What percent of KE of a moving particles is transferred to a stationary particle when it strikes the stationary particle 4times of its mass?

Question

Answer

Answer

Answer

64%

Answer

Transfer of Kinetic Energy in a Collision

When a moving particle collides with a stationary particle, a part of its kinetic energy is transferred to the stationary particle. The percentage of kinetic energy transferred can be determined using the principle of conservation of energy.

Conservation of Energy
According to the principle of conservation of energy, the total energy in a system remains constant before and after a collision. In the case of a collision between a moving particle and a stationary particle, the initial kinetic energy of the moving particle is equal to the final kinetic energy of both particles combined.

Calculation of Percentage of Kinetic Energy Transferred
To calculate the percentage of kinetic energy transferred, we need to consider the masses and velocities of the particles before and after the collision.

Let's assume the mass of the moving particle is 'm' and its initial velocity is 'u'. The mass of the stationary particle is '4m' (four times the mass of the moving particle). After the collision, let the velocities of the moving particle and the stationary particle be 'v1' and 'v2' respectively.

Using the principle of conservation of energy, we can write the equation as:

(1/2)mu^2 = (1/2)m(v1^2) + (1/2)(4m)(v2^2)

Simplifying the equation, we get:

mu^2 = (v1^2) + 4(v2^2)

The percentage of kinetic energy transferred can be calculated using the following formula:

Percentage of kinetic energy transferred = [(Initial KE - Final KE) / Initial KE] * 100

Substituting the values, we get:

Percentage of kinetic energy transferred = [(mu^2 - [(v1^2) + 4(v2^2)]) / (mu^2)] * 100

Conclusion
The percentage of kinetic energy transferred to the stationary particle when a moving particle strikes it can be calculated using the principle of conservation of energy. By applying the formula and substituting the given values, the exact percentage can be determined.

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