- τ = Fr(sinθ)
- KE = 1/2mv^2
- PE = mgh
- EPE = 1/2kΔx^2 (EPE = Elastic Potential Energy)
- W + q = ΔEtotal
- P = W/t
- P = ΔE/t (more generally)
Things to note:
- E of system + surroundings before = E of system + surroundings after
- (E leaving a system = E entering the surroundings), and (E entering a system = E leaving the surroundings)
- Total E of a system = The sum of all forms of E in that system
Static equilibrium = If all velocities are zero
Dynamic equilibrium = If all velocities are constant
In an equilibrium the upward force equals the downward force, the rightward force equals the leftward force, and the clockwise force equals the counter-clockwise force.
Isolated systems exchange neither work, heat or mass with its surroundings.
Closed Systems exchange work and heat, but do not exchange mass with its surroundings
Open Systems exchange work heat and mass with its surroundings.
Unit of E is the joule, or J, which is 1 kg m^2/s^2 which is the same as 1 N m
E = 1/2kΔx^2 (Elastic Potential Energy, sort of like Hooke's Law)
First law of Thermodynamics:
The Law of Conservation of Mechanical Energy states that when only conservative forces are acting, the sum of mechanical energies remains constant. Mechanical E before = mechanical E after.
K1 + U1 = K2 + U2
or (Conservative forces only, no heat)
0 = ΔK + ΔU
Conservative forces never do work because E is never lost or gained by the system.
Closed Systems exchange work and heat, but do not exchange mass with its surroundings
Open Systems exchange work heat and mass with its surroundings.
Unit of E is the joule, or J, which is 1 kg m^2/s^2 which is the same as 1 N m
E = 1/2kΔx^2 (Elastic Potential Energy, sort of like Hooke's Law)
First law of Thermodynamics:
- W + q = ΔEtotal
- ΔEtotal = ΔK + ΔU
- Hence, W + q = ΔK + ΔU
ΔU = Potential Energy
ΔK = Kinetic Energy
ΔEtotal = ΔEmechanical + ΔEinternal = ΔKE + ΔUpotential + ΔEinternal
Simplified equation of the Work-Kinetic Energy Theorem:
W = ΔK
Work done on a system:
W = fdcosθ = ΔK + ΔU
Using sign conventions, If work is done by a system, the W for that system is negative. The opposite is true. Concerning force, if the force acts in the direction of displacement (such as gravity acting on a skydiver), then the force is a positive value. The opposite is also true.
P = W/t or P = (F x displacement)/time, or P = ΔE/t
The Law of Conservation of Mechanical Energy states that when only conservative forces are acting, the sum of mechanical energies remains constant. Mechanical E before = mechanical E after.
K1 + U1 = K2 + U2
or (Conservative forces only, no heat)
0 = ΔK + ΔU
Conservative forces never do work because E is never lost or gained by the system.
The work done against conservative forces is conserved in potential energy. The work done against non-conservative forces is not conserved.
Three methods to calculate the work done by a conservative force:
- Fdcosθ
- ΔU
- Everything but ΔU
Ramp System:
Lever System:
Pulley System:
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