A white billiard ball with mass mw = 0.1 kg is moving with a speed of v = 0.5 m/s making angle 60 degree and collides with a black billiard ball with the same mass mb = 0.1 kg that is initially at rest. The distance between the black ball and the pocket is 10cm\ friction exist with 0.5N. does the black billiard ball enter the pocket. ??
No
To determine whether the black billiard ball enters the pocket, we need to consider the conservation of energy and the conservation of momentum during the collision.
1. Conservation of momentum:
The initial momentum of the white billiard ball can be calculated using the formula:
p_initial = m * v
where m is the mass of the white billiard ball (0.1 kg) and v is its speed (0.5 m/s).
Given that it makes an angle of 60 degrees, we need to find the horizontal and vertical components of its initial momentum:
horizontal component = p_initial * cos(angle)
vertical component = p_initial * sin(angle)
Since the black billiard ball is initially at rest, its initial momentum is zero:
p_black_initial = 0
During the collision, the momentum is conserved:
p_initial = p_white_final + p_black_final
2. Conservation of energy:
The kinetic energy before the collision is given by:
KE_initial = (1/2) * (m_white * v_white^2 + m_black * v_black^2)
The kinetic energy after the collision is given by:
KE_final = (1/2) * (m_white * v_white_final^2 + m_black * v_black_final^2)
Since the distance between the black ball and the pocket is mentioned (10 cm), we need to consider any friction during the motion.
Given that there is friction, it will oppose the motion, acting in the opposite direction of the ball's velocity. Its work will reduce the kinetic energy of the ball.
The work done by friction:
work = force * distance
Given: friction force = 0.5 N and distance = 10 cm = 0.1 m
work = 0.5 N * 0.1 m = 0.05 J
The change in kinetic energy due to friction:
ΔKE = -work = -0.05 J
Since energy is conserved, the change in kinetic energy before and after the collision should be equal:
ΔKE = KE_final - KE_initial
After solving for the final and initial velocities using the conservation of momentum equations, we can substitute them into the equations for kinetic energy to determine whether the black billiard ball will enter the pocket or not.
Please provide the final velocities or any additional information to solve the problem entirely.