AP Concepts and Problems Flashcards
Relationships between motion variables (with calculus)
v = dx/dt ; a = dv/dt ; x = ∫vdt ; v = ∫adt
Rules for drag force
- Drag force is proportional to just the velocity of the object. Because of it, we can simplify it (though not entirely true) to: F(drag) = kv where k is a constant.
- Drag force is parallel and in the same direction as the relative wind (typically opposite to the opposite direction of the object)
- In reality, drag force is more complex and its formula is given by: F(drag) = (1/2)pCA where p is momentum, C is the drag coefficient, and A is the cross-sectional area.
PROBLEM: If you know velocity according to one person what is the velocity according to another person?
V(ac) = V(ab) + V(bc)
Equations for object with constant acceleration
Vf^2-Vi^2=2a(xf-xi)
Vf=Vi+a(tf-ti)
(Vf-Vi)/(tf-ti)=a
Xf=xi+vi(tf-ti)+1/2(a(tf-ti)^2)
Change in x=(vf+vi)/2(tf-ti)
(when in more than one dimension, create another exact formula for y direction variables)
PROBLEM: Find the final velocity of objects after a totally inelastic collision.
p=mv
p total=m1v1+ m2v2 + …
vf=ptotal/(m1+m2+…)
Equations for a projectile
x(t) = xo + vxot
y(t) = yo + vyot + 1/2gt˄2
Law of static friction
Static friction opposes the direction of potential sliding. It will keep increasing until its maximum and then become kinetic friction.
(uk)(fN)≤Ffs
PROBLEM: A pulley holding up a block with multiple strands of rope
- Add up all the tensions
- T = (mg)/2 (If accelerations is 0)
- Fpull = (mg)/2 (If accelerations is 0)
PROBLEM: Find the terminal velocity of an object
Fnet = ma = m(dv/dt)
Fnet = dv/dt = a = 0
Relationship between average motion variables (displacement, average velocity, average acceleration)
x(t)=displacememt
v(t)=veolcity
a(t)=acceleration
x’(t)=v(t)
v’(t)=a(t)
x’‘(t)=a(t)
Conservation of momentum
Momentum is maintained when there are no external forces.
Elastic collision
m1v1 Initial +m2v2Initial = m1v1 Final+m2v2 Final
Inelastic collision
m1v1 Initial +m2v2Initial = VFinal(m1+m2)
PROBLEM: Draw the forces on an object on a ramp and break the forces into components
Newton’s 1st law
The default state of objects is constant speed straight line motion.
Newton’s 2nd Law for systems
Equation: Fnet(external)= m(total)*a(com)
Newton’s 3rd Law
If object A exerts a force on object B, then object B exerts a force on object A with the same magnitude but opposite direction.