You are lawn bowling and bowl a ball with a speed of 6.18 m/s. Unfortunately, your ball hits a large rock of mass 470 g, resulting in a perfectly elastic collision. If the final velocity of the ball after the collision is -3.43 m/s, what must the mass of the ball be?
To find the mass of the ball, we can use the principle of conservation of momentum. In an elastic collision, the total momentum before the collision is equal to the total momentum after the collision.
The momentum (p) of an object is given by the product of its mass (m) and velocity (v):
p = m * v
Before the collision, the momentum of the ball is:
momentum_before = m_ball * v_ball
After the collision, the momentum of the ball is:
momentum_after = m_ball * v_final
The momentum of the rock is:
momentum_rock = m_rock * v_rock
According to the conservation of momentum:
momentum_before = momentum_after + momentum_rock
Substituting the formulas for momentum, we get:
m_ball * v_ball = m_ball * v_final + m_rock * v_rock
Since we know the values for v_ball, v_final, and m_rock, we can solve for m_ball.
6.18 m/s * m_ball = -3.43 m/s * m_ball + 0.470 kg * 0 m/s
Simplifying the equation:
6.18 m_ball + 3.43 m_ball = 0.470 kg * 0 m/s
9.61 m_ball = 0
Dividing both sides by 9.61:
m_ball = 0 kg
Therefore, the mass of the ball must be 0 kg.
So the large rock must move..
energy: 1/2 M*6.18^2=1/2 M*(-3.43)^2 + 470*Vrock^2
momentum: M*6.18 = 470*Vrock+ M (-3.43)
solving for M, start with second equationi
M(6.18+3.43)=470Vrock
Vrock= M (9.61)/470 Put that into the energy equation, then solve for Mass of ball M.