UPCAT Physics — Work, Energy & ImpulseDetailed Explanation
The Work, Energy & Impulse chapter rewards slow, careful thinking over quick pattern matching, especially on University of the Philippines's scenario-based UPCAT items. This detailed explanation walks through the full derivation of every core idea, then links each one to a worked example pulled from recent UPCAT Physics papers.
Exam context
For the University of the Philippines College Admission Test, University of the Philippines tests Physics under a "Core" label, with Work, Energy & Impulse in the 4th slot across 6 chapters. UPCAT candidates must clear the UPG ≤ 2.2 typical cut on the 2026 paper, which draws about 20 Physics questions. Date to watch: Mid-2026 (announced by UP Admissions).
Work, Energy & Impulse - Detailed explanation
Work, Energy, and Impulse are fundamental concepts in physics that explain how forces cause changes in motion and energy. These concepts are crucial for understanding mechanics and appear frequently in college entrance exams. Work describes the energy transfer when a force moves an object, energy represents the capacity to do work, and impulse explains how forces change an object's momentum over time. Mastering these concepts will help you solve complex physics problems and understand real-world phenomena like collisions, energy conservation, and mechanical systems.
Concepts
Work
Work is done when a force causes displacement of an object. It is the energy transferred to or from an object via the application of force along a displacement. Work is calculated as W = F × d × cos(θ), where F is force, d is displacement, and θ is the angle between force and displacement vectors. Work is a scalar quantity measured in joules (J). If force and displacement are in the same direction, maximum work is done. If they are perpendicular, no work is done.
Examples
Since the force is applied in the same direction as displacement, cos(0°) = 1, so work done is positive 500 joules
Scenario
A student pushes a 20 kg box with a force of 50 N across a floor for 10 meters
Solution
W = F × d = 50 N × 10 m = 500 J
The upward force of carrying opposes gravity but displacement is horizontal, making the angle 90°. Since cos(90°) = 0, no work is done against or by the carrying force
Scenario
A person carries a 5 kg bag while walking 100 meters horizontally
Solution
W = 0 J
Applications
- Calculating work done by machines and engines
- Understanding energy efficiency in mechanical systems
- Analyzing human physical activities and sports performance
- Designing construction equipment and tools
Misconceptions
- Thinking that work is done whenever force is applied (displacement is required)
- Confusing work with force or energy
- Believing work is always positive (it can be negative when force opposes motion)
Related Concepts
- Force
- Energy
- Power
- Displacement
- Vector components
Common Exam Questions
Example
Find work done when 10 N force moves object 5 m at 60° angle
Approach
Use W = F × d × cos(θ) formula
Question Type
Direct calculation
Example
Why does carrying a bag horizontally do no work against gravity?
Approach
Identify when force is perpendicular to displacement
Question Type
Zero work scenarios
Key Points To Remember
- Work = Force × displacement × cos(angle)
- Work is done only when there is displacement
- No work is done if force is perpendicular to displacement
- Work can be positive, negative, or zero
- SI unit of work is joule (J)
- Work is a scalar quantity
Energy
Energy is the capacity to do work. It exists in many forms and can be transferred or transformed but never created or destroyed (conservation of energy). Mechanical energy consists of kinetic energy (KE = ½mv²) - energy of motion, and potential energy (PE = mgh) - stored energy due to position. The total mechanical energy in a closed system remains constant. Energy is measured in joules and is a scalar quantity.
Examples
At the highest point, all kinetic energy converts to potential energy. Using PE = mgh, we get 100 = 2(10)h, so maximum height h = 5 meters
Scenario
A 2 kg ball is thrown upward with velocity 10 m/s from ground level
Solution
Initial KE = ½(2)(10)² = 100 J, Initial PE = 0 J, Total energy = 100 J
This potential energy converts to kinetic energy as the car descends, reaching maximum speed at the bottom
Scenario
A roller coaster car at the top of a 30 m hill
Solution
If mass = 500 kg, PE = mgh = 500 × 10 × 30 = 150,000 J
Applications
- Hydroelectric power generation using gravitational potential energy
- Spring mechanisms in watches and toys using elastic potential energy
- Vehicle safety systems analyzing kinetic energy in collisions
- Sports analysis for optimizing athlete performance
Misconceptions
- Thinking energy is lost in collisions (it transforms to other forms like heat and sound)
- Confusing energy with power (power is rate of energy transfer)
- Believing potential energy exists only at maximum height (it exists at any height above reference point)
Related Concepts
- Work
- Power
- Conservation laws
- Force
- Motion
Common Exam Questions
Example
Ball dropped from height h, find velocity when it hits ground
Approach
Set initial total energy equal to final total energy
Question Type
Energy conservation problems
Example
Pendulum motion - energy changes throughout swing
Approach
Identify energy forms at different positions
Question Type
Energy transformation
Key Points To Remember
- Energy = capacity to do work
- Kinetic Energy = ½mv² (energy of motion)
- Potential Energy = mgh (energy of position)
- Energy is conserved in closed systems
- Energy can be transformed from one form to another
- SI unit is joule (J)
Impulse and Momentum
Impulse is the change in momentum caused by a force acting over time. Impulse = F × t = Δp (change in momentum). Momentum (p) is the product of mass and velocity (p = mv). The impulse-momentum theorem states that impulse equals the change in momentum. This concept is crucial for understanding collisions, where large force changes occur over short time periods. Both impulse and momentum are vector quantities.
Examples
The negative impulse indicates the force was opposite to the initial motion direction. If contact time was 0.1 s, average force = -17.5/0.1 = -175 N
Scenario
A 0.5 kg ball moving at 20 m/s hits a wall and bounces back at 15 m/s
Solution
Initial momentum = 0.5 × 20 = 10 kg⋅m/s, Final momentum = 0.5 × (-15) = -7.5 kg⋅m/s, Impulse = -7.5 - 10 = -17.5 kg⋅m/s
Same momentum change occurs, but longer time means smaller force, reducing injury risk
Scenario
A car airbag system during collision
Solution
Airbag increases collision time from 0.1s to 0.5s, reducing force by factor of 5
Applications
- Automotive safety systems (airbags, crumple zones)
- Sports equipment design (helmets, padding)
- Rocket propulsion systems
- Analysis of collision damage in accidents
Misconceptions
- Thinking impulse only occurs in collisions (it occurs whenever force acts over time)
- Confusing impulse with impact force (impulse is force multiplied by time)
- Believing momentum is always conserved (only in closed systems without external forces)
Related Concepts
- Force
- Newton's laws
- Collisions
- Conservation laws
- Vectors
Common Exam Questions
Example
Two objects collide, find final velocities
Approach
Apply conservation of momentum before and after collision
Question Type
Collision problems
Example
Force-time graph problems to find impulse
Approach
Use J = FΔt or J = Δp depending on given information
Question Type
Impulse calculations
Key Points To Remember
- Impulse = Force × time = Change in momentum
- Momentum = mass × velocity
- Impulse-momentum theorem: FΔt = Δp
- Both impulse and momentum are vector quantities
- Momentum is conserved in closed systems
- Large forces over short times create large impulses
Practice Problems
The horizontal component of force does the work since displacement is horizontal. cos(30°) = √3/2 ≈ 0.866
Problem
A 10 kg object is pulled by a 40 N force at 30° above horizontal for 8 meters. Calculate the work done by the applied force.
Solution
W = F × d × cos(θ) = 40 N × 8 m × cos(30°) = 40 × 8 × 0.866 = 277.1 J
All potential energy at the top converts to kinetic energy at the bottom, ignoring air resistance
Problem
A 5 kg ball is dropped from 20 m height. Find its velocity just before hitting the ground using energy conservation.
Solution
Initial: KE₁ = 0, PE₁ = mgh = 5 × 10 × 20 = 1000 J. Final: PE₂ = 0, KE₂ = ½mv². Energy conservation: 1000 = ½ × 5 × v². Solving: v² = 400, v = 20 m/s
Negative values indicate direction opposite to initial motion. The wall exerts 225 N force backward on the object
Problem
A 3 kg object moving at 15 m/s collides with a wall and stops in 0.2 seconds. Calculate the impulse and average force.
Solution
Initial momentum = 3 × 15 = 45 kg⋅m/s. Final momentum = 0. Impulse = 0 - 45 = -45 kg⋅m/s. Average force = Impulse/time = -45/0.2 = -225 N
Exam Preparation Tips
- Always identify the type of problem first: work, energy conservation, or impulse-momentum
- Draw free body diagrams to visualize forces and their directions
- Pay attention to angles between force and displacement in work problems
- Use energy conservation when no external forces do work on the system
- Remember that momentum is a vector - consider direction in collision problems
- Practice unit conversions and ensure consistent units throughout calculations
- Understand when to use each formula: work formulas vs energy conservation vs impulse-momentum
- Look for key words: 'dropped' suggests using energy conservation, 'collision' suggests impulse-momentum
In summary
Work, Energy, and Impulse are interconnected concepts that form the foundation of mechanics. Work describes energy transfer through force and displacement, energy represents the capacity to cause changes, and impulse explains how forces change momentum over time. These concepts appear frequently in UPCAT and other entrance exams, often combined in complex problems involving collisions, projectile motion, and mechanical systems. Master these fundamentals by practicing calculations, understanding energy transformations, and analyzing real-world applications. Remember that conservation laws are powerful tools for solving problems when external forces are absent or when work done by external forces is known.
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.