AP Physics Unit 2

When would \overrightarrow{R} be proportional to v ?

When we’re working with small objects

When would \overrightarrow{R} be proportional to v² ?

When we’re working with larger objects

What equation can \overrightarrow{R} be represented as?

\overrightarrow{R} = -bv

What is the equation for terminal speed?

v_T = \frac{mg}{b}

What is the derived equation for speed using terminal speed?

v = v_T(1-e^{\frac{t}{\tau}})

What does \tau mean?

\tau is the time constant and is equal to \frac{m}{b}

What is the derivative of the velocity function for resistive force?

a = ge^{\frac{-bt}{m}}

For objects at higher speeds/sizes, what does F_D equal?

F_D = \overrightarrow{R} = -Cv²

What is acceleration in terms of C?

a = g - (\frac{C}{2m})v²

What is terminal velocity in terms of C?

v_T = \sqrt{\frac{mg}{C}}

What is the sum of forces in horizontal circular motion?

\sum{F} = ma_c = m\frac{v²}{r}

If the force providing the centrifugal acceleration on an object vanishes, how would the object start moving?

in a direction tangential to when it was released

What is \sum F_y for conical pendulums?

\sum F_y = 0 \rightarrow Tcos\theta = mg

What is \sum F_x for conical pendulums?

\sum F_x = Tsin\theta = ma_c

What is v in conical pendulums (independent of m)?

v = \sqrt{Lgsin{\theta}tan{\theta}}

What is speed in a horizontal circle/plane dependent on mass/tension?

v = \sqrt{\frac{Tr}{m}}

What is the max speed an object can negotiate a curve?

v = \sqrt{\mu_sgr}

How do you find the angle of a banked curve?

tan\theta = \frac{v²}{rg}

What is the tension (at any point) of a vertical circle with non-uniform speed?

T = mg(\frac{v²}{Rg} + cos\theta)

What is the equation of T_{top}?

T_{top} + mg = ma_c

T_{top} = mg(\frac{v²}{Rg}-1)

What is the equation for T_{bot}?

T_{bot} - mg = ma_c

T_{bot} = mg(\frac{v²}{Rg}+1)

What is the equation for tension at any point in a vertical circle?

T’ -mgcos\theta = ma_c

What is the formula for v_{top} of a vertical circle?

v_{top} = \sqrt{Rg}