3.1 Work, Energy, and Power
Work

• In the simplest case work is done when a force is applied to an object and the object moves in the direction of the applied force.

W = Fs

• Only the component of the force in the direction of the displacement does work.

W = Fs cos θ

• If the displacement is zero, then so is the work.
• The SI unit of work and energy is the joule (J), where 1 J = 1 N.m.

Kinetic energy

• Kinetic energy is the energy due to motion.
• Kinetic energy increases linearly with mass and with the square of the velocity.

KE = ½ mv²

• The total work done on an object equals the change in its kinetic energy.

W = ΔKE = KE_f – KE_i

Potential energy

• Energy stored for later use is potential energy
• The potential energy of an object is determined by the amount of work required to move it from one location to another.

PE = mgh

Conservation of Energy

• In an ideal system (with no form of friction), energy is transformed from potential energy to kinetic energy and vice versa, but the sum of the two is constant.
• The sum of the potential and kinetic energies of an object is its mechanical energy, ME.

ME = PE + KE

Power

• Power is the rate at which work is done.

• The faster work is done, the greater the power.
• The SI unit of power is the watt (W), where 1 W = 1 J/s.
• Horsepower (hp) is defined as: 1 hp = 746 W

3.2 Machines

• Simple machines do not change the amount of work done, but they do make the task easier.
• A machine can be used to (i) multiply force, (ii) change the direction of the applied force (effort), or (iii) multiply speed.
• The mechanical advantage, MA, is the ratio of load to effort force.

• The ideal mechanical advantage, or velocity ratio, is the ratio of the distance moved by the effort to the distance moved by the load.

• The efficiency of a machine is the ratio of output work to input work.