UPCAT Physics — Work, Energy & ImpulseStudy Notes
Study notes for Work, Energy & Impulse that match the UPCAT 2026 syllabus. Built to mirror how University of the Philippines structures UPCAT Physics questions, these notes walk through each concept with examples, formulas, and practice questions designed for time-pressured exam conditions.
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 - Study notes
Understanding work, energy, and impulse is fundamental to physics and helps explain how forces affect motion and energy transfer. These concepts are interconnected and form the basis for analyzing mechanical systems. In this chapter, we'll explore how energy is transferred through work, how energy is conserved in mechanical systems, and how impulse relates to changes in momentum.
Summary
Work, energy, and impulse are interconnected concepts that describe how forces affect motion and energy transfer. Work is done when forces cause displacement, and it results in energy transfer. Mechanical energy, consisting of kinetic and potential energy, is conserved in systems without non-conservative forces. Energy continuously transforms between kinetic and potential forms in oscillating systems. Impulse equals the change in momentum and explains how forces applied over time affect an object's motion. Conservation of energy and momentum are powerful principles that help solve complex physics problems. Understanding these concepts is crucial for analyzing mechanical systems, collisions, and energy transformations in both natural phenomena and technological applications.
Sections
Work is done when a force causes displacement in the direction of the force. The mathematical definition of work is W = F × d × cos θ, where F is the applied force, d is the displacement, and θ is the angle between the force and displacement vectors. Work is measured in joules (J) in the SI system. Energy is the capacity to do work and exists in various forms. The two main types of mechanical energy are kinetic energy (energy of motion) and potential energy (stored energy due to position). The principle of energy conservation states that energy cannot be created or destroyed, only transformed from one form to another.
Heading
Work and Energy Fundamentals
Examples
- A student pushing a book across a table does positive work
- Lifting a bag from the floor to a shelf increases its potential energy
- A rolling ball has kinetic energy proportional to its mass and velocity squared
- A pendulum converts between kinetic and potential energy as it swings
Key Points
- Work = Force × Displacement × cos θ (measured in joules)
- Energy is the capacity to do work
- Kinetic energy: KE = ½mv² (energy of motion)
- Potential energy: PE = mgh (gravitational potential energy)
- Energy conservation: Total mechanical energy remains constant
- Power is the rate of doing work: P = W/t
Mechanical energy is the sum of kinetic energy and potential energy in a system. Kinetic energy (KE = ½mv²) represents the energy an object possesses due to its motion, while potential energy represents stored energy due to position or configuration. Gravitational potential energy (PE = mgh) depends on an object's height above a reference point, mass, and gravitational acceleration. In conservative systems, mechanical energy is conserved, meaning the total energy remains constant even as it transforms between kinetic and potential forms. At the highest point of motion, potential energy is maximum and kinetic energy is minimum. At the lowest point, kinetic energy is maximum and potential energy is minimum.
Heading
Types of Energy and Energy Transformations
Examples
- Roller coaster: PE converts to KE going downhill, KE to PE going uphill
- Bouncing ball: KE converts to elastic PE during compression
- Swinging pendulum: continuous energy transformation between KE and PE
- Water falling in a waterfall converts PE to KE
Key Points
- Mechanical energy = KE + PE
- At highest points: PE maximum, KE minimum
- At lowest points: KE maximum, PE minimum
- Energy transformations occur continuously in oscillating systems
- Total mechanical energy remains constant in conservative systems
- Non-conservative forces (friction) cause energy loss from mechanical systems
Impulse is the change in momentum of an object when a force is applied over a time interval. Mathematically, impulse J = F × Δt = Δp, where F is the average force, Δt is the time interval, and Δp is the change in momentum. Momentum is defined as p = mv, where m is mass and v is velocity. The impulse-momentum theorem states that the impulse applied to an object equals its change in momentum. This concept is particularly important in collision analysis and explains why airbags and crumple zones in cars are designed to increase collision time, thereby reducing the average force experienced by passengers.
Heading
Impulse and Momentum
Examples
- Car airbags increase collision time to reduce impact force
- Catching a ball by pulling hands back reduces impact force
- Karate chop: short time, large force creates large impulse
- Following through in sports increases contact time and impulse
Key Points
- Impulse J = F × Δt = change in momentum (Δp)
- Momentum p = mass × velocity (mv)
- Impulse-momentum theorem: J = Δp
- Longer collision time reduces average force
- Conservation of momentum applies in isolated systems
- Units: Impulse and momentum measured in kg⋅m/s or N⋅s
Conservation laws are fundamental principles in physics that state certain quantities remain constant in isolated systems. The law of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another. In mechanical systems, this means the sum of kinetic and potential energy remains constant when no external forces do work. The law of conservation of momentum states that in the absence of external forces, the total momentum of a system remains constant. These laws are powerful tools for solving complex physics problems and understanding natural phenomena.
Heading
Conservation Laws and Applications
Examples
- Elastic collision: both momentum and kinetic energy conserved
- Inelastic collision: momentum conserved, kinetic energy not conserved
- Rocket propulsion: momentum conservation explains forward thrust
- Hydroelectric power: gravitational PE converts to electrical energy
Key Points
- Energy conservation: Total energy in isolated system remains constant
- Momentum conservation: Total momentum in isolated system remains constant
- Conservation laws apply to collisions and explosions
- Energy can be transformed but total amount stays the same
- Momentum is a vector quantity - direction matters
- These laws help predict outcomes of interactions
When solving work, energy, and impulse problems, it's essential to identify the appropriate conservation law or principle to apply. For work-energy problems, determine whether mechanical energy is conserved or if non-conservative forces are present. Set up energy equations comparing initial and final states. For impulse-momentum problems, identify the forces acting and the time interval, then apply the impulse-momentum theorem. Always define your coordinate system clearly and consider vector directions for momentum problems. Check units throughout calculations and verify that answers make physical sense.
Heading
Problem-Solving Strategies
Examples
- Projectile motion: use energy conservation to find landing speed
- Collision problems: apply momentum conservation
- Inclined plane: consider both gravitational and normal forces
- Spring systems: account for elastic potential energy
Key Points
- Identify which conservation law applies to the problem
- Define initial and final states of the system
- Set up appropriate energy or momentum equations
- Consider whether forces are conservative or non-conservative
- Pay attention to vector directions in momentum problems
- Always check units and verify answers make physical sense
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.