Our Old Clock · Physics Brawl 2020 #FoL.11

Physics · mechanics

Problem

Our old clock is battery-powered and the capacity of the battery is E=1.2WhE = 1.2Wh. The hour hand is rh=5cmr_h = 5cm long and the minute hand is rm=8cmr_m = 8cm long. The linear density of each hand is τ=10g⋅m−1\tau = 10 g \cdot m^{-1}. The efficiency of the clockwork is η=7%\eta = 7\%. How long does it take for the clock to stop? The hands rotate continuously and any potential energy released during descending is lost.

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