In-the-figure-shown-below-the-block-of-mass-2-kg-is-at-rest-If-the-spring-constant-of-both-the-springs-A-and-B-is-100-N-m-and-spring-B-is-cut-at-t-0-then-magnitude-of-acceleration-of-block-immedi

Question Number 20989 by Tinkutara last updated on 09/Sep/17

In the figure shown below, the block of

mass 2 kg is at rest . If the spring constant

of both the springs A and B is 100 N / m

and spring B is cut at t = 0, then

magnitude of acceleration of block

immediately is

Commented by Tinkutara last updated on 09/Sep/17

Answered by dioph last updated on 09/Sep/17

t = 0^{-}

2 k x \sin 37 ° = m g

x = \frac{m g}{2 k \sin 37 °} ≅ \frac{2 \times 9.8}{2 \times 100 \times 0.6} ≅ 0.163 m

t = 0^{+}

F_{x} = k x \cos 37 ° ≅ 100 \times 0.163 \times 0.8

F_{x} ≅ 13.067 N

F_{y} = m g - k x \sin 37 °

F_{y} ≅ 9.8 N

a = \frac{\sqrt{F_{x}^{2} + F_{y}^{2}}}{m} ≅ \frac{16.334}{2}

a ≅ 8.167 m / s^{2}

Commented by Tinkutara last updated on 13/Sep/17

But spring force does not disappear

immediately, then why you have

neglected F_{x} = k x \cos 37 ° due to spring

B ?