sayid made a chart listing data of two colliding objects. collision: two objects stick together object mass…
sayid made a chart listing data of two colliding objects. collision: two objects stick together object mass before collision (kg) velocity before collision (m/s) mass after collision (kg) velocity after collision (m/s) x 300 10 400? y 100 -6 according to the law of conservation of momentum, what is the missing value in the chart? 4 6 10 16
Answer
Explanation:
Step1: Recall conservation - of - momentum formula
The law of conservation of momentum is $m_1u_1 + m_2u_2=(m_1 + m_2)v$, where $m_1$ and $m_2$ are the masses before collision, $u_1$ and $u_2$ are the velocities before collision, and $v$ is the velocity after collision. Here, $m_1 = 300$ kg, $u_1=10$ m/s, $m_2 = 100$ kg, $u_2=-6$ m/s, and $m_1 + m_2=400$ kg.
Step2: Calculate the left - hand side of the formula
$m_1u_1+m_2u_2=(300\times10)+(100\times(- 6))=3000-600 = 2400$ kg·m/s.
Step3: Solve for the velocity after collision
Since $m_1u_1 + m_2u_2=(m_1 + m_2)v$, then $v=\frac{m_1u_1 + m_2u_2}{m_1 + m_2}$. Substituting the values, we get $v=\frac{2400}{400}=6$ m/s.
Answer:
6