1 Kinetic Energy W =1 2 kx2 = 1 2(640)(0.02)2 = 0.128J Suppose that a single constant force F acts on a particle in its direction of motion and causes it to accelerate, increasing in speed from an initial value v0 up to a final value v. Substituting a = F/m in the equation of motion v2 = v20 +2ax, we have v2 = v20 + 2Fx m . The workdone by the force is W = Fx, so W =1 2mv2 − 1 2mv20. (47) (48) This is the work-energy theorem. It says that the work done on a particle is equal to the increase in the kinetic energy of the particle. The work-energy theorem is valid even if the force is varying. The kinetic energy of an object of mass m with speed v is defined as K.E = 1 2mv2 It is also measured in joules (unit of work done). Definition: Energy of a system is a measure of its ability to do work. (49) Example: Calculate the kinetic energy of the earth orbiting the sun at a speed of 2.98 × 104m/s. (mass of earth is 5.98 × 1024kg). Solution: 7.2 Power K.E = 1 2mv2 = 1 2 ×5.98×1024× (2.98× 104)2 = 2.66× 1033J. Power is the rate of doing work or of transferring energy.
