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The momentum (p) of an object can be calculated from knowledge of its mass (m) and velocity (v) using the formula:
p = m • v
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The ultimate goal of this analysis is to determine the post-collision velocity of the two carts. The following strategy will prove effective.
- Since the mass and the before-collision velocity of each cart is given, the momentum values can be calculated (see Formula Frenzy section). Since one of the carts is moving west, its momentum will be a negative value (see Know the Law section).
- The total momentum of the system is simply the sum of the individual momentum values of the two carts. Once individual values have been calculated, the total momentum of the system before the collision can be determined.
- The post-collision velocities of the two carts are not known. The momentum of each individual cart must be written in terms of the unknown velocity v. Since the carts are stuck together, they move with the same velocity; so the same variable v can be used for each cart's velocity. For instance, for a 0.500-kg cart, the momentum can be represented as 0.500•v; and for a 0.750-kg cart, the momentum can be represented as 0.750•v. Together, the total system momentum after the collision would be 0.500•v + 0.750•v or 1.250•v.
- Since the system is said to be isolated (see Define Help section), the post-collision momentum of the system is the same as the pre-collision momentum. The post-collision momentum is not known as an actual value; it is represented in terms of the unknown velocity v. Set the expression for momentum in terms of v equal to the pre-collision momentum. Then solve for the variable v. This is the post-collision velocity of each cart.
- Now that v is known, the post-collision momentum of each individual cart can be calculated and entered into the cells of the table. The total momentum for the system can be calculated as well. This total system momentum should be the same as before the collision. If not, you will need to recheck your work.
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Isolated System and External Forces:
A system of two colliding objects is considered to be an isolated system if the only momentum-changing forces exerted during the collision are the forces between the two objects themselves. If a third object exerts a force capable of changing one or both of the object's momentum during the collision, then this is considered an external force and the system is not isolated.
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Momentum as a Vector:
Momentum is a vector and has a direction. The direction of an object's momentum is in the same direction that the object is moving. An eastward moving object has an eastward momentum (+); a westward moving object has a westward momentum (-).
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