Question

A car of mass 1000 kg moves with 18 kilometre per hour collides with a spring of spring constant 6250 N/m. What is the maximum compression of the spring?​

Answer 1

$\huge\mathcal\colorbox{hotpink}{{\color{white}{SoluTioɴ~↓}}}$

Here,

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$\large\rm\red{m}$ = 1000kg

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$\large\rm\pink{v}$ = 18km h${}^{ - 1}$ = 18 × $\large\frac{5}{18} ms { }^{ - 1} = 5ms {}^{ - 1}$

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$\large\rm\purple{k}$ = 6.5 × 10³N m ${}^{ - 1}$

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• At maximum compression χm , the kinetic energy of the car is converted entirely into the potential energy of the spring.

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∴ $\large\frac{1}{2}$ mv² = $\large\frac{1}{2}$ kx²m or xm = $\large\sqrt{\frac{m}{k}}v$

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• Substituting the given values we get,

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$\large\bf\green{xm}$ = $\large\sqrt{ \frac{1000kg}{6.25 \times 10 {}^{2} n \: m{}^{ - 1} } }$ × 5ms ${}^{ - 1}$

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= 0.4 × 5m = $\large\red{2m}$

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$\large{\underline{\overline{\blue{\bold{\boxed{\sf{Final\:Answer\:}}}}}}}$

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• The maximum compression of the spring is 2m.

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ㅤHope it Helps uh Dear!! ❤

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ㅤᕼᗩᑭᑭY ᒪᗴᗩᖇᑎíᑎᘜ ☃️

Answer 2

Answer in attachment

The answer is 2 m.

Hope it will help you .