Force, Work, Power, and Energy
Introduction
This chapter covers the fundamental concepts of force and its rotational effect (moment of force), the conditions for equilibrium, work and its calculation, power, and the different forms of mechanical energy.
Moment of Force (Torque)
The turning effect of a force about a point is called the moment of force.
Moment of force = Force × Perpendicular distance from the pivot
τ = F × d
- Units: N m (Newton-metre)
- Clockwise moment — tends to rotate the body clockwise (taken as negative in some sign conventions).
- Anticlockwise moment — tends to rotate the body anticlockwise (taken as positive).
Principle of Moments
When a body is in rotational equilibrium, the sum of clockwise moments about any point equals the sum of anticlockwise moments about that point.
Σ Clockwise moments = Σ Anticlockwise moments
Equilibrium
A body is said to be in equilibrium when it is under the action of forces that produce no change in its state of rest or uniform motion.
Conditions for Equilibrium
- Translational equilibrium: The vector sum of all forces acting on the body is zero (ΣF = 0).
- Rotational equilibrium: The sum of all moments about any point is zero (Στ = 0).
Types of Equilibrium
| Type | Response to displacement | Example |
|---|---|---|
| Stable equilibrium | Returns to original position | A ball in a bowl |
| Unstable equilibrium | Moves further away | A ball on a convex surface |
| Neutral equilibrium | Stays in new position | A ball on a flat surface |
Centre of Gravity
The centre of gravity (CG) is the point where the entire weight of the body is considered to act.
- For a uniform rod: CG is at the midpoint.
- For a uniform sphere: CG is at the geometric centre.
- For a uniform triangular lamina: CG is at the centroid.
- The stability of a body increases when the CG is lower and the base is wider.
Work
Work is said to be done when a force causes displacement in the direction of the force (or has a component in that direction).
W = F × s × cosθ
Where F = force, s = displacement, θ = angle between force and displacement.
- If θ = 0°: W = Fs (maximum work)
- If θ = 90°: W = 0 (force perpendicular to displacement)
- If θ = 180°: W = −Fs (force opposite to displacement)
Units: Joule (J). 1 J = 1 N × 1 m.
Energy
Energy is the capacity to do work. It has the same units as work (Joule).
Kinetic Energy (KE)
Energy possessed by a body by virtue of its motion.
KE = ¹/₂ mv²
Potential Energy (PE)
Energy possessed by a body by virtue of its position or configuration.
Gravitational PE = mgh
Law of Conservation of Energy
Energy can neither be created nor destroyed — it can only be converted from one form to another. The total energy of an isolated system remains constant.
Power
Power is the rate at which work is done or energy is transferred.
P = W / t = F × v (where v is the average velocity)
Units: Watt (W). 1 W = 1 J/s. Also measured in horsepower: 1 HP = 746 W.
Worked Numerical
A force of 20 N acts on a body at an angle of 60° to the horizontal. The body moves 5 m along the horizontal. Find (a) work done by the force, (b) power if the work is done in 4 seconds.
Solution: (a) W = Fs cosθ = 20 × 5 × cos 60° = 20 × 5 × 1/2 = 50 J (b) P = W/t = 50 / 4 = 12.5 W
Common Mistakes and Fixes
| Mistake | Fix |
|---|---|
| Forgetting the cosθ factor in work | Work = Fs cosθ, not just Fs |
| Confusing mass and weight in PE | PE = mgh (m = mass in kg) |
| Incorrect moment arm | Use PERPENDICULAR distance from pivot |
| Mixing up torque units (Nm vs J) | Torque is in Nm (not Joules) |
ICSE Exam Focus
This chapter carries 8–10 marks. Key topics: moment of force (numericals), equilibrium conditions, work formula with angle, KE/PE problems, and conservation of energy.
Marks Blueprint: Moment of force — 3 marks, Work and energy — 4 marks, Centre of gravity/Equilibrium — 2 marks.
Self-Test Questions
-
A force of 30 N is applied at a distance of 0.5 m from the pivot at 90°. Find the moment of force.
-
A body of mass 10 kg is raised to a height of 5 m. Find its potential energy. (g = 10 m/s²)
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A car of mass 1000 kg is moving at 20 m/s. Find its kinetic energy.
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A force of 50 N acts at 30° to the horizontal, displacing a body by 8 m. Find the work done.
-
State the law of conservation of energy with an example.
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Differentiate between stable and unstable equilibrium with examples.
