Conservation of Momentum for explosion

In summary, the problem involves two blocks of equal mass colliding on the x-axis with one block initially moving at 5 m/s and the other at rest. After an explosion that doubles their total kinetic energy, the question is to find the final speed of the originally moving block. Using the equations for momentum and kinetic energy, we can set up an equation equating the initial and final momentum, and the initial and final kinetic energy. This leads to the equation 25 J = (1/2)Mv1^2 + (1/2)Mv2^2, which can be used to solve for the final speed of the originally moving block.
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possum30540
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Homework Statement


A block moves at 5 m/s in the positive x direction and hits an identical block, initially at rest. A small amount of gunpowder had been placed on one of the blocks. The explosion does not harm the blocks but it doubles their total kinetic energy. After the explosion, the blocks move along the x-axis and the orginally moving block has a speed of:


Homework Equations


momentum = mass * velocity

kinetic energy = (1/2) m *(v)^2

conservation on momentum: the total initial momentum = the total final momentum


The Attempt at a Solution


since the mass of the two cars is the same, the mass = M
v1 = velocity of cart 1
v2 = velocity of cart 2

before the collision, the total kinetic energy is 12.5M J
before the collision, the total momentum is 5M kg*m/s

after the collision, the total kinetic energy is 25M J

initial momentum = final momentum
5M = Mv1 + Mv2

This is where I am stuck. I don't know what the next step is and if someone would help me along it would be very much appreciated.
 
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  • #2
You say that the total kinetic energy after the collision is 25M J. Write the equation fror that!
 
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  • #3
The problem says the initial kinetic energy is doubled. So 2 * 12.5 = 25 J
 
  • #4
Yes, you said that before. Now USE it! Write the equation for total kinetic energy after the collision-explosion and set it equal to 25.
 
  • #5
25 J = (1/2)Mv1^2 + (1/2)Mv2^2
 
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What is the law of conservation of momentum?

The law of conservation of momentum states that, in a closed system, the total momentum before an event (such as an explosion) is equal to the total momentum after the event. This means that the total amount of momentum in a system remains constant, even if individual objects within the system are moving at different speeds or in different directions.

How does the conservation of momentum apply to explosions?

In an explosion, the initial momentum of all the particles involved is equal to the final momentum of those particles plus any external forces acting on them. This means that the total momentum of all the fragments and debris from an explosion will equal the momentum of the original object or system prior to the explosion.

Why is the conservation of momentum important for understanding explosions?

The conservation of momentum is important for understanding explosions because it helps explain and predict the behavior of objects and particles after an explosion occurs. By applying this law, scientists can calculate the direction and speed of fragments and debris from an explosion, and determine the amount of force and energy involved in the event.

What factors can affect the conservation of momentum in an explosion?

The conservation of momentum can be affected by external forces, such as air resistance or friction, as well as internal forces, such as the strength of the explosive material and the shape and density of the objects involved. The angle and speed at which the fragments and debris are propelled can also impact the conservation of momentum.

How is the conservation of momentum in an explosion related to other laws of physics?

The conservation of momentum is closely related to other laws of physics, such as Newton's laws of motion and the law of conservation of energy. These laws work together to explain the behavior of objects in motion and the transfer of energy in a system. The conservation of momentum is also a fundamental principle in understanding the motion of particles in both macroscopic and microscopic systems.

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