Warm up – Do old way A boy pulls a large box with a mass of 50 kg up a frictionless incline (𝜃=35°). He pulls it up to a vertical height of 10 m above the ground. At that point, the rope breaks and the box goes sliding down the incline. What is the velocity of the box once it gets back down to the ground? Assume the velocity is zero at top of incline.

Example - Use Work Energy Theorem A student slides a 0.75 kg textbook across a table, and it comes to rest after traveling 1.2 m. Given that the coefficient of kinetic friction between the book and the table is 0.34, use the Work-Energy theorem to find the book’s initial speed.

Physics Honors AB –Day 1/11/16 Potential Energy and Conservation of Energy

Agenda Potential Energy Mechanical Energy Gravitational Potential Energy Elastic Potential Energy Mechanical Energy Conservation of Mechanical Energy

Potential Energy Stored energy Gravitational Potential Energy associated with an object due to the position of object relative to the Earth or some other gravitational source Elastic Potential Energy energy stored in a stretched or compressed elastic object

Gravitational Potential Energy Equation: 𝑃𝐸=𝑚𝑔ℎ h is measured off adjustable point of zero gravitational potential energy

Examples A ball (m=2 kg) is carried to the top of a cliff that is 50 m high. It then is dropped off the cliff and hits the ground. It then rolls into a hole that is 5 m deep. What is the potential energy at the top of the cliff_________ the bottom of the cliff_________ in the hole___________

Gravitational Potential Energy – not on Earth 𝑈=− 𝐺𝑚𝑀 𝑅

Elastic Potential Energy Equation 𝑃𝐸 𝐸𝑙𝑎𝑠𝑡𝑖𝑐 = 1 2 𝑘 ∆𝑥 2 𝑘 𝑖𝑠 𝑡ℎ𝑒 𝑠𝑝𝑟𝑖𝑛𝑔 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 Spring Constant – expresses how resistant a spring is to being compressed or stretched

Elastic Potential Energy A spring with a force constant, k, of 5.2 N/m has a relaxed length of 2.45 m. When a mass is attached to the end of the spring and allowed to come to rest, the vertical length of the spring is 3.57 m. Calculate the elastic potential energy stored in the spring. Assume the velocity is zero at top of incline.

Conservation of Energy The total energy of the system is constant All the energy in the system can change forms but will be the same total amount 𝐸 𝑖 = 𝐸 𝑓 “Energy can neither be created or destroyed it merely changes forms.”

Mechanical Energy The sum of kinetic and all forms of Potential Energy 𝑀𝐸=𝐾𝐸+ 𝑃𝐸 𝑔𝑟𝑎𝑣𝑖𝑡𝑎𝑡𝑖𝑜𝑛𝑎𝑙 + 𝑃𝐸 𝑒𝑙𝑎𝑠𝑡𝑖𝑐 Mechanical Energy is often conserved; in absence of non conservative force 𝑀𝐸 𝑖 = 𝑀𝐸 𝑓

Conservation of Mechanical Energy The form of energy will change but the amount of mechanical energy will stay constant

Example Problem A boy pulls a large box with a mass of 50 kg up a frictionless incline (𝜃=35°). He pulls it up to a vertical height of 10 m above the ground. At that point, the rope breaks and the box goes sliding down the incline. What is the velocity of the box once it gets back down to the ground?

Conservation of Mechanical Energy v = 0 m/s

Conservation of Mechanical Energy v = 0 m/s

Can Work Be Conservative?

Which is more Work Frictionless Ramp

Which is more Work Frictionless Ramp

Which is more Work Frictionless Ramp

Which is more Work Frictionless Ramp

Which is more Work Frictionless Ramp

Which is more Work Frictionless Ramp

Which is more Work Frictionless Ramp

Which is more Work Frictionless Ramp

Conservative Forces Forces that do work on an object such that energy is recoverable; energy is able to change forms reversibly The work done on an object is independent of the path taken

Let’s Do the Math m = 5 kg 𝜃=35° d=9 𝑚 ∆𝑦=5.16 𝑚

Non – Conservative Forces Forces that do work on an object such that energy is not recoverable; some energy changes form irreversibly The work done on an object is dependent on the path taken

Now with Friction m = 5 kg 𝜃=35° d=9 𝑚 ∆𝑦=5.16 𝑚 Friction = 5N

Examples of Conservative and Non-Conservative Forces Gravity Friction Elastic Air Resistance