Draw a plots of mechanical energy, potential energy and kinetic energy versus displacement for different position of a motion of a block attached to a spring.
The equation of mechanical energy for a block attached to the end of spring at the point between maximum distance $x_{m}$ and zero is,
$\mathrm{E}=\frac{1}{2} k x_{m}^{2}$
Equation of potential energy is $\mathrm{V}(x)=\frac{1}{2} k x_{m}^{2}$ and equation of kinetic energy is $\mathrm{K}=\frac{1}{2} m v_{m}^{2}$ At equilibrium position $x=0$ the speed is maximum and hence the kinetic energy is maximum that means $\frac{1}{2} m v_{m}^{2}=\frac{1}{2} k x_{m}^{2}$
displacement |
kinetic energy[k] |
potential energy[v] |
total energy[e] |
$x_{m}$ | $0$ | $\frac{1}{2} k x_{m}^{2}$ | $\frac{1}{2} k x_{m}^{2}$ |
$0 $ | $\frac{1}{2} m v_{m}^{2}$ | $0$ | $\frac{1}{2} k x_{m}^{2}$ |
$-x_{m}$ | $0$ | $\frac{1}{2} k x_{m}^{2}$ | $\frac{1}{2} k x_{m}^{2}$ |
$A$ block of mass $m$ moving with a velocity $v_0$ on a smooth horizontal surface strikes and compresses a spring of stiffness $k$ till mass comes to rest as shown in the figure. This phenomenon is observed by two observers:
$A$: standing on the horizontal surface
$B$: standing on the block
According to observer $B$, the potential energy of the spring increases
As shown in figure there is a spring block system. Block of mass $500\,g$ is pressed against a horizontal spring fixed at one end to compress the spring through $5.0\,cm$ . The spring constant is $500\,N/m$ . When released, calculate the distance where it will hit the ground $4\,m$ below the spring ? $(g = 10\,m/s^2)$
The potential energy of a weight less spring compressed by a distance $ a $ is proportional to
A $2\ kg$ block slides on a horizontal floor with a speed of $4\ m/s$. It strikes a uncompressed spring, and compresses it till the block is motionless. The kinetic friction force is $15\ N$ and spring constant is $10,000\ N/m$. The spring compresses by ............. $\mathrm{cm}$
Two blocks of mass $2\ kg$ and $1\ kg$ are connected by an ideal spring on a rough surface. The spring in unstreched. Spring constant is $8\ N/m$ . Coefficient of friction is $μ = 0.8$ . Now block $2\ kg$ is imparted a velocity $u$ towards $1\ kg$ block. Find the maximum value of velocity $'u'$ of block $2\ kg$ such that block of $1\ kg$ mass never move is