High-speed stroboscopic photographs show that the head of a golf club of mass 231g is traveling at 59.0m/s just before it strikes a 47.1g golf ball at rest on a tee. After the collision, the club head travels (in the same direction) at 44.3m/s. Calculate the speed of the golf ball just after impact.
momentum lost by club=momentum gained by ball
231(59-44.3)=47.1(Speed)
calculate speed.
To solve this problem, we will apply the principle of conservation of linear momentum. The momentum before the collision should be equal to the momentum after the collision.
Before the collision:
The momentum of the club head is given by:
P_initial_club = m_club * v_initial_club
where
m_club = mass of the club head = 231g = 0.231 kg (converting grams to kilograms)
v_initial_club = initial velocity of the club head = 59.0 m/s
The momentum of the golf ball is zero since it is at rest:
P_initial_ball = m_ball * v_initial_ball
where
m_ball = mass of the golf ball = 47.1g = 0.0471 kg (converting grams to kilograms)
v_initial_ball = initial velocity of the golf ball = 0 m/s
After the collision:
The momentum of the club head after the collision is given by:
P_final_club = m_club * v_final_club
where
v_final_club = final velocity of the club head = 44.3 m/s
The momentum of the golf ball after the collision is given by:
P_final_ball = m_ball * v_final_ball
where
v_final_ball = final velocity of the golf ball (which we need to find)
Applying the principle of conservation of momentum:
P_initial_club + P_initial_ball = P_final_club + P_final_ball
(m_club * v_initial_club) + (m_ball * v_initial_ball) = (m_club * v_final_club) + (m_ball * v_final_ball)
(0.231 kg * 59.0 m/s) + (0.0471 kg * 0 m/s) = (0.231 kg * 44.3 m/s) + (0.0471 kg * v_final_ball)
Simplifying the equation:
13.629 kg⋅m/s = 10.1633 kg⋅m/s + (0.0471 kg * v_final_ball)
Rearranging the equation to solve for v_final_ball:
(0.0471 kg * v_final_ball) = 13.629 kg⋅m/s - 10.1633 kg⋅m/s
(0.0471 kg * v_final_ball) = 3.4657 kg⋅m/s
v_final_ball = 3.4657 kg⋅m/s / 0.0471 kg
v_final_ball ≈ 73.57 m/s
Therefore, the speed of the golf ball just after impact is approximately 73.57 m/s.