A hockey puck, mass 0.130 kg, moving at 40.0 m/s, strikes an octopus thrown on the ice by a fan. The octopus has a mass of 0.270 kg. The puck and octopus slide off together. Find their velocity.
According to the Law of conservation of linear momentum for the inelastic collision
m1v=(m1+m2)u.
Then u=m1v/m1+m2=(0.13x40)/0.4=13 m/s
To find the velocity of the puck and octopus together after the collision, 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.
Momentum (p) is defined as the product of mass (m) and velocity (v):
p = m * v
Before the collision, the momentum of the puck can be calculated as:
puck momentum before = (mass of puck) * (initial velocity of puck)
= (0.130 kg) * (40.0 m/s)
The momentum of the thrown octopus can be calculated as:
octopus momentum before = (mass of octopus) * (initial velocity of octopus)
= (0.270 kg) * (0 m/s) [since the octopus is at rest initially]
The total momentum before the collision is the sum of these momenta:
total momentum before = puck momentum before + octopus momentum before
After collision, the total momentum remains the same. Let's denote the final velocity of the puck and octopus together as V.
total momentum after = (total mass) * (final velocity)
= (mass of puck + mass of octopus) * V
According to the conservation of momentum, we can equate the total momentum before and after the collision:
total momentum before = total momentum after
[(mass of puck) * (initial velocity of puck)] + [(mass of octopus) * (initial velocity of octopus)]
= [(mass of puck + mass of octopus) * V]
Now we can solve this equation to find the final velocity (V) of the puck and octopus together after the collision:
V = [((mass of puck) * (initial velocity of puck)) + ((mass of octopus) * (initial velocity of octopus))] / (mass of puck + mass of octopus)
Substituting the given values into the equation, we can calculate the final velocity.