A 2.7-kg block is moving to the right at 1.0 m/s just before it strikes and sticks to a 2.2-kg block initially at rest. What is the total momentum of the two blocks after the collision?
To find the total momentum of the two blocks after the collision, we need to understand the principle of conservation of momentum. According to this principle, the total momentum of a closed system remains constant before and after a collision, provided no external forces act on it.
In this case, the initial momentum of the 2.7-kg block is given by its mass (m1 = 2.7 kg) multiplied by its velocity (v1 = 1.0 m/s). So, the initial momentum of the first block is:
initial momentum of block 1 (p1) = m1 * v1
Now, the second block is initially at rest, so its initial momentum is zero:
initial momentum of block 2 (p2) = 0
Since there is no external force acting on these blocks during the collision, the total momentum before the collision (Σp_initial) is equal to the sum of individual momenta:
Σp_initial = p1 + p2
After the collision, the two blocks will stick together, making them move as a single object. Let's call the final velocity of the combined blocks as 'v_final'. According to the principle of conservation of momentum:
Σp_initial = Σp_final
Considering that the mass of the combined blocks will be the sum of their individual masses (m_total = m1 + m2) and applying the conservation of momentum equation, we can calculate the final velocity:
(m1 * v1) + (m2 * 0) = (m1 + m2) * v_final
Given the values of m1, m2, and v1, we can calculate v_final. Finally, the total momentum of the two blocks after the collision is given by the product of the total mass and the final velocity:
total momentum after the collision = (m1 + m2) * v_final