Question

a 2.00 kg friction-less block is attached to an ideal spring with force constant 315 N/m.Initially, the spring is neither stretched nor compressed , but the block is moving in the negative direction at 12.0 m/s. find:-a) the amplitude.b) the maximum acceleration of the block.c) the maximum force the spring exerts on the block.

Answer 1

Answer

given,

mass of block, m = 2 Kg

spring constant, k = 315 N/m

speed of the block, v = 12 m/s

a) Amplitude of the motion

   $A = v \sqrt{\dfrac{k}{m}}$

   $A =\dfrac{12}{\sqrt{\dfrac{315}{2}}}$

         A = 0.956 m

b) maximum acceleration of the block

    $a_{max}= A \dfrac{k}{m}$

    $a_{max}= 0.956\times \dfrac{315}{2}$

    $a_{max}= 150.57\ m/s^2$

c) maximum Force

  $F_{max} = m a_{max}$

  $F_{max} = 2\times 150.57$

  $F_{max} = 301.14\ N$