Conservation of energy and momentum Problem

In summary, a 16 kg block with a small explosive charge inside it explodes, splitting into two fragments and adding 76.8 joules of kinetic energy. The other 6kg fragment slides a distance of 4.08m along the rough surface before coming to rest. This can be solved using conservation laws and the equations for conservation of momentum and conservation of energy.
  • #1
rzn972
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Homework Statement



A 16 kg block is initially at rest on a rough horizontal surface (uk= .2). The block has a small explosive charge inside it. The charge explodes, splinting the block into two fragments and adding 76.8 joules of kinetic energy. The other 10kg slides 1.47m along the rough surface before coming to Rest. How far does the other 6kg fragment slide along the rough surface before it comes to rest?
Must be solved using conservation laws.

Homework Equations





The Attempt at a Solution


Using conservation of momentum:
6va = 10vb
vb= .6 va
line 1: 76.8 = .5 * 6 *va^2 + .5* 10 * vb^2
va = 4
line 2: .5 * 6 * 4^2 + -.2 * 6 * g * da= 0
da= 4.08
I am not sure where the equation from line 1 and 2 came from.
Is line 1 using work = change in kinetic energy?
I am not sure what equation is used for line 2.
 
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  • #2
line 1 computes total kinetic energy after explosion
line 2 uses the work of friction force and sets it equal to the change in kinetic energy
 

1. What is the conservation of energy and momentum problem?

The conservation of energy and momentum problem is a fundamental principle in physics that states that the total energy and momentum of a closed system remains constant over time. This means that energy and momentum can be transferred between different forms, but the total amount in the system remains constant.

2. How does the conservation of energy and momentum problem relate to Newton's laws of motion?

The conservation of energy and momentum problem is closely related to Newton's laws of motion, specifically the first and third laws. The first law states that an object at rest will stay at rest, and an object in motion will stay in motion, unless acted upon by an unbalanced force. The third law states that for every action, there is an equal and opposite reaction. These laws demonstrate the conservation of momentum and energy, as any change in motion or energy in a system must be due to an outside force or interaction.

3. What is an example of the conservation of energy and momentum problem in action?

One example of the conservation of energy and momentum problem is a collision between two objects. During the collision, energy and momentum are transferred between the two objects, but the total energy and momentum of the system remains constant. This can be observed in everyday situations, such as a game of pool or a car crash.

4. Are there any exceptions to the conservation of energy and momentum problem?

While the conservation of energy and momentum is a fundamental principle, there are some situations where it may not apply. One example is in the quantum world, where energy can fluctuate and momentum is not always conserved. Additionally, in very high energy scenarios, such as near black holes, the laws of physics as we know them may break down.

5. How is the conservation of energy and momentum problem used in real-world applications?

The conservation of energy and momentum is used in numerous real-world applications, from designing efficient machines and vehicles to understanding the behavior of celestial bodies in space. It is also crucial in the field of renewable energy, as the conversion of energy from one form to another must follow the principles of conservation of energy and momentum.

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