A body of mass 1 kg falls freely from a height of 100 m, on a platform of mass 3 kg which is mounted on a spring having spring constant k=1.25×10⁶ N/m. The body sticks to the platform and the spring's maximum compression is found to be x. Given that g=10 m s⁻², the value of x (in cm) will be close…

Question

A body of mass 1 kg falls freely from a height of 100 m, on a platform of mass 3 kg which is mounted on a spring having spring constant k=1.25×10⁶ N/m. The body sticks to the platform and the spring's maximum compression is found to be x. Given that g=10 m s⁻², the value of x (in cm) will be close to .

Accepted Answer

2. Speed just before impact: v=√2gh=√2000 m/s, so v²=2000. The body sticks (perfectly inelastic): 1× v=4v'⇒ v'²=(v²)/(16)=125. Kinetic energy after sticking: 1/2×4×125=250 J. Compression: 1/2kx²≈250 J (the extra 4g x≈0.8 J of gravity work over 2 cm is negligible): x²=(500)/(1.25×10⁶)=4×10⁻⁴. x=0.02 m =2 cm.

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