Work and Energy — Free Physics Review Games.
This unit covers work, kinetic energy, potential energy and conservation of energy — essential concepts for Physics. Use our interactive study games to test your understanding, or review questions in traditional format below.
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This unit covers work, kinetic energy, potential energy and conservation of energy — essential concepts for Physics. Use our interactive study games to test your understanding, or review questions in traditional format below.
Key Concepts Breakdown
1 Work
Work is done on an object when a force causes displacement in the direction of the force. The formula is W = Fd cosθ, where θ is the angle between the force and displacement vectors. Work is a scalar quantity measured in joules (J).
Key Points
- W = Fd cosθ; if force is parallel to motion, cosθ = 1 and W = Fd
- If force is perpendicular to motion (θ = 90°), no work is done
- Work can be negative when force opposes displacement (e.g., friction)
- Net work = sum of work done by all forces acting on the object
A person pushes a 20 kg box 5 m across the floor by applying a 40 N force at 30° above horizontal. How much work does the applied force do?
Use W = Fd cosθ = 40 × 5 × cos30° = 200 × 0.866 ≈ 173 J. Only the horizontal component of the force (40 cos30°) contributes to work because displacement is horizontal. The vertical component does no work since it is perpendicular to motion.
2 Kinetic Energy
Kinetic energy (KE) is the energy an object possesses due to its motion, given by KE = ½mv². The work-energy theorem states that the net work done on an object equals the change in its kinetic energy: W_net = ΔKE. This is one of the most frequently tested relationships on exams.
Key Points
- KE = ½mv²; KE is always ≥ 0 (scalar, never negative)
- Doubling speed quadruples KE; doubling mass only doubles KE
- Work-energy theorem: W_net = KE_f − KE_i
- Units: joules (J) = kg·m²/s²
A 1,000 kg car traveling at 20 m/s brakes to a stop. How much work does the braking force do?
Initial KE = ½(1000)(20²) = 200,000 J. Final KE = 0 J. By the work-energy theorem, W_net = ΔKE = 0 − 200,000 = −200,000 J. The negative sign indicates the braking force acts opposite to the direction of motion, removing energy from the car.
3 Potential Energy
Potential energy is stored energy due to an object's position or configuration. Gravitational PE = mgh (measured from a reference point), and elastic PE = ½kx² for springs. On exams, you must correctly identify the reference height and apply the appropriate formula.
Key Points
- Gravitational PE: PE_g = mgh; h is measured from the chosen reference level
- Elastic PE: PE_e = ½kx², where k is spring constant and x is compression/stretch
- PE depends only on position, not on the path taken to get there
- When an object moves against gravity, PE increases; when it falls, PE decreases
A 2 kg ball is held 5 m above the ground. What is its gravitational potential energy relative to the ground? (g = 10 m/s²)
PE = mgh = (2)(10)(5) = 100 J. If the reference level were set at 2 m above the ground instead, then h = 3 m and PE = 60 J — this shows that PE values depend on the chosen reference, but changes in PE do not. Always note the reference level given in the problem.
4 Conservation of Energy
In a closed system with no non-conservative forces (like friction), total mechanical energy is conserved: KE_i + PE_i = KE_f + PE_f. When friction or air resistance is present, energy is lost to heat and you must account for it: KE_i + PE_i = KE_f + PE_f + W_friction. This principle is central to most multi-step energy problems.
Key Points
- Total mechanical energy E = KE + PE remains constant without friction
- With friction: E_initial = E_final + |W_friction| (energy lost to heat)
- At maximum height, v = 0, so all energy is PE; at lowest point, all energy is KE
- You can set the reference level anywhere — choose the lowest point to simplify math
A 3 kg ball is released from rest at the top of a frictionless ramp 4 m high. What is its speed at the bottom? (g = 10 m/s²)
Set the reference level at the bottom of the ramp. At the top: KE = 0, PE = mgh = (3)(10)(4) = 120 J, so E_total = 120 J. At the bottom: PE = 0, so all energy is kinetic: ½mv² = 120 J → v² = 80 → v ≈ 8.9 m/s. Because the ramp is frictionless, no energy is lost and the conversion is complete.
Questions, answered.
What is Work and Energy?
Work and Energy is Unit 3 of Physics, covering work, kinetic energy, potential energy and conservation of energy.
How to study for Physics Unit 3?
Start with the Quick Summary above, review the Key Concepts, then test yourself with our interactive study games. Aim for 80%+ accuracy before moving on.
How many questions are in this unit?
This unit has 27+ review questions across 5 different game modes.