A 100-g bullet (c=0.030 cal / g · ^∘ C) is initially at 20 ^∘ C. It is fired straight upward wit

step 1 we have to find the value of how much ice is melted 400 gram bullet and specific heat is 0 .030

A 100-g bullet (c=0.030 cal / g · ^∘ C) is initially at 20...

A 100-g bullet $\left(c=0.030 \mathrm{cal} / \mathrm{g} \cdot{ }^{\circ} \mathrm{C}\right)$ is initially at $20{ }^{\circ} \mathrm{C}$. It is fired straight upward with a speed of $420 \mathrm{~m} / \mathrm{s}$, and on returning to the starting point strikes a cake of ice at exactly $0^{\circ} \mathrm{C}$. How much ice is melted? Neglect air friction.

A 100-g bullet $\left(c=0.030 \mathrm{cal} / \mathrm{g} \cdot{ }^{\circ} \mathrm{C}\right)$ is initially at $20{ }^{\circ} \mathrm{C}$. It is
fired straight upward with a speed of $420 \mathrm{~m} / \mathrm{s}$, and on returning to the starting point strikes a cake of ice at exactly $0^{\circ} \mathrm{C}$. How much ice is melted? Neglect air friction.

Key Concepts

Latent Heat of Fusion

Latent heat of fusion is the energy needed to change a substance from a solid to a liquid state without changing its temperature. In the problem context, it is the energy that is used to melt the ice once the temperature has reached 0°C.

Inelastic Collision and Energy Transfer

In an inelastic collision, objects collide and some of the kinetic energy is converted into other forms, such as thermal energy. In this type of collision, the bullet’s kinetic energy is not conserved as kinetic energy but is instead transformed into heat which can be used to melt ice.

Specific Heat Capacity

Specific heat capacity is a material property that measures the amount of energy required to raise the temperature of a unit mass by one degree Celsius. It is relevant for understanding how much energy is absorbed or released by materials when their temperature changes, particularly in energy partitioning during collisions.

Conservation of Energy

This concept states that energy in an isolated system remains constant, although it can change forms. In this context, the bullet’s kinetic energy is ultimately transformed into thermal energy, demonstrating how the energy from motion can be used to cause phase changes, such as melting ice.

Kinetic Energy

Kinetic energy is the energy of motion, which depends on the mass and velocity of an object. Here, the bullet’s kinetic energy, derived from its mass and firing speed, is the source of the thermal energy that eventually melts the ice.

Transcript

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