Physics
Work-Energy Theorem
The work-energy theorem states that the net work done on an object equals its change in kinetic energy: W_net = ΔKE = ½m·v_f² - ½m·v_i². It's the link between forces, displacement, and motion — and often the fastest way to find a final speed.
How to Approach Work-Energy Theorem
Compute the work done by each force
W = F·d·cos(θ) for constant forces along a line. For variable forces, W = ∫F·dx. For springs, W = ½k·x_i² - ½k·x_f². Sum the works to get W_net.
Set W_net = ΔKE
ΔKE = ½m·v_f² - ½m·v_i². Equate to the net work and solve for whatever is unknown — usually v_f if v_i and the forces are given.
Account for non-conservative forces
Friction does negative work (always opposes motion). Include it in W_net. If friction work is unknown, you may need to use energy conservation including a thermal term.
Frequently Asked Questions
What's the difference between work and energy?+
Energy is a property of state — an object has KE because it's moving. Work is a process — energy gets transferred to or from an object by a force acting over a distance.
Can work be negative?+
Yes — when force and displacement point in opposite directions. Friction always does negative work on a sliding object. Negative work removes KE; the object slows down.
Is work-energy theorem the same as conservation of energy?+
They're closely related but distinct. Conservation: total mechanical energy stays constant if only conservative forces act. Work-energy: net work (any forces) equals ΔKE. The theorem is more general.
Related Topics
More step-by-step guides in Physics and adjacent subjects.
Stuck on a Work-Energy Theorem problem?
Snap a photo or type the question. ScanSolve walks you through every step — same as the worked examples above. 5 free solves per day, no card required.