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Word Problem Exercises: Physics - Momentum

Momentum is a vector quantity defined as the product of an object's mass and its velocity. Since velocity is a vector quantity and mass is a scalar quantity, momentum's vector nature is dependent on the vector properties of the object's velocity. If an object is moving in a positive direction, then it also has a positive momentum. Momentum can be represented by the variable p and has units of kg m/sec.
 
In a collision, momentum is always conserved. This means that the sum of all the momenta in each object before a collision is equal to the sum of all the momenta afterwards. This is called the Law of Conservation of Momentum.
 
 
In the following questions, a diagram represents the set up of two colliding blocks with varying masses and velocity. The vector above a block denotes the velocity of that block. A block with no vector is assumed to be stationary.
 
Let's look at an example.
 
 
In this example, the 1-kilogram block is moving to the right at 4 m/sec towards a stationary 2-kilogram block.
 
 
The second diagram represents the state of the blocks following the collision. The 1-kilogram block is now stationary and the 2-kilogram block moves off to the right at an unknown velocity. We will use the Law of Conservation of Momentum to determine the unknown velocity of the 2-kilogram block.
 
 
Through the use of conservation of momentum, we calculated that the 2-kilogram left the collision moving to the right at 2 m/sec (our velocity is positive).
 
 
In addition to conservation of momentum, we should also examine a collision with respect to whether kinetic energy (KE = ½mv2)  is lost (inelastic collisions) or conserved (elastic collisions).
 
Let's examine the energies in this collision.
 
Before: KE = ½(1)(4)2 + ½(2)(0)2 = 8 J
After: KE = ½(1)(0)2 + ½(2)(2)2 = 4 J
 
This is an inelastic collision since 50% of the original energy was lost to sound and heat.

Question Group #1
Directions and/or Common Information: Read each problem carefully and refer to the given diagrams. After applying the Law of Conservation of Momentum to solve for the missing velocity, calculate the kinetic energy before and after the collision to determine whether the collision was inelastic or elastic.


As shown below, a 5-kilogram block, initially moving to the right at 4 m/sec, collides with a stationary 4-kilogram block.
 
 
A student hypothesizes that the 5-kg block will stop after the collision. How fast would he calculate that the 4-kg block should be traveling after the collision?
1. 





As shown below, a 2-kilogram block is moving left at 6 m/sec towards a stationary 3-kilogram block.
 
 
Once again, a student hypothesizes that the 2-kg block will stop as a result of the collision. Based on this expected outcome, how fast does he think that the 3-kg block should be traveling after the collision?
2. 





As shown below, a 1-kilogram block moving to the right at 8 m/sec is going to collide with a 2-kilogram block moving towards it at 1 m/sec.
 
 
A measuring probe reveals that the 1-kg block rebounds backwards towards the left at 5 m/sec. Calculate how fast the 2-block be traveling after the collision?
3. 





As shown below, a 2-kilogram block moving to the right at 4 m/sec is going to collide with a stationary 4-kilogram block.
 
 
After the collision, the two blocks stick together and leave as one "6-kg block." Calculate their final velocity.
4. 





As shown below, a 4-kilogram block is moving to the right at 4 m/sec towards a slower moving 2-kilogram block which is also traveling to the right but at only 1 m/sec.
 
 
If the 4-kg bock loses half of its speed as a consequence of the collision, then how fast will the 2-kg block be moving after the collision?
5. 








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