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18.) A solid of mass 2 kg moving withvelocity 10 m/s strikes an ideal weightless spring andproduces a compression of 25 cm in it. Calculate theforce-constant of the spring.Ans. 3200 N/m.ck of mass 980 8​

Answer»

\blue{\bold{\underline{\underline{Answer:}}}}

\green{\tt{\therefore{Value\:of\:k=3200\:N/m}}}

\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}

\green{\underline{\bold{<klux>GIVEN</klux>:}}} \\ \tt: \implies Mass \: of \: solid (m)= 2 \: kg \\ \\ \tt: \implies Velocity \: of \: solid(v) = 10 \: m/s \\ \\ \tt: \implies Compression \: in \: spring(x) = 25 \: cm \\ \\ \red{\underline{\bold{To \: Find:}}} \\ \tt: \implies Spring \: constant(k) =?

• ACCORDING to given QUESTION :

\green{ \tt \circ} \: x = \frac{25}{100} = 0.25 \: m \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies \frac{1}{2} {kx}^{2} = \frac{1}{2} {mv}^{2} \\ \\ \tt: \implies k \times ({0.25)}^{2} = 2 \times {10}^{2} \\ \\ \tt: \implies k \times 0.0625 = 2 \times 100 \\ \\ \tt: \implies k = \frac{200}{0.0625} \\ \\ \tt: \implies k = \frac{2000000}{625} \\ \\ \green{\tt: \implies k = 3200 \: N/m} \\ \\ \green{ \tt \therefore Spring \: constant \: is \: 3200 \: N/m}


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