Work-Energy Theorem
Statement and derivation of the work-energy theorem, relating net work done to the change in kinetic energy, typically introduced for constant forces.
What is Work-Energy Theorem?
Work is done when a force causes displacement. It is the product of the component of force in the direction of displacement and the magnitude of the displacement. It is a scalar quantity.
Key formula / rule: Kinetic Energy
Key points
- State the Work-Energy Theorem.
- Derive the Work-Energy Theorem for a constant force.
- Apply the Work-Energy Theorem to solve problems involving changes in kinetic energy.
- Relate net work done to the change in kinetic energy.
Common exam trap
Calculating work done by only one force instead of the net force.
Definitions
- Term
Work
- Meaning
Work is done when a force causes displacement. It is the product of the component of force in the direction of displacement and the magnitude of the displacement. It is a scalar quantity.
- Term
Kinetic Energy
- Meaning
The energy possessed by an object due to its motion. It depends on the object's mass and velocity.
- Term
Net Work
- Meaning
The algebraic sum of the work done by all individual forces acting on an object.
Learning objectives
State the Work-Energy Theorem.
Derive the Work-Energy Theorem for a constant force.
Apply the Work-Energy Theorem to solve problems involving changes in kinetic energy.
Relate net work done to the change in kinetic energy.
Formulae
- Name
Kinetic Energy
- Note
m is mass, v is velocity.
- Expression
KE = ½ mv²
- Name
Work-Energy Theorem
- Note
Wnet is the net work done, ΔKE is the change in kinetic energy.
- Expression
Wnet = ΔKE
- Name
Change in Kinetic Energy
- Note
vf is final velocity, vi is initial velocity.
- Expression
ΔKE = KEf - KEi = ½ m(vf² - vi²)
- Name
Work done by constant force
- Note
F is force magnitude, d is displacement magnitude, θ is the angle between force and displacement.
- Expression
W = Fd cos θ
Prerequisites
Understanding of force, mass, and acceleration.
Knowledge of displacement and velocity.
Basic understanding of kinetic energy.
Concept of work done by a force (W = Fd cos θ).
Common mistakes
Calculating work done by only one force instead of the net force.
Confusing work done with displacement or force.
Incorrectly calculating kinetic energy (e.g., forgetting the 1/2 factor or squaring velocity).
Not considering the direction of forces and displacement when calculating work.
Keywords
Work
Kinetic Energy
Net Work
Change in Energy
Force
Displacement
Velocity
Classical Mechanics
Practice preview
A body of mass 2 kg experiences a net work of 10 J done on it. If its initial kinetic energy was 5 J, what is its final kinetic energy?…
easy
A 0.2 kg ball is thrown vertically upwards with an initial speed of 10 m/s. Ignoring air resistance, what is the work done by gravity on the ball when it reaches its maximum height? (Take g = 10 m/s^2)…
hard
The Work-Energy Theorem relates the net work done on an object to which of the following?…
easy