Work is force times displacement; net work equals change in kinetic energy.
Work W=∫F·dr; the work-energy theorem says net work equals the change in kinetic energy ½mv². Work by gravity is mg·Δh and by a spring ½k(x₁²-x₂²). Friction does negative work and dissipates energy as heat.
Stopping a 1000 kg car from 20 m/s requires 200 kJ of work by brakes.
Work and energy give a shortcut to speed and displacement when forces vary, and they connect mechanics with power and heat.
Work is force times displacement; net work equals change in kinetic energy.
Work and energy give a shortcut to speed and displacement when forces vary, and they connect mechanics with power and heat.
It needs only the start and end states, not the path or time, so it skips the need to solve for the motion at every point.
Yes. When the force opposes the displacement, as with friction or braking, the work is negative and kinetic energy decreases.
Typical applications include finding the speed of a sled after it slides down a hill, estimating the energy absorbed by a crash barrier and computing how much work a crane does to lift a load.
Study "Newton's second law applications" first (topic 26 of 106 in Engineering Mechanics). It covers the groundwork this topic builds on.
Work is scalar in joules. Normal forces do no work in sliding. Useful for variable forces.
Stopping a 1000 kg car from 20 m/s requires 200 kJ of work by brakes.
The next topic is "Potential energy", which builds directly on this one.
It is classed as Beginner in Engineering Mechanics (topic 27 of 106). It is an entry-level topic. It relies only on basic school mathematics and the ideas introduced earlier in this discipline.
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