A block hangs freely from the end of a spring. A boy then slowly pushes the block upwards so that the spring becomes strain free. The gain in gravitational potential energy of the block during this process is equal to:
Correct answer: C. Work done on the block by the boy plus the loss of energy stored in the spring
- A. Work done by the boy against the gravitational force acting on the block
- B. Loss of energy stored in the spring minus the work done by the tension in the spring
- C. Work done on the block by the boy plus the loss of energy stored in the spring
- D. Work done on the block by the boy minus the work done by the tension in the spring
Explanation
Let xo be the initial extension of the spring. Then the initial energy stored in the spring is: ½kxo2The gain in gravitational potential energy: mgh = mgxoThe work done increases the gravitational potential energy and decreases the spring's potential energy. The total energy gained = gain in the gravitational potential energy - loss in spring's potential energy. Therefore, work done by the boy (wb) = gain in the gravitational potential energy - loss in spring's potential From here you can see that the gain in the gravitational potential energy of the block = work done by the boy + loss in the spring's potential energy. Therefore, option C is the correct one.
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Work transfers energy when a force causes displacement, while kinetic energy, gravitational potential energy and power describe motion, position and the rate of energy transfer. The work-energy theorem links net work with change in kinetic energy, and efficiency accounts for energy losses rather than treating them as energy destruction.
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