Applied mechanics

A ladder of weight W is placed against a wall as shown in the figure. Calculate the minimum angle of inclination of the ladder with ground so that the ladder doesn't slip under its own weight. Assume coefficient of friction for all surfaces as 0.3.

Deduce the relationship of radial and transverse components of velocity and acceleration for a particle moving along the curve path. The acceleration of a particle is defined by the relation, $a=k{t}^2$, knowing that velocity is $-32\text{ m/sec}$ when time is zero second and again velocity is $+32\text{ m/sec}$ when time is $4\text{ sec}$. (a) Determine, the value of the constant $K$, (b) Write the equations of motion knowing also that position of the particle is zero at the instant of $4\text{ sec}$.

Derive an expression to determine motion of particle when acceleration is the given function of time. The motion of particle is defined by position vector $\vec{r}=3t^2\vec{i}+4t^3\vec{j}+5t^4\vec{k}$ where $r$ is in meter and $t$ in seconds. At the instant $t=4$ seconds, find the normal and tangential component of acceleration and radius of curvature.