar quantity measured in joules (J)
- Power measures how quickly work is done, measured in watts (W)
- No work is done if force is perpendicular to displacement or if there's no displacement
- Negative work occurs when force opposes motion (like friction or air resistance)
Definitions
Term
Work
Definition
The energy transferred to or from an object via the application of force along a displacement
Importance
Fundamental concept linking force, motion, and energy transfer in mechanical systems
Term
Power
Definition
The rate at which work is done or energy is transferred per unit time
Importance
Essential for understanding efficiency of machines and energy consumption
Section Title
Work and Power
Common Mistakes
- Confusing work with force - work requires both force AND displacement
- Forgetting to use the cosine of the angle when force is not parallel to displacement
- Mixing up power and work units - power is watts (J/s), work is joules
- Assuming work is always positive - it can be negative when force opposes motion
Formulas
Example
A 2 kg ball moving at 10 m/s has KE = ½ × 2 × 10² = 100 J
Formula
KE = ½mv²
Variables
KE = kinetic energy (J), m = mass (kg), v = velocity (m/s)
Application
Calculate energy of moving objects like cars, projectiles, or rotating wheels
Example
A 5 kg book on a 2 m shelf has PE = 5 × 9.8 × 2 = 98 J
Formula
PE = mgh
Variables
PE = gravitational potential energy (J), m = mass (kg), g = 9.8 m/s², h = height (m)
Application
Calculate stored energy due to position in gravitational field
Example
A spring with k = 100 N/m compressed by 0.1 m stores PE = ½ × 100 × 0.1² = 0.5 J
Formula
PE_elastic = ½kx²
Variables
PE_elastic = elastic potential energy (J), k = spring constant (N/m), x = compression/extension (m)
Application
Calculate energy stored in springs, rubber bands, or elastic materials
Exam Tips
- Always square the velocity correctly in KE calculations
- Choose a consistent reference point for measuring heights
- Remember that energy is always positive (it's the square of velocity or height)
- Use conservation of energy when mechanical energy is constant
Key Points
- Kinetic energy depends on mass and velocity - doubling velocity quadruples KE
- Gravitational potential energy depends on mass, height, and gravitational field strength
- Elastic potential energy is stored in compressed or stretched springs
- Energy can be converted from one form to another but total energy is conserved
- At maximum height, KE = 0 and PE is maximum; at ground level, PE = 0 and KE is maximum
Definitions
Term
Kinetic Energy
Definition
The energy possessed by an object due to its motion
Importance
Explains why moving objects can do work and cause damage upon impact
Term
Potential Energy
Definition
The energy stored in an object due to its position or configuration
Importance
Represents the capacity to do work when the object's position changes
Term
Mechanical Energy
Definition
The sum of kinetic and potential energies in a mechanical system
Importance
Total mechanical energy is conserved in systems without friction or air resistance
Section Title
Kinetic Energy and Potential Energy
Common Mistakes
- Forgetting the ½ factor in kinetic energy formula
- Using wrong reference point for measuring height in potential energy
- Confusing elastic potential energy with gravitational potential energy
- Not recognizing that velocity squared means small velocity changes have large energy effects
Formulas
Example
A pendulum bob at the top has PE = mgh, KE = 0. At the bottom: PE = 0, KE = mgh
Formula
E_total = KE + PE = constant
Variables
E_total = total mechanical energy (J), KE = kinetic energy (J), PE = potential energy (J)
Application
Analyze motion in gravitational fields, pendulums, and roller coasters
Example
A car accelerating from 10 m/s to 20 m/s: ΔKE = ½m(20²) - ½m(10²) = 150m J
Formula
W_net = ΔKE = KE_final - KE_initial
Variables
W_net = net work done (J), ΔKE = change in kinetic energy (J)
Application
Calculate work done by all forces acting on an object
Exam Tips
- Identify all energy forms present at different points in the motion
- Set up energy equations: Initial total energy = Final total energy
- Use conservation of energy for problems involving height changes
- Apply work-energy theorem when forces other than gravity are involved
Key Points
- Energy cannot be created or destroyed, only transformed from one form to another
- In ideal systems without friction, mechanical energy (KE + PE) remains constant
- Energy transformations occur continuously in pendulums, roller coasters, and falling objects
- Real systems lose mechanical energy to heat due to friction and air resistance
- The work-energy theorem states that work done equals change in kinetic energy
Definitions
Term
Conservation of Energy
Definition
The principle that energy cannot be created or destroyed, only converted between forms
Importance
Fundamental law of physics that governs all energy transformations in the universe
Term
Work-Energy Theorem
Definition
The net work done on an object equals its change in kinetic energy
Importance
Connects the concepts of work and energy, useful for solving complex motion problems
Section Title
Conservation of Energy
Common Mistakes
- Ignoring friction and air resistance when applying conservation of energy
- Forgetting to include all forms of energy in the system
- Mixing up initial and final energies in calculations
- Not recognizing when energy is lost to non-mechanical forms like heat
Formulas
Example
A 1000 kg car traveling at 20 m/s has momentum p = 1000 × 20 = 20,000 kg·m/s
Formula
p = mv
Variables
p = momentum (kg·m/s), m = mass (kg), v = velocity (m/s)
Application
Calculate momentum of moving objects in collisions and impacts
Example
A 0.5 kg ball changes velocity from 10 m/s to -5 m/s. Δp = 0.5(-5) - 0.5(10) = -7.5 kg·m/s
Formula
J = Δp = FΔt
Variables
J = impulse (N·s), Δp = change in momentum (kg·m/s), F = average force (N), Δt = time interval (s)
Application
Analyze impacts, collisions, and force applications over time
Example
Two cars collide: m₁v₁ + m₂v₂ = m₁v₁' + m₂v₂' (before = after)
Formula
p_initial = p_final (for isolated systems)
Variables
p = momentum of the system before and after collision
Application
Solve collision problems where total momentum is conserved
Exam Tips
- Always define positive direction before solving momentum problems
- Draw before and after diagrams for collision problems
- Remember that momentum is conserved even in explosive situations
- Use impulse-momentum theorem when force and time are given
Key Points
- Momentum is the product of mass and velocity - a measure of motion quantity
- Impulse is the change in momentum caused by a force acting over time
- Newton's second law can be expressed as F = Δp/Δt
- In collisions, total momentum is conserved when no external forces act
- Impulse equals the area under a force-time graph
Definitions
Term
Momentum
Definition
The product of an object's mass and velocity, representing its quantity of motion
Importance
Fundamental quantity in analyzing collisions and interactions between objects
Term
Impulse
Definition
The change in momentum of an object, equal to the product of average force and time
Importance
Explains why extending contact time reduces force in impacts (airbags, padding)
Term
Conservation of Momentum
Definition
In an isolated system, total momentum remains constant before and after collisions
Importance
Key principle for analyzing all types of collisions and interactions
Section Title
Momentum and Impulse
Common Mistakes
- Forgetting that momentum is a vector - direction matters
- Not considering the sign of velocity when calculating momentum changes
- Confusing impulse with momentum - impulse is the CHANGE in momentum
- Applying conservation of momentum when external forces are present
Connections
- Work-Energy Theorem connects force concepts with energy changes
- Conservation of Energy applies to all physical processes, not just mechanical systems
- Momentum conservation explains recoil in guns and rocket propulsion
- Impulse-momentum theorem explains safety features in cars and sports equipment
- Power concepts relate to efficiency in machines and human activities
- Energy transformations occur in all natural processes and technological applications
Exam Strategy
Focus on understanding the physical meaning of each formula before memorizing them. Practice drawing energy bar charts and momentum diagrams for visual problem-solving. Always identify what's conserved (energy or momentum) in each problem type. For collision problems, set up before-and-after equations systematically. Remember that work, energy, and power problems often require identifying multiple steps, so break complex problems into smaller parts. Pay attention to units and signs (positive/negative) as they indicate directions and energy flow.
Quick Review Questions
A 2 kg object moves 5 m when acted upon by a 10 N force parallel to its motion. How much work is done?
W = F × d = 10 N × 5 m = 50 J. Since force is parallel to displacement, cos(0°) = 1.
What is the kinetic energy of a 4 kg object moving at 6 m/s?
KE = ½mv² = ½ × 4 kg × (6 m/s)² = ½ × 4 × 36 = 72 J
If a 3 kg ball is dropped from 10 m height, what is its potential energy initially?
PE = mgh = 3 kg × 9.8 m/s² × 10 m = 294 J
A 1500 kg car traveling at 25 m/s brakes to a stop. What is its change in momentum?
Δp = m(v_final - v_initial) = 1500(0 - 25) = -37,500 kg·m/s. Negative indicates direction change.
If a machine does 500 J of work in 10 seconds, what is its power output?
P = W/t = 500 J / 10 s = 50 W
Ready to practise for the UPCAT 2026?
Super Tutor's AI review plan adapts to your weak areas and builds a weekly practice schedule around your target UPCAT exam date.