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Question: Which of the following is true when an object of mass m moving on a horizontal frictionless surface hits and sticks to an object of mass M > m, which is initially at rest on the surface?
When a moving object of mass m hits and sticks to an object of mass M (greater than m) that is initially at rest, the two objects will move together after the collision. This is an example of a perfectly inelastic collision. The important concept here is the conservation of momentum principle. In the absence of external forces, the total momentum before collision is conserved after the collision. If the velocity of the object with mass m before the collision is v, then the total initial momentum is m*v. After the collision, since the two objects are moving together, if we denote their common velocity as V, the total final momentum is (M+m)*V. By conservation of momentum, we can get: m*v = (M + m)*V So the velocity V of the joint object after the collision would be: V = (m*v) / (M + m); This indicates that the combined object will move in the same direction as the object of mass m was initially moving, but with a slower speed due to the larger total mass.
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