A 90.0-g disk traveling 3.00 m/s to the right collides with a 75.0-g disk traveling
8.00 m/s to the left. After the collision, the heavier disk is traveling 7.00 m/s to the
left. What is the velocity of the lighter disk after the collision?
Do I have this setup right?
(90.0*3.00+75.0*(-)8.00-75.0*(-)7.00) ÷90.0
coolio, momentum problem
m₁v₁ + m₂v₂ = m₁v₁' + m₂v₂'
(90.0 g)(3.00 m/s) + (75.0 g)(-8.00 m/s) = (90.0 g)(-7.00 m/s) + (75.0 g)v₂'
If you solve it out, v₂' should be 4 m/s
Made a mistake, I had to divide by 75.0 so that the 90.0 cancels out. Thank you
To solve this problem, 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.
The momentum of an object can be calculated by multiplying its mass by its velocity. Therefore, the initial momentum of the system (before the collision) can be written as:
Initial momentum = (mass of the first disk) * (velocity of the first disk) + (mass of the second disk) * (velocity of the second disk)
Using the values given in the problem, we can calculate the initial momentum:
Initial momentum = (90.0 g) * (3.00 m/s) + (75.0 g) * (-8.00 m/s)
Please note that since the second disk is traveling to the left, its velocity should be negative.
Now, let's calculate the final momentum of the system (after the collision). We know that the heavier disk is traveling 7.00 m/s to the left. Let's denote the velocity of the lighter disk as 'v'. The final momentum can be written as:
Final momentum = (mass of the first disk) * (velocity of the first disk after collision) + (mass of the second disk) * (velocity of the second disk after collision)
Using the information given in the problem, we can rewrite the final momentum equation as:
Final momentum = (90.0 g) * (v) + (75.0 g) * (-7.00 m/s)
Since the total momentum before and after the collision should be equal, we can set the initial momentum equal to the final momentum:
(90.0 g) * (3.00 m/s) + (75.0 g) * (-8.00 m/s) = (90.0 g) * (v) + (75.0 g) * (-7.00 m/s)
Now, we can solve this equation for 'v' to find the velocity of the lighter disk after the collision.