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Principle of Conservation of Energy: Energy cannot be created or destroyed, only converted from one form to another. The total energy in an isolated system remains constant. [2]
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Work vs Power: Work is the product of force and distance in the direction of the force (W=Fd); Power is the rate at which work is done or energy is transferred (P=W/t). [2]
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Energy Transfers: Kinetic energy (KE) → Gravitational Potential Energy (GPE). Some energy is also transferred to the surroundings as thermal energy due to air resistance. [2]
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Efficiency: In real machines, some energy is always dissipated as heat/sound due to friction or electrical resistance, meaning not all input energy is converted to useful output. [2]
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Increase Power: (1) Increase the current flowing through the motor; (2) Increase the efficiency of the motor (e.g., better lubrication). [2]
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KE=21mv2=0.5×0.015×4002=1200 J [2]
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W=mgh=200×10×12=24,000 J [2]
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P=W/t=24,000/15=1600 W [2]
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Q=mcΔθ=0.8×4200×(100−20)=0.8×4200×80=268,800 J [3]
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Q=mcΔθ=0.2×4200×(85−30)=0.2×4200×55=46,200 J [3]
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Pout=0.72×500=360 W [2]
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ΔKE=21mv2−0=0.5×1200×202=240,000 J [2]
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P=Fv=(mg)v=(50×10)×0.5=250 W [2]
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W=F×d→2.5=F×0.05→F=50 N [2]
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E=P×t=60×(5×3600)=60×18,000=1,080,000 J (or 1.08 MJ) [3]
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mgh=21mv2→10×3=0.5×v2→v2=60→v=7.75 m/s [3]
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Mass per second = 100/60=1.67 kg/s. P=(m/t)gh=1.67×10×20=334 W [3]
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Q=1.5×4200×50=315,000 J. Useful power = 0.9×2000=1800 W. t=315,000/1800=175 s [4]
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ΔGPE=ΔKE→mg(hA−hB)=21mv2→10(40−15)=0.5v2→250=0.5v2→v2=500→v=22.36 m/s [4]
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Total energy for each = 100×3600=360,000 J.
LED thermal loss = 20%×360,000=72,000 J.
Incandescent thermal loss = 85%×360,000=306,000 J.
Difference = 306,000−72,000=234,000 J [4]