Work in science
In daily language, studying hard is "work". In science, work is done only when a force moves an object in the direction of the force.
Two conditions must both hold:
a force acts on the object, and
the object is displaced.
Pushing hard against a wall that doesn't move does no work on the wall, however tired you get. A coolie holding a load on their head while standing still does no work on the load either.
Work done by a constant force
W = F × s
where F is the force and s the displacement in the direction of the force. The SI unit is the joule (J): 1 J of work is done when a force of 1 N moves an object 1 m in its direction.
Work is a scalar: it has size but no direction.
Example. A force of 20 N pushes a box 5 m along the floor. W = 20 × 5 = 100 J.
Positive, negative and zero work
Case | Example | Work |
|---|---|---|
force along the displacement | pulling a trolley forward | positive |
force opposite to the displacement | friction on a sliding block; braking | negative (W = −F × s) |
force at right angles to the displacement | gravity on a ball moving horizontally; the Moon's orbit | zero |
Energy
An object that can do work has energy. Energy is measured in joules, the same unit as work. Energy comes in many forms: kinetic, potential, heat, chemical, electrical, light and sound.
Kinetic energy
Energy due to motion is kinetic energy:
KE = ½ m v²
Example. A 50 kg cyclist moving at 4 m/s has KE = ½ × 50 × 16 = 400 J.
Since KE depends on v², doubling the speed makes the kinetic energy four times as large. That is why a speeding vehicle is far more dangerous.
The work done on an object equals its change in kinetic energy: W = ½mv² − ½mu².
Potential energy
Energy stored because of position or shape is potential energy. A stretched rubber band, a wound spring and water in a dam have it.
Gravitational potential energy of an object of mass m at height h above the ground:
PE = m g h
Example. A 2 kg book on a shelf 1.5 m high: PE = 2 × 9.8 × 1.5 = 29.4 J.
The potential energy depends only on the height, not on the path taken to raise the object.
Conservation of energy
Energy can neither be created nor destroyed; it can only change from one form to another. The total energy before and after any change remains the same.
Example: a falling ball. A ball of mass m is dropped from height h. At the top, it has PE = mgh and KE = 0. As it falls, PE decreases and KE increases. Just before it hits the ground, PE = 0 and KE = mgh. At every point in between, PE + KE = mgh, ignoring air resistance.
Other transformations: a battery turns chemical energy into electrical energy; a bulb turns electrical energy into light and heat; plants turn light energy into chemical energy.
Power
Two people may do the same work, but one may do it faster. Power is the rate of doing work:
P = W ⁄ t
The SI unit is the watt (W): 1 W = 1 J/s. Larger units: 1 kW = 1000 W.
Example. A boy of mass 40 kg climbs 15 steps, each 20 cm high, in 10 s. Work done = mgh = 40 × 10 × 3 = 1200 J (taking g = 10 m/s²). Power = 1200 ÷ 10 = 120 W.
The commercial unit of energy
The joule is too small for household electricity bills, so we use the kilowatt hour (kWh): the energy used in one hour at a rate of 1 kW.
1 kWh = 1000 W × 3600 s = 3.6 × 10⁶ J
One kWh is one "unit" on an electricity bill.
Example. A 100 W bulb used 10 hours a day for 30 days uses 0.1 kW × 300 h = 30 kWh, which is 30 units.
Summary
Work = force × displacement in the direction of the force; it can be positive, negative or zero.
KE = ½mv²; PE = mgh; energy is conserved, only changing form.
Power = work ÷ time, in watts; 1 kWh = 3.6 × 10⁶ J.