AP Physics C: Mechanics [Work, Energy, & Power]

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Work Equation [Constant Force]

W = F \Delta r \cos \theta
Units in Joules

Work Equation [Non-constant Force]

W = \int_{x_i}^{x_f} F_x dx

Hooke’s Law

F_s = -k\Delta x
k is the spring constant, it is non-negative. K is in Nm.

Work done by a Spring Force

W_{F_s} = -\Delta U = \int_{x_i}^{x_f} F_s = \frac{{kx_i}²}{2} -\frac{{kx_f}²}{2}

Kinetic Energy

K = \frac{1}{2}mv²
Units in Joules

Potential Energy

U = mgh
Units in Joules

Conservation of Mechanical Energy

E_i = E_f
Applies to systems where only conservative forces act, non-conservatives forces do not conserve energy within the system.

Work due to Friction Force

W_{friction} = \Delta E

Power Equations

P_{avg} = \frac{\Delta W}{\Delta t}
P_{inst.} = \frac{dW}{dt}
Units in Watts

Power of a Constant Force

P = Fv
(dot product)