Question

A block of mass 'm' is attached to a spring in natural length of spring constant 'k'. The other end 'A' of the spring is moved with a constant velocity 'v' away from the block. Find the maximum extension in the spring –

• A. $\frac { 1 } { 4 } \sqrt { \frac { \mathrm { mv } ^ { 2 } } { \mathrm { k } } }$
• B. $\sqrt { \frac { \mathrm { mv } ^ { 2 } } { \mathrm { k } } }$
• C. $\frac { 1 } { 2 } \sqrt { \frac { \mathrm { mv } ^ { 2 } } { \mathrm { k } } }$
• D. $2 \sqrt { \frac { \mathrm { mv } ^ { 2 } } { \mathrm { k } } }$

Answer 1

Answer: (B)

$\sqrt { \frac { \mathrm { mv } ^ { 2 } } { \mathrm { k } } }$

Answer 2

Consider an observer moving with speed v with point A in the same direction.

In the frame of observer, block will have initial velocity v towards left.

During maximum extension, the block will come to rest with respect to the observer. Now, by energy conservation, $\frac { 1 } { 2 } \mathrm { mv } ^ { 2 } = \frac { 1 } { 2 } \mathrm { kx } _ { \max } ^ { 2 }$

\ x_max = $\sqrt { \frac { \mathrm { mv } ^ { 2 } } { \mathrm { k } } }$