Elastic Potential Energy The energy stored in a

Elastic Potential Energy • The energy stored in a spring when work is done in compressing or stretching it is called elastic potential energy. • Recall that according to Hook’s law Fs = kx – where k is the spring constant and x is the compression or elongation of the spring

Elastic Potential Energy • Consider the diagram and graph on the board (sketch in your notes)

Elastic Potential Energy • The work done in displacing the mass to the right is converted into the spring’s potential energy (elastic potential energy). • The work is equal to the area under the graph. The area is a triangle, so the area is equal to ½ (base • height)

Elastic Potential Energy • So, the work is equal to W = ½ x • Fs • Substituting Fs = kx into the above, we get W = ½ k x 2 • Since the work done is converted into the springs potential energy, we get PEs = ½ k x 2 (reference tables)

Practice Problem • A spring whose constant is 2. 0 newtons per meter is stretched 0. 40 meter from its equilibrium position. What is the increase in the elastic potential energy of the spring?

Class Demonstration Part I - Work Done To Stretch a Spring Part II - Work Done To Accelerate a Cart

Lab - Making The Grade

Work – Energy Relationship • If there is no friction or air resistance, all the work done in lifting an object to a new height is equal to the objects increase in potential energy. • The change in potential energy depends only on the change in height, not on the path taken.

Work – Energy Relationship • When there is no friction or air resistance, the work done in raising the car is independent of the path taken.

Work – Energy Relationship • If we assume no friction or air resistance, which path would require the most gasoline (or energy) to get to point D?

Conservative Forces Re-Visited • When work done against a force is independent of the path taken, the force is said to be a conservative force. – Gravitational force and the elastic force of a spring are examples of conservative forces. • Air resistance and friction are examples of nonconservative forces. The work done against a nonconservative force is dependent upon the path.

Mechanical Systems • Recall that the sum of the potential energy and kinetic energy is called the total mechanical energy. • Define a closed system as one in which there are no external forces doing work on the system, no external work is being done by the system, and there is no transfer of energy into or out of the system.

The Ideal Mechanical System • An ideal mechanical system is a closed system in which no nonconservative force (such as friction or an applied force) acts.

The Ideal Mechanical System • In an ideal mechanical system, the sum of the kinetic and potential energies is constant, or the changes in kinetic and potential energies is zero. ΔPE = -ΔKE PEi + KEi = PEf + KEf

Lab Cut Short

The Ideal Mechanical System • The change (decrease) in potential energy is equal to the change (increase) in kinetic energy.

The Downhill Skier • Ideal mechanical system - until the skier hits the unpacked snow.