An object of mass m has an elastic collision with another object initially at rest, and continues to move in original direction but with one-third its original speed. What is the mass of the other object in terms of m?
To solve this problem, let's use the conservation of momentum and kinetic energy.
Conservation of momentum states that the total momentum before the collision is equal to the total momentum after the collision. In this case, since the second object is initially at rest, the total momentum before the collision is just the momentum of the first object.
Let's denote the initial speed of the first object as v and the final speed as vf. According to the question, the final speed is one-third of the initial speed, so vf = v/3.
The momentum before the collision is given by the product of the mass and the initial velocity: p = m * v.
After the collision, the momentum of the first object is still m * vf, but since the first object continues to move in the original direction, its velocity should be positive. Therefore, the momentum of the first object after the collision is m * vf.
Using the conservation of momentum, we can equate the initial and final momenta:
m * v = m * vf
Substituting vf = v/3, we get:
m * v = m * (v/3)
Simplifying the equation, we can cancel out the mass:
v = v/3
Multiplying through by 3, we have:
3v = v
This implies that v = 0, which means there is no initial velocity for the first object. However, this would result in no collision, which contradicts the given information.
Therefore, a contradiction is reached, and it seems that there is no solution to this problem.