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)