Common Exam 3 8:30-9:45 am Friday, Nov. 20th (Arrive by 8:15 am)

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Work and Energy

Conservative vs. Non-conservative forces Last class… Gravitational Potential Energy Spring force and spring potential energy

Conservation of Mechanical Energy Work by Non-conservative force Today… Power

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1 Work done on a system by nonnon--conservativeconservative force

What if non-conservative forces do work on an object, in addition to conservative force? Non-conservative force: friction force, tension, force from a hand, …

Example: Surface with friction

Normal force Friction force Displacement

Gravitational force

First, let’s review sliding on surface without friction

Normal force

Height v1 Displacement v h1 2 h 2 Gravitational force 0

1122 EE= Æ mgh+=+ mv mgh mv mech,1 mech ,2 11222 2

Æ EEmech,2−=Δ= mech ,1 E mech 0

2 Now, with friction…… Normal force

Height Friction force v1 Displacem ent v h1 2 h 2 Gravitational force 0

v2 with friction is smaller than v2 without friction. Æ Æ EEmech,2−=Δ≠ mech ,1 E mech 0 Mechanical energy changes Relation between Δ E & friction force? mech ΔEWmech= friction

Generally, Δ=EWmech non− conservative (see text for proof)

Work done on a system by nonnon--conservativeconservative force

If non-conservative forces do work on an object, in addition to conservative force,

Æ Mechanical energy changes by the a mount o f wor k don e by the non -conservati ve force.

Δ=EEmech mech,, f − E mech i = W non− conservative

Emech = K +U

3 Example: Surface with friction

K1 = 45 J

Displacement = 2 m

K2 = ?

30o

Mass of the dog = 10 kg

Friction force = 10 N

Find the final kinetic energy, K2.

Thermal energy and Work done by friction force

Mechanical energy is reduced by friction force.

Where has this mechanical energy gone?

Observation : Friction heats up the object and the surface

Some Mechanical Energy is converted to Thermal Energy

Δ=EWthermal friction =−=−Δ W friction E mech

ΔEthermal + ΔEmech = 0 Æ EEEtotal=+ mech thermal is conserved. Total energy of the whole system, dog + surface, is conserved.

4 Many types of energy

Mechanical energy, thermal energy, chemical energy, light energy, electric energy, magnetic energy,………

General principle of Conservation of Energy

Total energy of an isolated system is conserved.

(in 1D)

r r In 2D & 3D, Power: = FvcosθF ,v

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5 Work done by a force r r r r Force W = F d cosθ F ,d ≡ F ⋅d θ

Displ acement

Power done by a force Force r r r r P = F v cosθ F ,v ≡ F ⋅v θ

Velocity

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Example Killer whales are known to accelerate very fast. Calculate the average power a killer whale with mass 8000 kg would need to generate to reach a speed of 12.0 m/s from rest in 6.0 s. Assume water resistance is negligible.

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