Interactive physics simulator
Zero Work
Explore how forces can act on moving objects without transferring energy. Analyze the three conditions under which mechanical work equals exactly zero.
Zero Work Lab
Analyze why force, displacement, or vector angles prevent mechanical energy transfer in real time.
Live Telemetry
- Applied Force (F)
- 0.0 N
- Displacement (s)
- 0.0 m
- Angle (θ)
- 0°
- Work Done (W)
- 0.0 J
Understanding Zero Work
In physics, zero work occurs when a force is applied to an object, but no energy is transferred to or from it. Mechanical work is only performed if there is a force acting along the direction of displacement.
Recall the fundamental definition of mechanical work done:
where:
- F is the magnitude of the force (Newtons, N).
- s is the displacement of the object (meters, s).
- θ is the angle between the force and displacement vectors.
Based on this formula, work done becomes exactly zero under three specific physical conditions:
2. Zero Displacement (s = 0): Force is applied, but the object does not move.
3. Perpendicular Force (cos θ = 0): Force is perpendicular to displacement (θ = 90°).
Condition 1: Space Coast (F = 0)
In frictionless deep space, an object will drift at constant velocity forever due to inertia (Newton's First Law). Although it covers displacement (s > 0), there is no net force acting on it (F = 0). By W = 0 · s · cosθ = 0J, no work is done on the asteroid, and its kinetic energy remains perfectly constant.
Condition 2: Pushing a Wall (s = 0)
If you push hard against a massive solid wall, you exert a massive force (F > 0). However, since the wall remains stationary (s = 0), the work done is exactly W = F · 0 = 0J. Biological fatigue (expending chemical energy in your muscles) does not translate to mechanical work done on the wall.
Solved Examples
A space probe of mass m = 250 kg drifts at a constant velocity of v = 12 m/s through frictionless deep space. Calculate the net force acting on the probe, the displacement it covers in s = 500 meters, and the net work done on the probe during this drift.
- Identify the given values: Mass m = 250 kg, velocity v = 12 m/s, displacement s = 500 m.
- Identify the net force: Since the probe drifts at a constant velocity, it is in equilibrium. According to Newton's First Law, the net force acting on it is exactly F = 0 N.
- Recall the work equation: W = F · s · cos(θ).
- Substitute values: W = 0 N · 500 m · cos(θ) = 0 Joules.
- Explain the outcome: Zero work is performed because the applied force is zero (Condition 1: F = 0). According to the Work-Energy Theorem, since net work is zero, the change in kinetic energy is zero (ΔKE = 0). The probe's speed and kinetic energy (KE = 1/2 · 250 · 12² = 18,000 J) remain perfectly constant.
Answer: Net Force F = 0 N, Work Done W = 0 J
A strong person exerts a constant horizontal push force of F = 850 N against a massive concrete security door, trying to push it open. If the door remains completely stationary and does not move at all, calculate the work done by the person on the door.
- Identify the given values: Push force F = 850 N, displacement s = 0 meters (door does not move).
- Recall the work formula: W = F · s · cos(θ).
- Substitute the values: W = 850 N · 0 m · cos(0°) = 0 Joules.
- Explain the biological vs mechanical difference: The person exerts effort and consumes chemical energy (feeling tired and warm), but from a physics perspective, no mechanical work is done on the door because there is no displacement (Condition 2: s = 0).
Answer: Work Done W = 0 J
A satellite of mass m = 800 kg orbits the Earth in a perfect circular orbit at a constant speed. The gravitational force acting on the satellite is Fg = 7200 N. Calculate the work done by gravity on the satellite over one full orbit.
- Identify the variables: Satellite mass m = 800 kg, gravitational centripetal force Fg = 7200 N (acting radially inward).
- Analyze the displacement direction: For a circular orbit, the instantaneous displacement/velocity vector is tangential to the circle at every point.
- Determine the angle θ: The radial gravity force vector is perpendicular to the tangential displacement vector, making the angle θ = 90° at all times.
- Calculate the work done by gravity: W = Fg · s · cos(90°). Since cos(90°) = 0, W = 7200 N · s · 0 = 0 Joules (Condition 3: θ = 90°).
- Conclusion: Gravity does zero work on the satellite in a circular orbit. This is why the satellite's speed and kinetic energy remain perfectly constant while orbiting.
Answer: Work Done W = 0 J
Common Mistakes
- Equating biological effort with mechanical work. Straining to lift a heavy box does zero mechanical work until the box actually moves.
- Assuming circular orbits speed up. In perfect circular orbits, the force of gravity is perpendicular to the motion. It performs zero work, keeping orbital speed constant.
- Forgetting that normal forces can do work. While horizontal sliding normal forces do zero work (θ = 90^°), vertical normal forces inside a moving elevator lift the passenger and do positive/negative work.
Condition 3: Perpendicular Force
When force is perpendicular to displacement (θ = 90^°), the cosine term is zero. For example, carrying a suitcase horizontally. The lifting force acts vertically upward, but displacement is horizontal:
Similarly, centripetal magnetic force (F = qv × B) does zero work on charges because it always acts perpendicular to velocity.
Practice Questions
1. A student holds a heavy physics textbook stationary at arm's length for 2 minutes. If the book is held 1.5 meters above the floor, does the student perform mechanical work on the book?
No. Although holding the book requires muscle exertion and expends biological energy, the book remains stationary. Since its displacement is zero (s = 0), the mechanical work done on the book is W = F · s = F · 0 = 0 Joules.
2. Why is the work done by a centripetal force in circular motion always zero?
Centripetal force pulls radially inward toward the center of the path, while the object moves tangentially. This makes the force vector perpendicular to the displacement vector at all times (θ = 90°). Since cos(90°) = 0, the work done W = Fs cos(90°) is always exactly zero.
3. A wooden block slides down a frictionless ramp. Does the normal force from the ramp do any work on the block?
No. The normal force acts perpendicular to the surface of the ramp, while the block's displacement is parallel along the ramp surface. The angle between normal force and displacement is exactly 90°, so the normal force does zero work (WN = N · s · cos(90°) = 0 J).
4. If the net work done on an object is zero, what happens to its kinetic energy and speed?
According to the Work-Energy Theorem (Wnet = ΔKE), if the net work done is zero, the change in kinetic energy is zero (ΔKE = 0). Since kinetic energy remains constant, the object's speed must remain perfectly constant (it either remains at rest or moves at a constant velocity).
FAQ
Frequently Asked Questions
What is zero work in physics?
Zero work is done when a force is applied to an object but no mechanical energy is transferred to or from it. This happens under three physical conditions: (1) the applied force is zero (F = 0), (2) the displacement of the object is zero (s = 0), or (3) the force is perpendicular to the displacement (θ = 90°, cos(90°) = 0).
What are the three conditions for zero work?
The three conditions are: (1) Zero Force: no force acts on the moving object; (2) Zero Displacement: force is applied but the object does not move; (3) Perpendicular Angle: the force is applied at exactly 90° relative to the direction of motion.
Why is work done zero when pushing a solid wall?
Even if you exert a large force on a solid wall, the wall does not move, meaning displacement s = 0. According to the work formula W = F · s · cos(θ), if s = 0, then the work done W is exactly zero.
Does a person do work while carrying a heavy box and walking horizontally?
No, the person does zero work *on the box* along the direction of walk. The lifting force supporting the box is vertical, while the displacement is horizontal. The angle between them is exactly 90°, and cos(90°) = 0, resulting in zero work done by the lifting force.
Why does the centripetal force of a circular orbit do zero work?
In a perfect circular orbit, the centripetal force (e.g., gravity) points radially inward toward the center, while the instantaneous velocity and displacement are tangential. The angle between force and displacement is always exactly 90°. Since cos(90°) = 0, the centripetal force does zero work on the satellite.
Does gravity do work on a satellite in a circular orbit?
No, gravity does zero work because the gravitational pull is perpendicular to the satellite's tangential velocity at every point in the circular orbit. This is why the satellite's orbital speed and kinetic energy remain constant.
Can an object move if the work done on it is zero?
Yes. An object can move at a constant velocity (zero acceleration) in frictionless deep space. Here, the net force is zero (F = 0), so the net work done is zero, but the object continues to displace indefinitely under its own inertia.
Does the normal force on a block sliding on a flat table do work?
No, the normal force acts perpendicular to the surface of contact (θ = 90° to the displacement along the table), so it does exactly zero work.
How does the Work-Energy Theorem explain zero work?
The Work-Energy Theorem states W_net = ΔKE. If the net work done on an object is zero, the change in kinetic energy is zero (ΔKE = 0). This means the object's speed remains perfectly constant (either remaining at rest or continuing at a constant velocity).
What is the angle between force and displacement for zero work to occur?
Zero work occurs when the angle θ between the force vector and displacement vector is exactly 90° (or π/2 radians), because the cosine of 90° is exactly 0.
Why does a magnetic force do zero work on a moving charge?
A magnetic force (F = qv x B) is always perpendicular to the velocity (v) of the moving charge. Because the force is perpendicular to the instantaneous displacement, the work done by the magnetic field on the charge is always zero, only changing its direction of motion, not its speed.
Is holding a heavy weight stationary above your head doing work?
No, because the displacement is zero (s = 0). While your muscles expend biological energy and feel fatigued, no mechanical work is done on the weight because it does not move.