Work and Energy• Modified 3rd Equation

• Multiply by ½ m

• ma = Force

• Work equals change in Kinetic Energy

• All scalars, use only magnitudes!

• Units N-m, or kg m2/s2 Joules (J)

Work vs. Energy

• Product of force, distance, and how they’re working together increases or decreases the magnitude of v.

• How force and distance work together is very important.– If f and d inline, magnitude of v increases.– If f and d partially inline, magnitude of v increases a little.– If f and d perpendicular, magnitude of v remains constant.– If f and d partially opposed, magnitude of v decreases a little.– If f and d opposed, magnitude of v decreases.– If f but no d v remains constant.

Work and Energy

Work equals change in Kinetic Energy

Potential Energy• Work of spring relaxing from xi to xf

• Work of rock falling from yi to yf

Conservation of KE + PE

• Loss of Potential Energy = Gain of Kinetic Energy

any springy things? height change?

• Rearranging

• Result

If only gravity/elastic forces are acting, or gravity/elastic forces plus forces that do no work,then sum of kinetic + potential energy is conserved//

Potential Energy• Without potential energy

• With potential energy

• Don’t do both, or you’ll be double-counting!

KE+PEKE+PE

KE+PE KE+PE

Forces and Work• Gravity (PE)

• Elastic (PE)

• Electrostatic (PE – next semester)

• Molecular/ Nuclear (PE – take more physics)

• Any other force whose work only depends on endpoints (PE)

• Normal (Never does work)

• Circular(Never does work)

• Friction (Requires fudge factor)

• Applied Forces (Requires fudge factor, or may not be appropriate for work/energy)

Friction and Energy

• Friction is always (-) nonconservative work

KE+PE KE+PE

Work friction

Examples

Example 1

• Child on sled Forces acting: gravity, normal, friction

• If no friction, her final velocity would be higher

Example 2 – Part A

• Ski – Slope Forces acting: gravity, normal, friction

• Initial energy

• Work lost to friction

• Final energy

Example 2 – Part B

• Ski – Level surface

• Initial energy for level slide portion

• Final energy for level slide portion

• Work lost to Friction

Example 3

• Crate on level floor Forces acting: applied, friction, normal

• Initial energy

• Work done (both parts)

• Final energy

Example 4• Block on spring with friction Forces acting: elastic, friction, normal

• Initial and final energy

•Work lost to friction

Example 5• Problem 56 Forces acting: elastic, normal, friction