PHYSICS · Multi-part · CBSE · Physics · Work, Energy and Power · Work, Energy and Power
Problem
In a laboratory investigation, a cart is attached simultaneously to two ideal springs that act in parallel, each fixed to a rigid wall on the opposite side of the cart. One spring has a known force constant k1=3.0×102Nm−1. The second spring has an unknown force constant k2.
With both springs attached, the cart is displaced 0.150m horizontally from equilibrium and released from rest. Electronic sensors determine that the maximum elastic potential energy stored in the combined spring system at that displacement is 5.0J relative to the common equilibrium position.
All motion is horizontal and frictionless.
(a) Derive an algebraic expression for k2 in terms of k1, the measured potential energy U, and the common displacement Δx.
(b) Calculate the numerical value of k2 using the measured quantities provided.
(c) The displacement measurement has an uncertainty of ±0.005m, while the energy measurement is considered exact for this analysis. Determine the percentage uncertainty in the calculated value of k2, showing your reasoning clearly.
(d) Discuss one procedural improvement to the experimental setup that could reduce the uncertainty found in part (c), and explain why it would be effective.