momentum_lesson_5.doc - MOMENTUM LESSON 5 Momentum Conservation in Explosions Recall total system momentum is conserved for collisions between objects

momentum_lesson_5.doc - MOMENTUM LESSON 5 Momentum...

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MOMENTUM LESSON 5 Momentum Conservation in Explosions Recall, total system momentum is conserved for collisions between objects in an isolated system . For collisions occurring in isolated systems, there are no exceptions to this law. WHAT IS AN ISOLATED SYSTEM? The principle of momentum conservation can be applied to explosions. In an explosion, an internal impulse acts in order to propel the parts of a system (often a single object) into a variety of directions. After the explosion, the individual parts of the system (which is often a collection of fragments from the original object) have momentum. If the vector sum of all individual parts of the system could be added together to determine the total momentum after the explosion, then it should be the same as the total momentum before the explosion. Just like in collisions, total system momentum is conserved.
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DEMO: Consider two low-friction carts at rest on a track. The system consists of the two individual carts initially at rest. The total momentum of the system is zero before the explosion . The spring is compressed between the two carts. The string is cut, the plunger is released, and an explosion-like impulse sets both carts in motion along the track in opposite directions. One cart acquires a rightward momentum while the other cart acquires a leftward momentum. If 20 units of forward momentum are acquired by the rightward-moving cart, then 20 units of backwards momentum is acquired by the leftward-moving cart. The vector sum of the momentum of the individual carts is 0 units. Total system momentum is conserved. Equal and Opposite Momentum Changes Just like in collisions, the two objects involved encounter the same force for the same amount of time directed in opposite directions. This results in impulses which are equal in magnitude and opposite in direction. And since an impulse causes and is equal to a change in momentum, both carts encounter momentum changes which are equal in magnitude and opposite in direction. If the exploding system includes two objects or two parts, this principle can be stated in the form of an equation as: MOMENTUM (before) = MOMENTUM (after) 0 = m 1 Δv 1 + m 2 Δv 2
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If the masses of the two objects are equal, then their post-explosion velocity will be equal in magnitude (assuming the system is initially at rest). WHAT HAPPENS IF THE MASSES ARE NOT EQUAL? If the masses of the two objects are unequal, then they will be set in motion by the explosion with different speeds. Yet even if the masses of the two objects are different, the momentum change of the two objects (mass • velocity change) will be equal in magnitude. In each of these systems, is total system momentum conserved? In each of the above situations, the impulse on the carts is the same - a value of 20 kg•cm/s (or cN•s). Since the same spring is used, the same impulse is delivered.
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Since each cart experiences the same impulse, each cart encounters the same momentum change in every situation - a value of 20 kg•cm/s.
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