Maximum Spring Elongation for a Block on a Horizontal Ideal Spring

In summary, the question involves a 2-kg block attached to an ideal spring with a spring constant of 200N/m. When the spring is at its equilibrium length, the block is given a speed of 5m/s. The maximum elongation of the spring can be determined by applying the conservation of mechanical energy equation at equilibrium and at maximum elongation. The solution suggests that the answer should be 5 meters, but based on the given information, the correct answer should be 0.5 meters.
  • #1
anthonych414
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Homework Statement



A 2-kg block is attached to a horizonal ideal spring with a spring constant of 200N/m. When the spring has its equilibrium length the block is given a speed of 5m/s. What is the maximum elongation of the spring.

Homework Equations



Conservation of mechanical energy, PEspring=0.5kx^2 KE=0.5mv^2

The Attempt at a Solution



It seems like a fairly simple question to me, applying conservation of mechanical energy at equilibrium and at maximum elongation we get 0 + 0.5kx^2 = 0 + 0.5mv^2, so x =√(mv^2/k) = 0.5 meters, however the solution says the answer should be 5 meters, can anyone tell me what I'm missing here?
 
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  • #2
Your result looks good. Maybe a typo in the question? Perhaps they meant for the initial velocity to be 50 m/s.
 

FAQ: Maximum Spring Elongation for a Block on a Horizontal Ideal Spring

What is the law of conservation of energy?

The law of conservation of energy is a fundamental principle in physics that states that energy cannot be created or destroyed, but can only be transferred or transformed from one form to another.

What are the different forms of energy?

There are several forms of energy, including kinetic energy (energy of motion), potential energy (stored energy), thermal energy (heat), chemical energy (stored in bonds between atoms), nuclear energy (stored in the nucleus of an atom), and electromagnetic energy (energy of light and other forms of radiation).

How is energy conserved in a closed system?

In a closed system, energy is conserved because it cannot enter or exit the system. This means that the total amount of energy in the system remains constant, even as it may change forms or be transferred between objects within the system.

What is the relationship between energy and work?

Work is the transfer of energy from one object to another. When work is done on an object, energy is transferred to that object, causing it to move or change in some way. Similarly, when work is done by an object, it is using energy to cause another object to move or change.

How does the conservation of energy apply to everyday life?

The law of conservation of energy applies to all natural phenomena, including everyday life. For example, when we turn on a light bulb, the electrical energy is converted into light and heat energy. When we exercise, our bodies convert chemical energy into kinetic energy. Understanding this principle can help us make more efficient use of energy and reduce waste.

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