A block of mass $m$ is moving with initial velocity $u$ towards a stationary spring of stiffness constant $k$

Question

A block of mass $m$ is moving with initial velocity $u$ towards a stationary spring of stiffness constant $k$ attached to the wall as shown in the figure. Maximum compression of the spring is: (The friction between the block and the surface is negligible).

Accepted Answer

1. **Identify the Principle:** Since friction is negligible, the total mechanical energy of the system is conserved. The initial kinetic energy of the block is converted into the elastic potential energy of the spring at maximum compression.
2. **Formulate Equations:**
   - Initial Kinetic Energy ($K_i$) = $\frac{1}{2}mu^2$
   - Final Potential Energy ($U_f$) at maximum compression $x_m$ = $\frac{1}{2}kx_m^2$ [Class 11 Physics, Ch 5, Sec 5.9, Eq 5.15].
   - At maximum compression, the block momentarily comes to rest, so final kinetic energy is zero.
3. **Apply Conservation of Energy:**
   $$ K_i = U_f $$
   $$ \frac{1}{2}mu^2 = \frac{1}{2}kx_m^2 $$
4. **Solve for Maximum Compression ($x_m$):**
   $$ mu^2 = kx_m^2 $$
   $$ x_m^2 = \frac{m}{k}u^2 $$
   $$ x_m = u\sqrt{\frac{m}{k}} $$ [Class 11 Physics, Ch 5, Example 5.8].

Step-by-Step Solution

Practice All PHYSICS Questions