Q4.14 Lift Off (T)

Two discs, each of mass m are connected by a stiff spring. Can you press the top disc down so far that when released it will spring back and lift the bottom disc off the table? Discuss the application of energy conservation to this problem.
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Hint

How big must the tension in the spring be if the lower plate is about to ‘lift off’?
 

Solution

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Solution

Yes, the lower disc can be lifted. If the spring expands sufficiently that the tension force across it is greater than mg, there will be a net upward force on the lower disc.

In terms of energy conservation, potential energy is stored in the compressed spring. When the spring is expanded, energy is also stored. When the disc is about to lift off, the total mechanical energy consists of the potential energy stored in the spring, the gravitational potential energy of the upper mass, and the kinetic energy of the upper mass; this sum must be equal to the sum of the potential energy stored when the spring was compressed plus the gravitational potential energy of the upper mass in the compressed position.