Physics

Physics

Problem

In a classroom experiment, a student lifts a school bag of mass 4 kg4\,\text{kg} from the floor to a table 2 m2\,\text{m} high. In the same room, another student compresses a spring of spring constant 200 N m−1200\,\text{N\,m}^{-1} by 0.10 m0.10\,\text{m}. a. (i) Identify the type of potential energy stored in each activity. b. (ii) Calculate the magnitude of potential energy stored in the lifted bag. Take g=9.8 m s−2g = 9.8\,\text{m\,s}^{-2}. c. (iii) Calculate the magnitude of potential energy stored in the compressed spring. d. (iv) Which activity stores more potential energy and by how much? Show your working.
Intuitive explanation

This problem is about gravitational potential energy versus elastic potential energy—two different ways objects can store energy. The key insight is that both scenarios involve doing work against a force (gravity in one case, the spring force in the other), and that work gets stored as potential energy. Calculate each energy separately using PEgrav=mghPE_{\text{grav}} = mgh and PEelastic=12kx2PE_{\text{elastic}} = \frac{1}{2}kx^2, then compare to see which system stores more energy for the effort involved.

Intuitive explanation

This problem is about gravitational potential energy versus elastic potential energy—two different ways objects can store energy. The key insight is that both scenarios involve doing work against a force (gravity in one case, the spring force in the other), and that work gets stored as potential energy. Calculate each energy separately using PEgrav=mghPE_{\text{grav}} = mgh and PEelastic=12kx2PE_{\text{elastic}} = \frac{1}{2}kx^2, then compare to see which system stores more energy for the effort involved.

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