An object of mass 2m moving at velocity 3v collides with a stationary object of mass 4m. The objects stick together after the collision. What is the finalspeed and the change in total kinetic energy immediately after the collision?Final speedChange in total kinetic energyA.V3 mv^2B.V6 mv^2C.2v3mv^2D.2v6 mv^2
Question
An object of mass 2m moving at velocity 3v collides with a stationary object of mass 4m. The objects stick together after the collision. What is the finalspeed and the change in total kinetic energy immediately after the collision?Final speedChange in total kinetic energyA.V3 mv^2B.V6 mv^2C.2v3mv^2D.2v6 mv^2
Solution
The problem involves the principle of conservation of momentum and the calculation of kinetic energy.
Step 1: Conservation of Momentum Before the collision, the momentum is only from the moving object, which is mass * velocity = 2m * 3v = 6mv. After the collision, the momentum is shared between both objects, which now have a combined mass of 2m + 4m = 6m.
So, we set the initial momentum equal to the final momentum and solve for the final velocity (Vf):
Initial momentum = Final momentum 6mv = (6m)Vf Vf = v
So, the final speed is v.
Step 2: Change in Total Kinetic Energy The initial kinetic energy is (1/2) * mass * velocity^2 = (1/2) * 2m * (3v)^2 = 9mv^2. The final kinetic energy is (1/2) * total mass * velocity^2 = (1/2) * 6m * v^2 = 3mv^2.
The change in kinetic energy is final - initial = 3mv^2 - 9mv^2 = -6mv^2.
So, the final speed is v and the change in total kinetic energy is -6mv^2. The correct answer is not listed in the options provided.
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