AP Physics Unit 4 Formulas

p² = ?

p² = (mv)²

What does K equal in terms of p?

K = \frac{p²}{2m}

What does p equal in terms of K?

p = \sqrt{2Km}

What does F equal in terms of momentum?

F = \frac{d\overrightarrow{p}}{dt} 

What does d\overrightarrow{p} equal?

d\overrightarrow{p} = \sum \overrightarrow{F}dt

What does \Delta \overrightarrow{p} equal?

\Delta \overrightarrow{p} = \overrightarrow{p_f} - \overrightarrow{p_i} = \int_{t_1}^{t_2}\overrightarrow{F}dt = \overrightarrow{I}

Is impulse a property of a particle?

no

What does thrust equal?

F_{thrust} = M\frac{dv}{dt} = |v_e\frac{dM}{dt}| 

Rocket propulsion equation for \Delta v

v_f - v_i = v_eln(\frac{M_i}{M_f})

What does v_e mean?

exhaust gas velocity

What does the net force on a system equal in terms of rocket propulsion?

\sum \overrightarrow{F} = \overrightarrow{F_{net}} = -v_e\frac{dM}{dt}

How to calculate the x-position of center of mass?

x_{cm} = \frac{\sum m_ix_i}{\sum m_i} H

How to calculate the y-position of center of mass?

y_{cm}=\frac{\sum m_{i}y_{i}}{\sum m_{i}}

What does \lambda equal?

\lambda = \frac{M}{L}

Equation for the velocity of the center of mass of 2+ particles

v_{cm} = \frac{1}{M}\sum m_iv_i

Momentum and center of mass for a system of particles?

Mv_{cm} = \sum m_iv_i = \sum p_i = p_{tot}  

Acceleration of the center of mass?

a_{cm}=\frac{1}{M}\sum m_{i}a_{i}

Acceleration of the center of mass and force?

Ma_{cm} = \sum F_i

Post-collision momentum of a glancing collision in the x-direction

p_x = m_1v_{1f}cos(\theta) + m_2v_{2f}cos(\phi)

Post-collision momentum of a glancing collision in the y-direction

p_y = m_1v_{1f}sin(\theta) + m_2v_{2f}sin(\phi) 

Is momentum always conserved during a glancing collision?

Yes

Is momentum always conserved during an elastic collision?

yes

Is momentum always conserved during a perfectly inelastic colllision?

yes

Is kinetic energy always conserved during an elastic collision?

yes

Is kinetic energy always conserved during a perfectly inelastic collision?

no

Is kinetic energy always conserved during a glancing collision?

no