Solving Two Physics Questions: Rotational Inertia & Equilibrium Temp.

In summary, the conversation discusses two questions from a recent competition. The first one involves an Atwood's machine with two masses connected by a cord and a pulley. After being released from rest, the 400-g mass falls 60 cm and the 300-g mass rises 60 cm in 4.00 seconds. The task is to find the rotational inertia of the pulley, which has an answer of 0.0546. The second question involves four 100-g ice cubes at -20° C being dropped into 800 g of water at 44° C. The goal is to find the equilibrium temperature of the mixture, with answer choices of 0° C, 1.41° C, 2
  • #1
anuragpapineni
1
0
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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  • #2


Please post your working for each.
 

Related to Solving Two Physics Questions: Rotational Inertia & Equilibrium Temp.

1. What is rotational inertia and how is it calculated?

Rotational inertia, also known as moment of inertia, is a measure of an object's resistance to changes in its rotational motion. It is calculated by multiplying the mass of an object by the square of its distance from the axis of rotation.

2. How does the shape of an object affect its rotational inertia?

The shape of an object plays a significant role in determining its rotational inertia. Objects with a larger radius have a greater rotational inertia compared to objects with a smaller radius, even if they have the same mass. Additionally, objects with a greater distribution of mass away from the axis of rotation have a higher rotational inertia.

3. What is equilibrium temperature and how is it calculated?

Equilibrium temperature is the temperature at which the heat lost by an object is equal to the heat gained by its surroundings, resulting in a steady state. It is calculated by setting the heat lost by the object equal to the heat gained by its surroundings and solving for the temperature.

4. How does the type of material affect equilibrium temperature?

The type of material plays a crucial role in determining equilibrium temperature. Materials with a lower specific heat capacity will reach equilibrium temperature faster compared to materials with a higher specific heat capacity, as they can absorb and release heat more quickly.

5. Can rotational inertia and equilibrium temperature be applied to real-world situations?

Yes, both rotational inertia and equilibrium temperature have practical applications in real-world situations. For example, understanding rotational inertia is important for designing vehicles and machinery that require rotational motion. Equilibrium temperature is also used in industries such as manufacturing and food processing to ensure that materials and products are at a consistent temperature.

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