Two billiard balls collide on a frictionless table. Calculate the final velocities of the balls if one ball is initially at rest and the other has an initial velocity of 4 m/s.
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To solve this problem, we can use the principle of conservation of momentum, which states that the total momentum of an isolated system remains constant before and after a collision.
Let's assume that the mass of the first ball at rest is represented by m1, and the mass of the second ball with an initial velocity of 4 m/s is represented by m2.
The momentum of an object is calculated by multiplying its mass by its velocity (p = m * v).
Before the collision, the momentum of the first ball is zero since it is at rest (p1 = m1 * 0 = 0), and the momentum of the second ball is given by p2 = m2 * 4 m/s.
The total momentum before the collision is the sum of the individual momenta of the two balls: p_initial = p1 + p2 = 0 + m2 * 4 m/s = 4m2.
After the collision, the momentum of the first ball will be p1' and the momentum of the second ball will be p2'.
According to the conservation of momentum, the total momentum after the collision must also be 4m2: p_final = p1' + p2' = 4m2.
Since we know that the first ball initially has zero velocity (and therefore zero momentum), the momentum of the first ball after the collision will also be zero: p1' = 0.
Thus, p2' = 4m2.
To find the final velocity of the second ball, we can use the equation p = m * v, rearranged to solve for velocity: v = p / m.
The final velocity of the second ball (v2') can be calculated as v2' = p2' / m2 = (4m2) / m2 = 4 m/s.
Therefore, the final velocities of the two balls after the collision are:
- The first ball: v1' = 0 m/s (remains at rest)
- The second ball: v2' = 4 m/s (no change in velocity)
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