In a glancing collision between two identical steel spheres, which of the following statements are correct? (Assume this collision is perfectly elastic. Select all that apply.)
a) The velocities of the spheres after the collision in the direction perpendicular to the incoming direction will be equal in magnitude and opposite in direction.
b) The sum of the velocity vectors of the two spheres in the original direction of the incoming sphere after the collision will be equal to that of the incoming sphere.
c) Linear momentum will be conserved in this collision.
d) Kinetic energy in this collision will be conserved.
To determine which of the statements are correct in a glancing collision between two identical steel spheres, we can analyze the principles of momentum and kinetic energy conservation.
a) The statement "The velocities of the spheres after the collision in the direction perpendicular to the incoming direction will be equal in magnitude and opposite in direction" is correct. In an elastic collision, the spheres will exchange momentum, resulting in equal and opposite velocities in the perpendicular direction. This is due to the conservation of angular momentum.
b) The statement "The sum of the velocity vectors of the two spheres in the original direction of the incoming sphere after the collision will be equal to that of the incoming sphere" is incorrect. In an elastic collision, the sum of the velocity vectors after the collision will not be equal to the velocity of the incoming sphere. Some energy is transferred between the spheres during the collision, and the velocities will adjust accordingly.
c) The statement "Linear momentum will be conserved in this collision" is correct. In an elastic collision, linear momentum is conserved. This means that the total momentum before the collision is equal to the total momentum after the collision.
d) The statement "Kinetic energy in this collision will be conserved" is incorrect. In a glancing elastic collision, kinetic energy is not conserved. Some kinetic energy is converted to potential energy and then back to kinetic energy, resulting in energy loss due to deformation and friction during the collision.
Therefore, the correct statements are:
a) The velocities of the spheres after the collision in the direction perpendicular to the incoming direction will be equal in magnitude and opposite in direction.
c) Linear momentum will be conserved in this collision.