Three balls with masses m1, m2, m3 can slide without friction along a straight horizontal line, with ball 2 located between balls 1 and 3 (Fig.). It is known that m1 >> m2, m3 >> m2. Determine the maximum velocities of the two outer balls if they were initially at rest and the middle ball was moving with speed v0. The impacts are considered absolutely elastic.
Sorry, this is a research exchange platform, not a "do my freshman homework for me" forum.
Answering it with the hope that the Research instinct in you will ignite.
we assume the mass of each ball is the same.
Before the collision:
- Middle ball: Mass = m, Velocity = v0
- Outer balls: Mass = m, Velocity = 0
After the collision:
- Middle ball: Velocity = ?
- Outer balls: Velocity = v1 and v2 (to be determined)
Since the total momentum is conserved, we have:
0 = m * v0 + m * (v1 + v2)
assume the maximum velocity is denoted by vmax.
Case 1: The momentum is transferred to the left outer ball (v1 = vmax, v2 = 0):
0 = m * v0 + m * vmax
Case 2: The momentum is transferred to the right outer ball (v1 = 0, v2 = vmax):
0 = m * v0 + m * 0 + m * vmax
Simplifying each case:
Case 1: v0 = vmax
Case 2: v0 = -vmax
Since velocity cannot be negative in this context, the maximum velocity of the outer balls is vmax = v0.
Hence, both outer balls will have a maximum velocity equal to the initial velocity of the middle ball (v0) after the collision.
I agree with @Jügen Weippert that this is not the place for freshman homework. Looking at the answer of @Mohammad Imam I would recommend to read the task carefully before giving an answer: "It is known that m1 >> m2, m3>> m2" which determines the possible solutions.
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