The diagram below depicts a variety of situations involving explosion-like impulses acting between two carts on a low-friction track. velocity change) will be equal in magnitude.Yet even if the masses of the two objects are different, the momentum change of the two objects (mass If the masses of the two objects are unequal, then they will be set in motion by the explosion with different speeds. 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). If the exploding system includes two objects or two parts, this principle can be stated in the form of an equation as: And since an impulse causes and is equal to a change in momentum, both carts encounter momentum changes that are equal in magnitude and opposite in direction. This results in impulses that are equal in magnitude and opposite in direction. Just like in collisions, the two objects involved encounter the same force for the same amount of time directed in opposite directions. The vector sum of the momentum of the individual carts is 0 units. 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. One cart acquires a rightward momentum while the other cart acquires a leftward momentum. The pin is tapped, the plunger is released, and an explosion-like impulse sets both carts in motion along the track in opposite directions. The spring is compressed and the carts are placed next to each other. One of the carts is equipped with a spring-loaded plunger that can be released by tapping on a small pin. The total momentum of the system is zero before the explosion. The system consists of the two individual carts initially at rest. Total system momentum is conserved.Īs another demonstration of momentum conservation, consider two low-friction carts at rest on a track. The vector sum of the individual momenta of the two objects is 0. If the ball acquires 50 units of forward momentum, then the cannon acquires 50 units of backwards momentum. After the explosion, the total momentum of the system must still be zero. Before the explosion, the total momentum of the system is zero since the cannon and the tennis ball located inside of it are both at rest. The system consists of two objects - a cannon and a tennis ball. In the exploding cannon demonstration, total system momentum is conserved. Due to the relatively larger mass of the cannon, its backwards recoil speed is considerably less than the forward speed of the tennis ball. The cannon experienced the same impulse, changing its momentum from zero to a final value as it recoils backwards. The impulse of the explosion changes the momentum of the tennis ball as it exits the muzzle at high speed. The fuel is ignited, setting off an explosion that propels the tennis ball through the muzzle of the cannon. The cannon is equipped with a reaction chamber into which a small amount of fuel is inserted. A homemade cannon is placed upon a cart and loaded with a tennis ball. Momentum conservation is often demonstrated in a Physics class with a homemade cannon demonstration. Just like in collisions, total system momentum is conserved. 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. After the explosion, the individual parts of the system (that is often a collection of fragments from the original object) have momentum. 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. This same principle of momentum conservation can be applied to explosions. For collisions occurring in isolated systems, there are no exceptions to this law. As discussed in a previous part of Lesson 2, total system momentum is conserved for collisions between objects in an isolated system.
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