A 1.1 kg block slides along a friction-less surface at 1.4 m/s. A second block, sliding at a faster 4.3 m/s, collides with the first from behind and sticks to it. The final velocity of the combined blocks is 2.6 m/s. What was the mass of the second block?
To find the mass of the second block, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
The momentum (p) of an object can be calculated by multiplying its mass (m) by its velocity (v):
p = m * v
Before the collision, the momentum of the first block can be calculated as:
p1 = m1 * v1,
where m1 is the mass of the first block (given as 1.1 kg) and v1 is the velocity of the first block (given as 1.4 m/s).
Similarly, the momentum of the second block before the collision can be calculated as:
p2 = m2 * v2,
where m2 is the mass of the second block (which we need to find) and v2 is the velocity of the second block (given as 4.3 m/s).
After the collision, the two blocks stick together and move with a final velocity of 2.6 m/s. The combined mass of the two blocks can be calculated as:
m1 + m2 = (m1 + m2) * v_final,
where m1 + m2 is the total mass of the two blocks and v_final is their final velocity.
Using the conservation of momentum, we have:
m1 * v1 + m2 * v2 = (m1 + m2) * v_final.
Now we can substitute the given values into the equation and solve for m2:
(1.1 kg * 1.4 m/s) + (m2 * 4.3 m/s) = (1.1 kg + m2) * 2.6 m/s.
Solving this equation will give us the mass of the second block (m2).