[Figure: a 4 kg block standing on the ground, a vertical spring resting on top of it and a 1 kg block on top of the spring.] Two bodies of masses 1 kg and 4 kg are connected by a vertical spring, as shown. The smaller mass executes simple harmonic motion of angular frequency 25 rad s⁻¹ and amplitud…

Question

[Figure: a 4 kg block standing on the ground, a vertical spring resting on top of it and a 1 kg block on top of the spring.] Two bodies of masses 1 kg and 4 kg are connected by a vertical spring, as shown. The smaller mass executes simple harmonic motion of angular frequency 25 rad s⁻¹ and amplitude 1.6 cm, while the bigger mass stays at rest on the ground. The maximum force exerted by the system on the floor is (take g=10 m s⁻²)

Accepted Answer

(3) 60 N. The spring constant follows from the upper mass: k=mω²=1×25²=625 N m⁻¹. The extra spring force at the extremes is kA=625×0.016=10 N. At equilibrium the floor carries 4g+1g=50 N; the greatest push comes when the upper mass is at its lowest point, adding 10 N. Maximum force on the floor =50+10=60 N.

Step-by-step solution

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