Engr Help

Principle of Work and Energy for Particles in a Plane

Key Concept: The principle of work and energy for a particle is just an integrated form of

Euler's First Law by integrating F and ma with respect to displacement instead of just starting

from F = ma.

In a Nut Shell: The principle of work and energy for a particle in a plane is that the work

done on the particle from position 1 to position 2 equals its change in kinetic energy from position 1 to position 2.

W_1-2= T₂ - T₁

Principle of Work and Energy for a Particle

where

W_1-2 = the work by all forces acting on the particle that actually do work in going from

position 1 to position 2

T₂ = the total kinetic energy of the particle in position 2

T₁ = the total kinetic energy of the particle in position 1

Note that both work and kinetic energy are scalar quantities (not vectors).

The key steps in applying the Principle of Work and Energy are as follows:

Step 1: Draw a free body diagram showing all external forces and moments acting on

the particle. Note that not all forces acting on the particle may actually do work.

Step 2: Calculate the work done in going from position 1 to position 2. Common forces

include those due to gravity, applied loads, friction, and spring loading.

Step 3: Calculate the kinetic energy of the particle in position 1 and in position 2.

The kinetic energy for a particle (center of mass of a body) results from translation only.

Total Kinetic Energy: T = ½ mv² (ft lb or N m)

where m = mass of particle , v = speed of the particle ½ mv² = kinetic energy of the particle

Work done by a spring W_1-2= ½ k ( d_i² – d_f²) (ft lb or N m)

where k = spring constant, (lb/ft, N/m) d_i = the initial extension of the spring, (ft, m) and

d_f = the final extension of the spring (ft, m)