Philadelphia Flyers player Mike Richards stands on the frictionless ice next to the goal. Neither Mike nor the goal are anchored to the ice. Frustrated after a recent playoff loss, 102.5kg Mike suddenly pushes on the goal, sending it across the ice a 2.80m/s. Mike recoils in the opposite direction at velocity 1.12m/s. Find the mass of the goal
m2 =m1•v1/v2 =102.5•1.12/2.8 = 41 kg
To find the mass of the goal, we can use the principle of conservation of momentum. According to this principle, the total momentum before the interaction must be equal to the total momentum after the interaction.
Let's denote the mass of the goal as m_goal and the mass of Mike Richards as m_mike. We are given the following information:
- Initial velocity of the goal, v_initial_goal = 0 m/s (since it is at rest)
- Final velocity of the goal, v_final_goal = 2.80 m/s
- Final velocity of Mike Richards, v_final_mike = -1.12 m/s (since he recoils in the opposite direction)
Using the conservation of momentum equation:
(m_mike * v_initial_mike) + (m_goal * v_initial_goal) = (m_mike * v_final_mike) + (m_goal * v_final_goal)
Since Mike Richards starts from rest (v_initial_mike = 0), the equation simplifies to:
m_goal * v_initial_goal = m_mike * v_final_mike + m_goal * v_final_goal
Plugging in the values:
0 * m_goal = 102.5 kg * (-1.12 m/s) + m_goal * 2.80 m/s
Simplifying further:
0 = -114.8 kg*m/s + 2.80 m/s * m_goal
Rearranging the equation to isolate m_goal:
2.80 m/s * m_goal = 114.8 kg*m/s
m_goal = 114.8 kg*m/s / 2.80 m/s
m_goal ≈ 41.0 kg
Therefore, the mass of the goal is approximately 41.0 kg.