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Chapter 10: Q. 46 (page 258)

A1000kgsafe is 2.0mabove a heavy-duty spring when the rope holding the safe breaks. The safe hits the spring and compresses it 50cm. What is the spring constant of the spring?

Short Answer

Expert verified

The spring constant of the spring isk=156,960N/m.

Step by step solution

01

Given information

The weight of the safe=1000kg

The distance between the safe and heavy-duty spring, h=2m

The safe hits the spring and compresses it 50cm.
02

Explanation

The potential energy of a mass at height h is taken as mgh. Energy stored in the spring with spring constant k when it is compressed by a distance x is 12kx2.

The safe hits the spring with KE,

localid="1649411903428" KE=mghKE=1000kg脳9.81m/s2脳2mKE=19620J

This energy is stored in the spring when it is compressed. That is

localid="1649411942679" KE=12kx219,620J=12k0.50m2k=2脳19,620J0.50m2k=156,960N/m

The energy is conserved. The potential energy of the safe is converted to the energy stored in the spring when the spring is compressed.

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