Energy Conservation: Block & Spring

In summary, an object of mass 4 kg slides down a frictionless inclined plane with an angle of 20°. It compresses a spring by 1 m before stopping. The object loses 53.7 J of gravitational potential energy when it touches the spring, and 67.1 J when it fully compresses it. The value of the spring constant is unknown, but can be calculated using the conservation of mechanical energy.
  • #1
mrnastytime
28
0

Homework Statement


An object of mass M = 4 kg slides from rest a distance d = 4 m down a frictionless inclined plane where it encounters a spring. It compresses the spring a distance D = 1 m before stopping. The inclined plane makes an angle q = 20° with the horizontal.

Homework Equations


When the block just touches the spring, how much gravitational potential energy has it lost?
U=53.7 J
After the mass has fully compressed the spring, what is its total loss of gravitational potential energy?
U=67.1 J
What is the value of the spring constant?
k=??

The Attempt at a Solution


U=Ui-Uf
U=53.7-67.1=-13.4
U=(1/2)kx^2
k=2U/x^2
k=2(-13.4)/(5)^2
k=1.07?
the answer is wrong. am i suppose to use the conservation of mechanical energy? because i am lost.
 
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  • #2
It is wrong to take the difference between 53.7 and 67.1.
The ramp is frictionless, so all of the PE (67.1 J) goes into the spring energy.
 
  • #3
thank you, i figured it out.
 

1. What is the concept behind energy conservation in a block and spring system?

The concept of energy conservation in a block and spring system is based on the principle of conservation of energy, which states that energy cannot be created or destroyed, but can only be transferred or transformed from one form to another. In this system, the potential energy stored in the spring is converted into kinetic energy as the block is released, and the total energy (potential + kinetic) remains constant throughout the motion.

2. How does the mass of the block affect energy conservation in this system?

The mass of the block does not affect energy conservation in this system, as the total energy remains constant regardless of the mass of the block. However, the mass of the block may affect the speed and amplitude of the oscillations as it affects the amount of potential energy stored in the spring.

3. What factors can affect the efficiency of energy conservation in a block and spring system?

The efficiency of energy conservation in a block and spring system can be affected by factors such as friction, air resistance, and the elasticity of the spring. Friction and air resistance can cause some of the energy to be lost to the surroundings, while the elasticity of the spring can affect the amount of potential energy stored and released.

4. Can the energy in a block and spring system be completely conserved?

No, the energy in a block and spring system cannot be completely conserved due to external factors such as friction and air resistance, which cause some energy to be lost to the surroundings. However, in an ideal system with no external forces, the energy can be conserved.

5. How is energy conservation in a block and spring system related to simple harmonic motion?

Energy conservation in a block and spring system is closely related to simple harmonic motion, as the potential energy stored in the spring and the kinetic energy of the block are constantly being converted back and forth throughout the motion. This results in the block moving in a repetitive pattern, known as simple harmonic motion.

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