Work and the Work–Energy Theorem
Work by constant and variable forces and its link to kinetic energy. (Physics › Work, Energy and Power, NEET UG syllabus.)
What is Work and the Work–Energy Theorem?
Work is done when a force causes a displacement of an object. It is a scalar quantity representing the energy transferred to or from an object by a force.
Key formula / rule: Work done by a constant force
Key points
- Define work in physics and differentiate it from everyday usage.
- Calculate work done by a constant force using the dot product.
- Calculate work done by a variable force using integration.
- State and apply the Work-Energy Theorem to solve problems involving motion and energy.
Common exam trap
Confusing work with effort or activity; in physics, work requires displacement.
Definitions
- Term
Work (Physics)
- Meaning
Work is done when a force causes a displacement of an object. It is a scalar quantity representing the energy transferred to or from an object by a force.
- Term
Kinetic Energy
- Meaning
The energy possessed by an object due to its motion. It depends on the object's mass and speed.
- Term
Work-Energy Theorem
- Meaning
A principle stating that the net work done by all forces acting on an object is equal to the change in its kinetic energy.
Learning objectives
Define work in physics and differentiate it from everyday usage.
Calculate work done by a constant force using the dot product.
Calculate work done by a variable force using integration.
State and apply the Work-Energy Theorem to solve problems involving motion and energy.
Identify situations where work done is positive, negative, or zero.
Relate work done to changes in kinetic energy.
Formulae
- Name
Work done by a constant force
- Note
θ is the angle between the force vector F⃗ and the displacement vector d⃗.
- Expression
W = F⃗ ⋅ d⃗ = Fd cosθ
- Name
Work done by a variable force
- Note
Integral is taken from initial to final position. F⃗ is the force vector, d⃗r is the infinitesimal displacement vector.
- Expression
W = ∫ F⃗ ⋅ d⃗r
- Name
Kinetic Energy
- Note
m is mass, v is speed. KE is always positive.
- Expression
KE = ½ mv²
- Name
Work-Energy Theorem
- Note
Wnet is the total work done by all forces acting on the object. KEf and KEi are final and initial kinetic energies.
- Expression
Wnet = ΔKE = KEf - KEi = ½ mvf² - ½ mvi²
Prerequisites
Basic vector algebra (dot product)
Basic calculus (integration)
Newton's Laws of Motion
Understanding of force and displacement
Concept of kinetic energy
Common mistakes
Confusing work with effort or activity; in physics, work requires displacement.
Incorrectly using the angle θ in W = Fd cosθ (it's the angle between F and d, not necessarily the angle with the horizontal).
Forgetting to consider all forces when calculating net work for the Work-Energy Theorem.
Applying W = Fd cosθ for variable forces; integration is required for variable forces.
Misinterpreting the sign of work (e.g., friction always does negative work if there's relative motion).
Not squaring the velocity correctly in the kinetic energy formula (½ mv²).
Keywords
Work
Force
Displacement
Constant Force
Variable Force
Kinetic Energy
Work-Energy Theorem
Joule
Scalar
Dot Product
Integration
Practice preview
When is the work done by a force on an object considered zero?…
easy
Which of the following is the SI unit of work?…
easy
A force F (in N) acting on a particle varies with its position x (in m) as shown in the graph below. Calculate the work done by the force as the particle moves from x = 0 m to x = 4 m. (The graph shows: From x = 0 to x …
medium