Please help!! I know how to work the problem to find velocities, but this one has me stumped!
A 2.0kg block slides along a frictionless surface at 1.0m/s . A second block, sliding at a faster 4.4m/s , collides with the first from behind and sticks to it. The final velocity of the combined blocks is 1.5m/s. What was the mass of the second block?
same old conservation of momentum
at first
p = 2 *1 + m * 4.4
at the end
p = (2+m) * 1.5
so
(2+m)(1.5) = 2 + 4.4 m
3 + 1.5 m = 2 + 4.4 m
etc
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 of an object is calculated by multiplying its mass by its velocity.
Before the collision, the momentum of the first block is given by:
Momentum1 = mass1 * velocity1
The momentum of the second block is given by:
Momentum2 = mass2 * velocity2
Since the two blocks collide and stick together, their final momentum will be the combined momentum of the two blocks:
Momentum_final = (mass1 + mass2) * final_velocity
Using the principle of conservation of momentum, we can set up the equation:
Momentum1 + Momentum2 = Momentum_final
(mass1 * velocity1) + (mass2 * velocity2) = (mass1 + mass2) * final_velocity
Plugging in the given values:
(2.0kg * 1.0m/s) + (mass2 * 4.4m/s) = (2.0kg + mass2) * 1.5m/s
Now we can solve this equation to find the mass of the second block. Rearranging the equation, we get:
2.0 + 4.4 * mass2 = 1.5 * (2.0 + mass2)
Simplifying further:
2.0 + 4.4 * mass2 = 3.0 + 1.5 * mass2
Rearranging and combining like terms:
2.4 * mass2 = 1.0
Finally, solving for mass2:
mass2 = 1.0 / 2.4
mass2 = 0.4167 kg, or approximately 0.42 kg.
Therefore, the mass of the second block is approximately 0.42 kg.