Two solid spheres form an isolated system. Sphere X moves with speed 6 cm s–1 in a straight linedirectly towards a stationary sphere Y, as shown.sphere X sphere Y6 cm s–1The spheres have a perfectly elastic collision. After the collision, sphere X moves with speed2 cm s –1 in the same direction as before the collision.What is the speed of sphere Y?A 2 cm s –1 B 4 cm s –1 C 6 cm s –1 D 8 cm s –1
Question
Two solid spheres form an isolated system. Sphere X moves with speed 6 cm s–1 in a straight linedirectly towards a stationary sphere Y, as shown.sphere X sphere Y6 cm s–1The spheres have a perfectly elastic collision. After the collision, sphere X moves with speed2 cm s –1 in the same direction as before the collision.What is the speed of sphere Y?A 2 cm s –1 B 4 cm s –1 C 6 cm s –1 D 8 cm s –1
Solution
In a perfectly elastic collision, the total momentum before the collision is equal to the total momentum after the collision.
Before the collision, the total momentum is the momentum of sphere X because sphere Y is stationary. The momentum of an object is calculated by multiplying its mass by its velocity.
Let's denote the mass of sphere X as m1 and the mass of sphere Y as m2.
Before the collision, the total momentum is m1 * 6 cm/s (because sphere Y is stationary, it doesn't contribute to the total momentum).
After the collision, sphere X moves with a speed of 2 cm/s and sphere Y moves with an unknown speed which we'll denote as v.
So, the total momentum after the collision is m1 * 2 cm/s + m2 * v.
Setting the total momentum before the collision equal to the total momentum after the collision gives us:
m1 * 6 cm/s = m1 * 2 cm/s + m2 * v
We can simplify this to:
4 m1 = m2 * v
Since the spheres are identical, m1 = m2. Therefore, we can substitute m1 for m2 in the equation:
4 m1 = m1 * v
Solving for v gives us:
v = 4 cm/s
So, the speed of sphere Y after the collision is 4 cm/s. Therefore, the correct answer is B) 4 cm/s.
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