Question

3. A solid of mass 2 kg moving with
velocity 10 m/s strikes an ideal weightless spring and
produces a compression of 25 cm in it. Calculate the
force-constant of the spring. Ans. 3200 N/m.​

Answer 1

Answer:

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Answer 2

Answer:

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

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

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

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

• According to given question :

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