A .5 kg mass moving to the right at 1 m/s collides with a 1.5 kg mass moving to the left at .5 m/s. After the collision, the .5 kg mass moves to the left at 1.25 m/s. What is the velocity of the 1.5 kg mass after the collision?1 m/s.5 m/s.25 m/s0 m/s
Question
A .5 kg mass moving to the right at 1 m/s collides with a 1.5 kg mass moving to the left at .5 m/s. After the collision, the .5 kg mass moves to the left at 1.25 m/s. What is the velocity of the 1.5 kg mass after the collision?1 m/s.5 m/s.25 m/s0 m/s
Solution
To solve this problem, we can use the principle of conservation of momentum. The total momentum before the collision should be 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 .5 kg mass is .5 kg * 1 m/s = .5 kgm/s. The momentum of the 1.5 kg mass is 1.5 kg * -.5 m/s = -.75 kgm/s. So, the total momentum before the collision is .5 kgm/s - .75 kgm/s = -.25 kg*m/s.
After the collision: We know that the .5 kg mass moves to the left at 1.25 m/s, so its momentum is .5 kg * -1.25 m/s = -.625 kg*m/s. We don't know the velocity of the 1.5 kg mass after the collision, so we'll call it v. Its momentum is 1.5 kg * v.
According to the principle of conservation of momentum, the total momentum before the collision (-.25 kgm/s) should be equal to the total momentum after the collision (-.625 kgm/s + 1.5 kg * v).
So, we can set up the equation -.25 kgm/s = -.625 kgm/s + 1.5 kg * v and solve for v:
-.25 kgm/s + .625 kgm/s = 1.5 kg * v .375 kgm/s = 1.5 kg * v v = .375 kgm/s / 1.5 kg v = .25 m/s
So, the velocity of the 1.5 kg mass after the collision is .25 m/s.
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