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: