Work and Energy. Work vs. Energy Product of force, distance, and how they’re working together increases or decreases the magnitude of v. How force and.

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