AP Physics Newton's Laws FRQ

FORMULAS:
To find acceleration with an Atwood machine off a table: (m2*g)/m1+m2

To find tension with an Atwood machine off a table: m1*a (mass 1 is the one on the table)

To find tension 1 with an Atwood machine with 3 masses: find acceleration with the equation then plug in acceleration into T=m1(a+g). Derived from F=ma, to T1-m1g=m1a, to T1=m1(g+a), then find a and plug back in

To find magnitude of acceleration with an Atwood machine with 3 masses: same as previous acceleration, g*(m3-m1-m2)/m1+m2+m3

To find the minimum distance in which the car will stop given a coefficient of friction and speed: v²/2(coefficient of friction)g; derived from f=coefficient of friction*normal force, to -f=-coefficient of friction*mg=ma, to a = -coefficient of friction*g, to deriving a = -v²/2x from the kinematics equation, to v²/2x=coefficient of friction*g, to x=v²/2coefficient of friction*g

To find the minimum distance in which the car will stop given a coefficient of friction and speed on an incline: f=coefficient of friction*normal force where normal force is equal to mgcos(angle), then find the net force = mgsin(angle)-coefficient of friction*mgcos(angle)=ma, solve for a=g(sin-coefficient of friction*cos), then plug in a into d=-v²/2a

To find the speed of the ball in circular motion when thread describes a cone: sqrt(g*length*tan(angle)sin(angle)), Tx=ma(which is the centripetal force), r = length*sin(angle), Tsin(angle)=mv²/lsin(angle), so mgtan(angle)=mv²/lsin(angle), which is sqrt(g*length*tan(angle)sin(angle))

To find the period of the ball to rotate once around the axis: 2pi*r/v, bc v=2pi*r/period

To find centripetal acceleration: find period, then 2pir/period = v, then a=v²/r

To find the force of the seat on the rider at the lowest point: m(g+a)

To find the force of the seat on the rider at the highest point: m(g-a)