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Ch. 19 - Heat and the First Law of Thermodynamics
Giancoli Douglas - Physics for Scientists and Engineers 5th edition
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Non è quello che usi tu?Cambia libro di testo
Capitolo 19, Problema 30

A 55-g bullet traveling at 250 m/s penetrates a block of ice at 0°C and comes to rest within the ice. Assuming that the temperature of the bullet doesn’t change appreciably, how much ice is melted as a result of the collision?

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Step 1: Calculate the initial kinetic energy of the bullet using the formula for kinetic energy: Kinitial = (1/2) m v2 , where m is the mass of the bullet (55 g converted to kg) and v is its velocity (250 m/s).
Step 2: Convert the kinetic energy into heat energy, assuming all the kinetic energy is transferred to the ice. The heat energy is equal to the initial kinetic energy of the bullet.
Step 3: Use the heat energy to calculate the mass of ice melted. The heat required to melt ice is given by Q = m Lf , where Lf is the latent heat of fusion for ice (334,000 J/kg). Rearrange the formula to solve for m , the mass of ice melted: m = Q / Lf .
Step 4: Substitute the value of the heat energy (from Step 2) and the latent heat of fusion into the formula to find the mass of ice melted.
Step 5: Ensure the units are consistent throughout the calculation (e.g., mass in kilograms, energy in joules) and interpret the result to determine how much ice is melted.

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Kinetic Energy

Kinetic energy is the energy possessed by an object due to its motion, calculated using the formula KE = 1/2 mv², where m is mass and v is velocity. In this scenario, the bullet's kinetic energy before impact is converted into heat energy upon colliding with the ice, leading to the melting of the ice.
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Intro to Rotational Kinetic Energy

Heat of Fusion

The heat of fusion is the amount of energy required to change a substance from solid to liquid at its melting point without changing its temperature. For ice, this value is approximately 334,000 J/kg. Understanding this concept is crucial for calculating how much ice melts as a result of the energy transferred from the bullet.
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Conservation of Energy

The principle of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another. In this problem, the kinetic energy of the bullet is transformed into thermal energy, which is then used to melt the ice, illustrating this fundamental concept in physics.
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