Work and Energy — Important Questions

Both mass and velocity

Kinetic energy is given by the formula KE = ½mv², where m is mass and v is velocity. From this formula, we can see that kinetic energy depends on both mass and velocity. If mass increases (keeping velocity constant), kinetic energy increases. If velocity increases (keeping mass constant), kinetic energy increases even more rapidly since velocity is squared in the formula. Height affects potential energy, not kinetic energy.

Mass and height

Potential energy is given by the formula PE = mgh, where m is mass, g is acceleration due to gravity, and h is height above the reference point. From this formula, we can see that potential energy depends on both mass and height. A heavier object at the same height has more potential energy. The same object at a greater height also has more potential energy. Velocity affects kinetic energy, not potential energy.

Work done per unit time

Power is defined as the rate of doing work, which means work done per unit time. The formula is P = W/t, where P is power, W is work done, and t is time taken. Power tells us how quickly work is being done. For example, a 100W bulb consumes 100J of energy every second. Two motors doing the same work but in different times have different power ratings - the faster one has higher power.

Watt (W)

The SI unit of power is Watt (W). One watt is the power when 1 joule of work is done in 1 second. Since power = work/time, the unit becomes J/s = W. Joule is the unit of work and energy, Newton is the unit of force, and Horse power is a non-SI unit of power where 1 HP = 746 W. The unit watt is named after James Watt, who improved the steam engine.