Work-Energy for a System of Particles

 

 

Work

 

A force is a force whether it is applied to a single particle or a system of particles. This means that the definition of work does not change. Work is still the amount of energy transferred by a force acting through a distance.

 

U = ∫F⋅dr

 

Caution! All of the forces acting on the system may not move through the same distance.

 

Kinetic and potential energy

 

 

Energies are additive. Therefore, the total kinetic (T) or potential (V ) energy of the system is just the sum of the energies of the individual particles and springs.

 

T = ∑(1/2)m_iv_i²

 

V_g = ∑m_igh_i     and     V_e = ∑(1/2)k_ix_i²

 

 

Work-energy balance

 

 

The equations that relate work and energy remain the same for a system of particles as they were for a single particle.

 

Work-energy balance: T₁ + V₁ + U_1-2,non = T₂ + V₂

 

Conservation of energy: T₁ + V₁ = T₂ + V₂