Question

(b) the mass of the ball is 6.4 kg.
(i) state the equation linking momentum, mass and velocity.
(ii) calculate the momentum of the ball before it hits the pin. give the unit.
momentum …………………, unit …………………
(c) (i) use the graph to determine the velocity of the ball after it hits the pin.
velocity = ………………… m/s
(ii) after the collision, the ball and the pin have the same velocity. calculate the mass of the pin.
mass = ………………… kg

Explanation:

Step1: State the momentum - mass - velocity equation

The equation is $p = mv$, where $p$ is momentum, $m$ is mass and $v$ is velocity.

Step2: Calculate the momentum before hitting the pin

Assume the velocity of the ball before hitting the pin is $v$ (not given in the problem - statement, if we assume a value for illustration purposes, say $v = 5$ m/s). Given $m=6.4$ kg. Using $p = mv$, we have $p=6.4\times5 = 32$ kg·m/s. The unit of momentum is kg·m/s.

Step3: Determine velocity after hitting the pin (assuming we can read from the graph)

Since the graph is not provided, assume the velocity after hitting the pin is $v_1$ (if we could read it from the graph).

Step4: Calculate the mass of the pin

Let the mass of the pin be $m_p$, the mass of the ball $m_b = 6.4$ kg. Before the collision, the momentum of the ball is $p_b=m_bv$. After the collision, the combined mass is $m_{total}=m_b + m_p$ and the velocity is $v_1$. By the law of conservation of momentum $m_bv=(m_b + m_p)v_1$. Then $m_p=\frac{m_bv}{v_1}-m_b$.

Answer:

(b)(i) $p = mv$
(b)(ii) Assuming $v = 5$ m/s, Momentum = 32, Unit = kg·m/s
(c)(i) (Value read from the non - provided graph)
(c)(ii) $m_p=\frac{m_bv}{v_1}-m_b$ (assuming $v$ is initial velocity of ball and $v_1$ is velocity after collision)