### Laws of Motion

goals
A ring of mass $m$ and radius $R$ rests in equilibrium on a smooth cone of semi-vertical angle ${45}^{o}$ as shown. The radius of the cone is $2R$. the radius of circular cross section of the ring is $r\left( r \ll R \right)$.
End A of a rod AB is being pulled on the floor with a constant velocity $v_0$ as shown. Taking the length of the rod as $l$, at an instant when the rod makes an angle $37^o$ with the horizontal, calculate
An isolated rail car originally moving with speed ${ v }_{ 0 }$ on a straight, frictionless, level track contains a large amount of sand. A release valve on the bottom of the car malfunctions, and sand begins to pour out straight down relative to the rail car.
A package is at rest on a conveyor belt which is initially at rest. The belt is started and moves to the right for $1.3s$ with a constant acceleration of  $\displaystyle 2 m/s^{2}$. The belt then moves with a constant deceleration $\displaystyle a_{2}$ and comes to a stop after a total displacement of $2.2m$. Knowing that the coefficients of friction between the package and the belt are $\displaystyle \mu_{s}=0.35$ and $\displaystyle \mu_{k}=0.25,$ determine
If the net external force on a body is zero, its acceleration: