1. More Conservation of Mechanical Energy
Unit 4 Presentation 2

2. Conservation of Mechanical Energy Reminder

3. 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

4. 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)

5. 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

6. 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

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

8. 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 = m and released,
(a) Find the speed of the block when it first reaches the equilibrium point
(b) Find the speed when x = m
(c) Repeat part (a) if friction acts on the block, with coefficient mk =
5 kg xi

9. 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

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

11. 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:

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

13. 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.