Question

Consider a block of mass $10\text{kg}$ collides with a spring of spring constant $10\text{N/m}$. The speed of block is $5\text{m/s}$, when the compression in spring is $2\text{m}$. Calculate the speed of the block, when compression is $5\text{m}$?

• A. $1\text{m/s}$
• B. $2\text{m/s}$
• C. $0.5\text{m/s}$
• D. $2.2\text{m/s}$

Answer 1

The correct option is B $2\text{m/s}$

Given initial velocity $v_i=5\text{m/s}$ when compression in spring is $x_i=2\text{m},$
let $v_f$ be velocity of block when compression in spring is $x_f=5\text{m}$

According to law of conservation of energy
$U_i+K_i=U_f+K_f$ [Sum of potential energy stored in spring and kinetic energy of block will be constant]
$\Rightarrow \frac{1}{2}K{x}_i^2+\frac{1}{2}m{v}_i^2=\frac{1}{2}K{x}_f^2+\frac{1}{2}m{v}_f^2$
$\Rightarrow \frac{1}{2}\times 10\times (2{)}^2+\frac{1}{2}\times 10\times 5^2=\frac{1}{2}\times 10\times 5^2+\frac{1}{2}\times 10\times v_f^2$
$\Rightarrow 10(5^2-v_f^2)=10(5^2-2^2)$
$\Rightarrow v_f=2\text{m/s}$