A trolley on a sloping track is filmed at a steady frames per second

PHYSICS · Multi-part · Fermi University Physics · Scientific Practice & Experimental Methods · Mathematical Methods for Physics · Calculus of change and accumulation

Mathematical Methods for Physics, Ch The derivative as a physical instrument

Problem

A trolley on a sloping track is filmed at a steady 1010 frames per second, so the frames are exactly 0.10 s0.10\,\mathrm{s} apart, and its position is read from a ruler in each frame to the nearest millimetre, each reading good to ±0.5 mm\pm0.5\,\mathrm{mm}. Data: x=0.100, 0.143, 0.192, 0.247, 0.308 mx=0.100,\,0.143,\,0.192,\,0.247,\,0.308\,\mathrm{m} at t=0.00, 0.10, 0.20, 0.30, 0.40 st=0.00,\,0.10,\,0.20,\,0.30,\,0.40\,\mathrm{s}. ((a)) Estimate the trolley's velocity at t=0.20 st=0.20\,\mathrm{s} from the forward difference (0.200.20 to 0.30 s0.30\,\mathrm{s}), the backward difference (0.100.10 to 0.20 s0.20\,\mathrm{s}) and the central difference (0.100.10 to 0.30 s0.30\,\mathrm{s}). ((b)) Here it is the positions, not the times, that carry the reading error. Give the resolution error of each of the three estimates. ((c)) Repeat the central difference over 0.000.00 to 0.40 s0.40\,\mathrm{s} with its resolution error. Do the forward and backward estimates show that the trolley is speeding up, or could their difference be reading error?

Browse the problem library