A 0.201-kg plastic ball moves with a velocity of 0.30 m/s. It collides with a second plastic ball of mass 0.105 kg, which is moving along the same line at a speed of 0.10 m/s. After the collision, both balls continue moving in the same, original direction. The speed of the 0.105-kg ball is 0.26 m/s. What is the new velocity of the 0.201-kg ball?
To find the new velocity of the 0.201-kg ball after the collision, we can use the law of conservation of linear momentum, which states that the total linear momentum of an isolated system remains constant before and after a collision.
The formula for linear momentum is given by:
p = m * v
Where p is the linear momentum, m is the mass of the object, and v is the velocity.
According to the conservation of linear momentum, we can write the equation:
(m1 * v1) + (m2 * v2) = (m1 * v1') + (m2 * v2')
Where m1 and m2 are the masses of the balls, v1 and v2 are their respective velocities before the collision, and v1' and v2' are their velocities after the collision.
Given:
m1 = 0.201 kg (mass of the 0.201-kg ball)
v1 = 0.30 m/s (velocity of the 0.201-kg ball)
m2 = 0.105 kg (mass of the 0.105-kg ball)
v2 = 0.10 m/s (velocity of the 0.105-kg ball)
v2' = 0.26 m/s (final velocity of the 0.105-kg ball)
Now, let's plug in the values into the equation and solve for v1':
(0.201 kg * 0.30 m/s) + (0.105 kg * 0.10 m/s) = (0.201 kg * v1') + (0.105 kg * 0.26 m/s)
0.0603 kg*m/s + 0.0105 kg*m/s = 0.201 kg * v1' + 0.0273 kg*m/s
0.0708 kg*m/s = 0.201 kg * v1' + 0.0273 kg*m/s
Subtracting 0.0273 kg*m/s from both sides:
0.0435 kg*m/s = 0.201 kg * v1'
Finally, divide both sides by 0.201 kg:
v1' = 0.0435 kg*m/s / 0.201 kg
v1' ≈ 0.216 m/s
Therefore, the new velocity of the 0.201-kg ball after the collision is approximately 0.216 m/s.