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30 Cards in this Set
- Front
- Back
Conservative Force
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Path does not matter in computing work (only use end points)
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Vector Dot Product of A*B
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A·B = ||A|| ||B|| cos(Θ)
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Vector Interpretation of Work
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Integral of {Force · ds}
(ds is a small piece of the path) |
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Work-Energy Theorem
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⌂Ke = Net Work
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Energy
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An object's capacity for doing work
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Gravitational Potential Energy (very close to the Earth)
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U = mgh
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Elastic Potential Energy for a Spring
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U(x) = (1/2) kx^2
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Is the spring force a conservative force?
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Yes, the spring force is a conservative force
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Work-Potential Energy Relationship
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Work = -⌂U
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Conservation of Energy
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At any given point:
Ke + Us + Ug = Constant Ke = Kinetic Energy Us = Potential Spring Energy Ug = Gravitational Potential Energy |
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Classical Turning Points
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Any point on a Potential Energy Graph at which Ke = 0 (that is, U = Etotal)
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Relationship between Force and Potential Energy
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F (x) = - dU(x) / dx
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Gravitational Potential Energy far from the Earth
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U(r) = -GMm / r
Derived from the fact that Gravitational Force = -GMm / (r^2) We know -dU/dx = F Integral of -F = -GMm / r |
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Power
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dW/dt OR dE/dt
Unit = Watt = Joule/second |
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Vector Representation of Power
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P = F · V
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Power required to accelerate a car of mass m:
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P = m*v*a
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Energy dissipated due to air drag for a car of mass m
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(1/2)C A p v^3
C = constant A = Cross-sectional area p = density v = velocity |
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Formula for Wind Power
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P = 1/2 E*p*A*v^3
Know P ~ v^3 E ~35-50% (efficiency) |
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Why are wind turbines not 100% efficient?
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Would require all air that passes through the system to lose all Ke (impossible). Hence only a portion of the air's Ke is converted.
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Formula for Hydro-power
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P = (⌂V/⌂t)pgH
Know P ~ (⌂V/⌂t) (P is proportional to flow rate) |
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Impulse
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Area beneath the Force Time graph
Units = Newton-second (same as linear momentum) |
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Linear Momentum
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p = mv
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Impulse-Momentum Theorem
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⌂p = Sum of Impulses
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When two particles interact, what is the magnitude of the impulse of particle A on B and particle B on A?
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They are equal in magnitude and opposite in direction
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Inelastic collision
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Objects collide, stick together. Energy is lost. Total velocity of system is decreased.
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Elastic Collisions
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Energy is conserved: a short, sharp, "bounding" collision.
Speed of approach of the objects = speed of separation of the objects |
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Thrust force for a rocket
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F = Velocity (exhaust) * d(mass fuel) / dt
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Rocket velocity equation:
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⌂v = v(exhaust) * ln(Mass(initial)/ Mass(final))
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Rotational Kinetic Energy
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Ke = 1/2 I w^2
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Parallel Axis Theorem
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Relates moment of inertia of an object about two different parallel axes, one through the CM:
I(axis) = I(cm) + Md^2 Thus we see that the axis through the CM has the lowest possible moment |