Conservation of Energy in a Block-Spring System

In summary, the energy of a block-spring system vibrating on a frictionless, horizontal surface with an amplitude of 4.5 cm is 24 J. When the mass of the block is doubled and the amplitude remains the same, the energy of the system remains constant. This is because the energy equation for the system is dependent on the spring constant and amplitude, not the mass of the block. Therefore, the energy of the system remains at 24 J.
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Homework Statement



A block–spring system vibrating on a frictionless, horizontal surface with an amplitude of 4.5 cm has an energy of 24 J. If the block is replaced by one whose mass is twice the mass of the original block and the amplitude of the motion is again 4.5 cm, what is the energy of the system?

Homework Equations



E= K+U = .5mv^2 + .5kx^2 = .5kA^2

The Attempt at a Solution



So if the spring constant doesn't change and the amplitude doesn't change, will the energy of the system stay constant even though the mass (m) is doubled? Initially I thought the energy of the system would be doubled, because I thought it made sense that it would take more energy to move a more massive object, but that was incorrect. Thanks in advance for any assistance
 
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FAQ: Conservation of Energy in a Block-Spring System

1. What is energy in a spring system?

Energy in a spring system refers to the potential and kinetic energy stored in a spring when it is stretched or compressed.

2. How is energy calculated in a spring system?

The potential energy of a spring can be calculated using the formula PE = 1/2kx², where k is the spring constant and x is the displacement from equilibrium. The kinetic energy can be calculated using the formula KE = 1/2mv², where m is the mass attached to the spring and v is the velocity. The total energy in a spring system is the sum of the potential and kinetic energy.

3. What is Hooke's Law and how does it relate to energy in a spring system?

Hooke's Law states that the force exerted by a spring is directly proportional to the displacement from equilibrium. This means that as the spring is stretched or compressed, the potential energy increases and the kinetic energy decreases. Hooke's Law is the basis for calculating the energy in a spring system.

4. Can energy be lost in a spring system?

In an ideal spring system, energy is conserved and no energy is lost. However, in real-life situations, some energy may be lost due to friction and other external factors. This is known as energy dissipation.

5. How is energy in a spring system used in real-world applications?

Energy in a spring system is used in various real-world applications such as bungee jumping, trampolines, and shock absorbers in vehicles. It is also used in devices like watches and pedometers to measure and store energy.

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