A billiard ball is moving in the x direction at 40.0 cm/s and strikes another billiard ball moving in the y direction at 30.0 cm/s. As a result of the collision, the first ball moves at 50.0 cm/s, and the second ball stops. What is the change in kinetic energy of the system as a result of the collision?Select one:a.some negative valueb.some positive valuec.No answer above is correct.d.0
Question
A billiard ball is moving in the x direction at 40.0 cm/s and strikes another billiard ball moving in the y direction at 30.0 cm/s. As a result of the collision, the first ball moves at 50.0 cm/s, and the second ball stops. What is the change in kinetic energy of the system as a result of the collision?Select one:a.some negative valueb.some positive valuec.No answer above is correct.d.0
Solution
To solve this problem, we first need to calculate the initial and final kinetic energy of the system.
The formula for kinetic energy is KE = 1/2 * m * v^2, where m is the mass and v is the velocity.
Assuming the masses of the two billiard balls are the same (since they are not given), we can denote the mass as m.
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Initial kinetic energy: KE_initial = 1/2 * m * (40.0 cm/s)^2 + 1/2 * m * (30.0 cm/s)^2
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Final kinetic energy: KE_final = 1/2 * m * (50.0 cm/s)^2 + 1/2 * m * (0 cm/s)^2
The change in kinetic energy is then ΔKE = KE_final - KE_initial.
If ΔKE is positive, then the kinetic energy of the system increased as a result of the collision. If ΔKE is negative, then the kinetic energy of the system decreased as a result of the collision. If ΔKE is zero, then the kinetic energy of the system remained the same.
Without doing the calculations, we can see that the final kinetic energy is less than the initial kinetic energy because the square of the final total velocity (50.0 cm/s) is less than the sum of the squares of the initial velocities (40.0 cm/s and 30.0 cm/s). Therefore, the change in kinetic energy of the system as a result of the collision is some negative value. So, the answer is a. some negative value.
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