Two objects of the same mass move along the same line in opposite directions. The first mass is moving with speed v. The objects collide in a perfectly inelastic collision and move with speed 0.100v in the direction of the velocity of the first mass before the collision. What was the speed of the second mass before the collision?Group of answer choices0.900v0.800vnone of these0.00v1.200v10.0v
Question
Two objects of the same mass move along the same line in opposite directions. The first mass is moving with speed v. The objects collide in a perfectly inelastic collision and move with speed 0.100v in the direction of the velocity of the first mass before the collision. What was the speed of the second mass before the collision?Group of answer choices0.900v0.800vnone of these0.00v1.200v10.0v
Solution
Let's solve this problem step by step:
- Let's assume the mass of both objects is "m".
- The first mass is moving with speed "v" in one direction.
- The second mass is moving in the opposite direction.
- After the collision, the objects stick together and move with a speed of 0.100v in the direction of the first mass's velocity before the collision.
- Let's denote the speed of the second mass before the collision as "v2".
Now, let's apply the principle of conservation of momentum:
Before the collision: Momentum of the first mass = mass of the first mass * velocity of the first mass = m * v Momentum of the second mass = mass of the second mass * velocity of the second mass = m * v2
After the collision: Momentum of the combined masses = (mass of the first mass + mass of the second mass) * velocity of the combined masses = 2m * 0.100v
According to the principle of conservation of momentum, the momentum before the collision should be equal to the momentum after the collision:
m * v + m * v2 = 2m * 0.100v
Simplifying the equation:
v + v2 = 0.200v
Now, let's solve for v2:
v2 = 0.200v - v v2 = 0.200v - 1v v2 = -0.800v
Since the speed cannot be negative, the speed of the second mass before the collision is 0.800v.
Therefore, the correct answer is 0.800v.
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