In figure, a block slides along a track from one level to a higher level by moving through an intermediate valley. The track is friction less until the block reaches the higher level. Then there is friction force which stops the block at a distance $d$. The block's initial speed ${\nu }_0$ is $6.0 \mathrm{m} {\mathrm{s}}^{-1}$, the height difference $h$ is $1.1 \mathrm{m}$, and the coefficient of kinetic friction $\mu$ is $0.60$. Find $d$.

In the figure, the stiffness of the spring is $k$ and the mass of the block is $m$. The pulley is fixed. Initially, the block $m$ is held such that the elongation in the spring is zero and then released from rest.

$\left(\mathrm{a}\right)$ Find the maximum elongation in the spring

$\left(\mathrm{b}\right)$ the maximum speed of the block $m$.

Neglect the mass of the spring and that of the string. Also, neglect the friction.

A spring-mass system $\left(m_1+\mathrm{massless} \mathrm{spring}+m_2\right)$ fall freely from a height $h$ before $m_2$ colliding inelastically with the ground. Find the maximum value of $h$ so that block $m_2$ will break off the surface. Assume $k=$ stiffness of the spring.

In an ideal pulley particle system, the mass $m_2$ is connected with a vertical spring of stiffness $k$. If the mass $m_2$ is released from rest, when the spring is deformed, find the maximum compression of the spring.