A 50.0 Kg ball rolling at 10.0 m/s eastward (on a frictionless surface) collides with a 20.0 Kg ball rolling westward at 20.0 m/s. After the collision the two balls stick together (coalesce). What is the momentum after the collision?
To find the momentum after the collision, we need to apply the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
The momentum (p) is defined as the product of an object's mass (m) and its velocity (v). Mathematically, it can be represented as:
p = m * v
Before the collision, we have two balls moving in opposite directions. Therefore, we can calculate the momentum for each ball separately, using their respective masses and velocities.
For the 50.0 kg ball moving eastward at 10.0 m/s, the momentum is:
p1 = m1 * v1 = 50.0 kg * 10.0 m/s = 500.0 kg*m/s (eastward)
For the 20.0 kg ball moving westward at 20.0 m/s, the momentum is:
p2 = m2 * v2 = 20.0 kg * (-20.0 m/s) = -400.0 kg*m/s (westward)
Since the balls stick together and coalesce after the collision, their final velocity will be the same. Let's call this final velocity v_f.
The total momentum after the collision is the sum of the two momenta before the collision, considering the direction:
p_total_after_collision = p1 + p2
= 500.0 kg*m/s (eastward) + (-400.0 kg*m/s) (westward)
Adding the opposite sign quantities, we get:
p_total_after_collision = 100.0 kg*m/s (eastward)
Therefore, the momentum after the collision is 100.0 kg*m/s eastward.