Question

$\underline{\underline{\sf{ \large{ \red{Question}:- }}}}$A smooth curved track terminates in a smooth horizontal part. A spring of spring constant 400N/m is attached at one end of a wedge fixed rigidly with the horizontal part. A 40g mass is released from rest at a height of 4.9m on the curved track. Find the maximum compression of the string.
$\underline{\underline{\sf{ \large{ \blue{Note}:- }}}}$
Solve using $\rm{\pink{Work\:-\:Energy\:\:Theorem}}$, not using conservation of mechanical energy.​

Answer 1

Given:

A smooth curved track terminates in a smooth horizontal part. A spring of spring constant 400N/m is attached at one end of a wedge fixed rigidly with the horizontal part. A 40g mass is released from rest at a height of 4.9m on the curved track.

To find:

Max compression in the spring.

Calculation:

According to Work-Energy theorem , the total work done by all the forces is equal to the change in kinetic energy.

• Initial KE was zero because the object started at that position.

• Final KE is also zero after max compression of spring.

$\therefore \: W_{gravity} + W_{spring} = \Delta KE$

$= > \: mgh - \dfrac{1}{2} k {x}^{2} = \Delta KE$

$= > \: mgh - \dfrac{1}{2} k {x}^{2} =0 - 0$

$= > \: mgh - \dfrac{1}{2} k {x}^{2} =0$

$= > \:( \dfrac{40}{1000} \times 9.8 \times 4.9) - (\dfrac{1}{2} \times 400 \times {x}^{2}) =0$

$= > \:1.9208 - 200 {x}^{2} =0$

$= > \: 200 {x}^{2} =1.9208$

$= > \: {x}^{2} =96.04 \times {10}^{ - 4}$

$= > \: x=9.8\times {10}^{ - 2} \: m$

$= > \: x=9.8 \: cm$

So, max compression is 9.8 cm.