Physics

Physics

Problem

The kinetic energy of a block is measured to be (600 ± 12) J(600\,\pm\,12)\,\text{J} and its speed is (15.0 ± 0.2) m ⁣/s(15.0\,\pm\,0.2)\,\text{m\!/s}. Using these data, the mass of the block is best reported as _____ with a percentage error of _____. a) 5.3 kg,  4.7%5.3\,\text{kg},\;4.7\% b) 5.3 kg,  2.4%5.3\,\text{kg},\;2.4\% c) 5.3 kg,  3.3%5.3\,\text{kg},\;3.3\% d) 5.6 kg,  3.3%5.6\,\text{kg},\;3.3\%
Intuitive explanation

Kinetic energy depends on both mass and speed through KE=12mv2KE = \frac{1}{2}mv^2, so you can rearrange to find mass. The key is recognizing that uncertainties in both measurements propagate into your final answer—you'll need to combine them using the rules for error propagation (treating KEKE and vv as independent variables). Calculate the mass first, then use partial derivatives or the relative uncertainty method to find how the errors add up.

Intuitive explanation

Kinetic energy depends on both mass and speed through KE=12mv2KE = \frac{1}{2}mv^2, so you can rearrange to find mass. The key is recognizing that uncertainties in both measurements propagate into your final answer—you'll need to combine them using the rules for error propagation (treating KEKE and vv as independent variables). Calculate the mass first, then use partial derivatives or the relative uncertainty method to find how the errors add up.

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