A 2.9 kg block slides along a frictionless surface at 1.3 m/s. A second block, sliding at a faster 5.0 m/s, collides with the first from behind and sticks to it. The final velocity of the combined blocks is 2.7 m/s.
What was the mass of the second block?
Conservation of momentum applies.
M1*V1i+M2*V2i= (M1+M2)Vf
solve for M2
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 should be equal to the total momentum after the collision.
Before the collision, the momentum of the first block (m1) is given by:
momentum of first block = mass of first block (m1) * velocity of first block (v1)
momentum of first block = m1 * 1.3 m/s
The momentum of the second block (m2) before the collision is given by:
momentum of second block = mass of second block (m2) * velocity of second block (v2)
momentum of second block = m2 * 5.0 m/s
The total momentum before the collision is:
total momentum before = m1 * 1.3 + m2 * 5.0
After the collision, the total momentum of the combined blocks is:
total momentum after = (m1 + m2) * 2.7
Since momentum is conserved, we can set the two equations equal to each other:
m1 * 1.3 + m2 * 5.0 = (m1 + m2) * 2.7
We have one equation with two unknowns (m1 and m2). However, we know the mass of the first block (m1) is 2.9 kg.
Plugging in this value, we get:
2.9 * 1.3 + m2 * 5.0 = (2.9 + m2) * 2.7
Simplifying this equation will allow us to solve for the mass of the second block (m2).