Elastic Potential Energy Notes PDF

ELASTIC POTENTIAL ENERGY  Elastic potential energy Elastic potential energy is the energy stored in an object when it is stretched or compressed. This type of energy is associated with elastic materials, such as springs, rubber bands, or any object that can return t...

ELASTIC POTENTIAL ENERGY  Elastic potential energy Elastic potential energy is the energy stored in an object when it is stretched or compressed. This type of energy is associated with elastic materials, such as springs, rubber bands, or any object that can return to its original shape after being deformed. When an object is stretched or compressed, work is done on the object, and this work is stored as potential energy. The amount of elastic potential energy stored depends on how far the object is stretched or compressed from its equilibrium (rest) position, and on the stiffness of the material, which is measured by its spring constant “k”.  Elastic potential energy The formula to calculate elastic potential energy stored in a spring or elastic material is: 1 𝑃𝐸 = k 𝑥 2 2 Where: PE = Elastic Potential Energy k = a measure of stiffness x = the displacement from the equilibrium position (how far the object is stretched or compressed)  Elastic potential energy The farther you stretch or compress the object the larger the x value will become, the more elastic potential energy is stored. A stiffer material will store more energy for the same amount of displacement (the larger the k value the more stiff the material will be).  Elastic potential energy is "stored" in the material and can be released when the object returns to its original shape, like when you release a stretched rubber band or let go of a compressed spring.  Kinetic Energy Calculation The energy of motion KE = W= F x d= mgh=1/2 mv2 Find the kinetic energy of an 4 Kg object moving at 5m/s. KE = 1/2 mv2 KE = ½ (4Kg)(5m/s) 2 KE = 50 Kg m 2 /s 2 KE = 50 J  SAMPLE PROBLEMS 150 𝑁 1. A spring with a spring constant k = is compressed by 𝑚 0.2 m from its equilibrium (a state of rest or balance due to the equal action of opposing forces) position. Calculate the elastic potential energy stored in the spring. 150 𝑁 1(150)(0.04) Given: k = By substitution: PE = Nm 𝑚 2 x = 0.2 m 1 150𝑁 2 PE = 0.2𝑚 PE = 3 Nm 1 2 𝑚 2 PE = 𝑘𝑥 1 150𝑁 2 PE = 0.04 𝑚2 PE = 3 J 2 𝑚  SAMPLE PROBLEMS 𝑁 2. A rubber band has a spring constant of 50 𝑚,and is stretched by 0.1 m. Calculate the elastic potential energy stored in the rubber band. 50 𝑁 1(50)(0.01) Given: k = By substitution: PE = Nm 𝑚 2 x = 0.1 m 1 50𝑁 2 PE = 0.1𝑚 PE = 0.25 Nm 2 𝑚 1 2 PE = 2 𝑘𝑥 1 50𝑁 PE = 0.01 𝑚2 PE = 0.25 J 2 𝑚  SAMPLE PROBLEMS 𝑁 3. A spring with a spring constant of 200 𝑚 has 10 J of elastic potential energy stored in it. How much is the spring compressed from its equilibrium position? Given: k = 200 𝑁 2 2𝑃𝐸 By substitution: 𝑥 = 0.1 𝑚2 𝑚 𝑥 = PE = 10 J = 10 Nm 𝑘 2 10 Nm 𝑥= 𝑥 = 0.316 𝑚 Required: x = ? 2𝑃𝐸 200 N 𝑥2 = 𝑚 PE = 1 𝑘𝑥 2 𝑘 2 𝑚 derive the formula for x 𝑥= 20 Nm 2 2𝑃𝐸 200N 2 PE= 𝑘𝑥 𝑥= 𝑘 𝑘𝑥 2 = 2 PE  Summary Energy is the ability to move Potential is stored energy (Statics) Dependent on height Kinetic is moving energy (Dynamics) Dependent on velocity Springs store energy dependent on distance and constant Power is how fast the work is done  ACTIVITY 250 𝑁 1. A spring with a spring constant k = is compressed by 0.15 m 𝑚 from its equilibrium position. Calculate the Elastic Potential Energy stored in the spring. 𝑁 2. A rubber band has a spring constant of 75 , and is stretched by 𝑚 0.25 m. Calculate the elastic potential energy stored in the rubber band. 𝑁 3. A spring with a spring constant of200 𝑚 has 4 J of elastic potential energy stored in it. How much is the spring compressed from its equilibrium position?