More Conservation of Mechanical Energy Unit 4 Presentation 2

Conservation of Mechanical Energy Reminder

Types of Mechanical Energy Kinetic: Energy of Motion Potential: Stored Energy We talked about Gravitational Potential Energy, but potential energy can be stored against forces other than gravity! Ex: Spring Potential Energy

Spring Force Springs are very important elements in modern technology Hooke’s Law: The negative sign is a symbol representing that the spring force is always directed in the opposite direction of the displacement of the spring F=spring force (N) k=spring constant (N/m) Dx=spring displacement (m)

Spring Force Spring is at equilibrium. x Spring is compressed; force is directed back outward opposite in direction to the compression. x Spring is stretched; force is directed back inward opposite in direction to the stretching. x Equilibrium (unstretched) position of the spring: xo

Hooke’s Law Example Calculate the force of recoil of a spring with spring constant k = 300 N/m that is pulled 30 cm from equilibrium. Since our distance x is positive (to the right), our force of -90N means that the force is directed to the left with a magnitude of 90N

Potential Energy of a Spring Springs also can store potential energy based on how far they are stretched or compressed. SI Units: Joule (J)

Spring Potential Energy Example A block with mass 5.00 kg is attached to a horizontal spring with spring constant k = 400 N/m. The surface that the block rests upon is frictionless. If the block is pulled out to xi = 0.0500 m and released, (a) Find the speed of the block when it first reaches the equilibrium point (b) Find the speed when x = 0.025 m (c) Repeat part (a) if friction acts on the block, with coefficient mk = 0.150. 5 kg xi

Spring Potential Energy Example (cntd) First, draw a free body diagram: Fn Fsp mg Next, consider conservation of energy: (KE + Ug + Usp)o = (KE + Ug + Usp)f Height doesn’t change, so we can cancel out the mgh terms

Spring Potential Energy (cntd) Now, substitute in known values: Now, lets find vx by changing the final spring extension length xf to 0.025 m:

Spring Potential Energy (cntd) Now, lets repeat part (a) while considering friction. To do this, we must calculate the work done by the frictional force and consider the Work-Kinetic Energy Theorem, remembering that this work is going to result in a loss of kinetic energy:

Power Power: The rate at which energy is transferred. SI Unit = Watt (J/sec) 1 horsepower = 550 ft * lb/sec = 746 W

Power Example Killer whales are known to reach 32 feet in length and have a mass of over 8000 kg. They are also very quick, able to accelerate up to 30 mi/hr in a matter of seconds. Disregarding the considerable drag force of water, calculate the average power that a killer whale with mass 8000 kg would need to reach a speed of 12.0 m/s from rest in 6.00 sec.