A proton with a speed of 4.20×104 km/s makes an elastic head-on collision with a stationary carbon nucleus. We can look up the masses of both particles.
Which of the following quantities can be calculated from only the known information?
A. The velocity of the proton and carbon nucleus after the collision.
B. The kinetic energy of each of the particles after the collision.
C. The momentum of each of the particles after the collision.
Since the collision is elastic everything listed may be calculated from conservation of momentum and conservation of energy.
To determine which of the quantities can be calculated from the known information, we can consider the conservation laws that apply to this collision: conservation of momentum and conservation of kinetic energy.
Let's go through the options:
A. The velocity of the proton and carbon nucleus after the collision:
Since the collision is described as elastic, both momentum and kinetic energy will be conserved. However, the problem statement only provides the initial speed of the proton and the fact that the carbon nucleus is stationary. Therefore, without any additional information, we cannot determine the velocities of the particles after the collision. So, the answer is NO.
B. The kinetic energy of each of the particles after the collision:
Since the collision is described as elastic, the total kinetic energy of the system will be conserved. However, to calculate the kinetic energy after the collision, we need the velocity of each particle. As we mentioned in option A, we do not have enough information to determine the velocities. So, the answer is NO.
C. The momentum of each of the particles after the collision:
According to the conservation of momentum, the total momentum before the collision must be equal to the total momentum after the collision. The initial momentum of the proton is given by its mass multiplied by its velocity, and since the carbon nucleus is initially stationary, its initial momentum is zero. Therefore, after the collision, the total momentum of the system will simply be equal to the momentum of the proton. Hence, by knowing the initial velocity and the masses of the particles, we can calculate the momentum of each particle after the collision. So, the answer is YES.
In conclusion, only option C, the momentum of each of the particles after the collision, can be calculated from the given information.