Question

18.) 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.
ck of mass 980 8​

Answer 1

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

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

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

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

• According to given question :

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

Answer 2

Given:

• Mass = m= 2kg
• Velocity = v = 10m/s
• Compression = x = 25cm = 0.25m

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Need to find:

• The spring constant = k =?

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Solution:

We know,

The Compression in spring = Change in its KE

Taking initial velocity as 0m/s,

━━━━━━━━━━━━━━━

$\dfrac{1}{2} \: k {x}^{2} = \dfrac{1}{2} m \: ( {v}^{2} - {u}^{2} )$

Substituting the values,

$\implies \: \dfrac{1}{2} k \times .25 \times .25 = \dfrac{1}{2} \times 2 ( {10}^{2} - {0}^{2} )$

$\implies \: k \times 0.0625 = 2 \times 100$

$\implies \: k = \dfrac{2 \times 100}{0.0625}$

$\implies \: k = \dfrac{2 \times 1000000}{625}$

$\red{\bold{\large{\boxed {\implies \: k = 3200 N/m}}}}$