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A ball of mass m and speed v collides head-on with a ball of 2m and speed v/2, as shown above. If the two balls stick together, their speed after the collision is 0?

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The statement that the speed of the two balls after the collision is 0 is incorrect.

Yes, if the two balls stick together after the collision, their speed will be 0. Here's why:

Conservation of Momentum:

In a closed system like this collision, the total momentum before the collision is equal to the total momentum after the collision. This can be written as:

m1v1 + m2v2 = (m1 + m2)v_final

where:

m1 and m2 are the masses of the balls

v1 and v2 are their respective velocities before the collision

v_final is their combined velocity after sticking together

Substituting the values:

m1 = m

m2 = 2m

v1 = v

v2 = v/2

v_final is what we want to find

Plugging these values into the equation, we get:

mv + (2m)(v/2) = (m + 2m)v_final

mv + mv = 3mv_final

2mv = 3mv_final

v_final = 2mv / 3mv

v_final = 2/3

However, the question states that the two balls are stuck together. This means that the combined mass (m + 2m) will move as a single object after the collision.

Therefore, the speed of the single object after the collision will be:

v final = (2mv) / (3mv) = 2/3 * v

Since v is the speed of the first ball before the collision, which is not equal to 0, we can conclude that v_final is not equal to 0.

Therefore, the statement that the speed of the two balls after the collision is 0 is incorrect.

User Leeladam
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