Solving Two Physics Questions: Rotational Inertia & Equilibrium Temp.

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SUMMARY

The discussion focuses on solving two physics problems involving an Atwood's machine and thermal equilibrium. The first problem calculates the rotational inertia of a pulley connected to two masses (300 g and 400 g) that move 60 cm in 4 seconds, resulting in a calculated inertia of 0.0546 kg·m². The second problem involves determining the equilibrium temperature when four 100-g ice cubes at -20° C are added to 800 g of water at 44° C, with potential answers including 1.41° C, 2.82° C, 5.64° C, and 11.3° C.

PREREQUISITES
  • Understanding of Atwood's machine dynamics
  • Knowledge of rotational inertia calculations
  • Familiarity with thermal equilibrium concepts
  • Ability to apply the principle of conservation of energy
NEXT STEPS
  • Study the principles of Atwood's machine dynamics in detail
  • Learn how to calculate rotational inertia for various shapes
  • Explore the concept of thermal equilibrium and heat transfer calculations
  • Practice solving problems involving conservation of energy in mechanical systems
USEFUL FOR

Students preparing for physics competitions, educators teaching mechanics and thermodynamics, and anyone interested in practical applications of physics concepts.

anuragpapineni
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Two masses, 300 g and 400 g, are connected by a cord that passes over a pulley with a radius of 6.64 cm (an Atwood's machine). When released from rest, the 400-g mass falls 60 cm and the 300-g mass rises 60 cm in 4.00 seconds. Find the rotational inertia of the pulley.

Four 100-g ice cubes at a temperature of -20° C are dropped into an insulated cup containing 800 g of water at a temperature of 44° C. Find the equilibrium temperature of the mixture.

These two questions were on a recent competition I was at. The first one had an answer of 0.0546 but I'm not sure how I got there. For the second I kept getting 0 degrees Celsius which was wrong. The other answer choices were
B. 1.41° C
C. 2.82° C
D. 5.64° C
E. 11.3° C

help solving either is appreciated
 
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Please post your working for each.
 

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