Spring problems are useful for British Physics Olympiad preparation because they connect a force model with an energy model. Before using conservation of mechanical energy, state what belongs to your system and which interactions could transfer energy out.
This is an original introductory exercise, not a released BPhO question.
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Specify the initial and final states
A 0.50 kg block is released from rest by an ideal spring of constant 200 N/m, initially compressed by 0.10 m. The track is horizontal and frictionless. Find the speed when the spring first reaches its natural length. Neglect the spring's mass.
Choose the block and spring as the system. Height does not change, and the stated model allows stored elastic energy to become kinetic energy.
Calculate the energy before the speed
Initial elastic energy is kx2/2 = 200 x 0.102/2 = 1.0 J. Thus mv2/2 = 1.0 J, giving v2 = 4.0 m2/s2 and v = 2.0 m/s.
The compression is in metres. The energy depends on its square, so a unit error in compression has a particularly large effect.
Change one assumption
If 0.25 J is transferred into thermal energy before the same final position, the block has only 0.75 J of kinetic energy. Its speed is then sqrt(3) m/s, approximately 1.73 m/s.
Do not keep using the frictionless equation after adding a loss. Conversely, do not invent a loss simply because real springs are imperfect; use the model specified in the question.
Make a prediction before recalculating
With the original assumptions, doubling compression gives four times the energy and twice the speed. Doubling mass at fixed compression reduces speed by a factor of sqrt(2).
Write the initial energy, final energy and any transfer in separate lines during review. Then explain why gravitational energy cancels here. A method becomes transferable when you can identify the condition that would make it fail.
Continue reading: British Physics Olympiad Mechanics: Momentum vs Kinetic Energy.
Contact Hanlin
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