Conservation of Energy and Springs. Block dropped onto a spring

In summary, the problem involves a 2.7 kg block being dropped from a height of 4.5 m onto a compressed spring. The question asks for the speed of the block when the spring is compressed by 15.0 cm. The equations used to solve the problem are potential energy (PE), kinetic energy (KE), and the spring constant (k). The attempt at a solution involved using PE=U(s) to find k, but there was uncertainty about the value obtained. Additionally, there was confusion about the value used for height (h) in the equation mgh + .5mv^2 = .5kx^2.
  • #1
coheedcoheed
1
0
1. Homework Statement [/b
A 2.7 kg block is dropped from rest from a height of 4.5 m above the top of the spring. When the block is momentarily at rest, the spring is compressed by 25.0 cm. What is the speed of the block when the compression of the spring is 15.0 cm?


Homework Equations


PE=mgh
KE=.5mv^2
U(s)=.5kx^2

The Attempt at a Solution



Ok so what I did at first was use PE= U(s) to find the spring constant, which i got to be 4026 N/m (I don't know if this is right, correct me if I'm wrong), after I found that, i used mgh + .5mv^2 = .5kx^2, where h was .1m, and x was .15 since it was compressed .15m. but its wrong. please help!
 
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  • #2
1) If the v = 7.52 m/s, I would ask how you found k? I* punched few numbers and had different k (~3000)
2)Why you are taking h to be 0.1 m? in mgh + .5mv^2 = .5kx^2
 

Related to Conservation of Energy and Springs. Block dropped onto a spring

1. What is the law of conservation of energy?

The law of conservation of energy states that energy cannot be created or destroyed, it can only change forms. In other words, the total energy of a system remains constant.

2. How does the law of conservation of energy apply to a spring?

When a block is dropped onto a spring, it compresses the spring and stores potential energy. This potential energy is then released as the spring returns to its original state, and the total energy of the system remains constant.

3. What is the relationship between potential energy and kinetic energy in a spring system?

In a spring system, potential energy and kinetic energy are interchangeable. As the block is dropped onto the spring, its potential energy is converted into kinetic energy. As the spring returns to its original state, the kinetic energy is converted back into potential energy.

4. How does the mass of the block affect the spring's potential and kinetic energy?

The mass of the block affects the amount of potential energy stored in the spring as well as the speed at which the spring returns to its original state. A heavier block will compress the spring more, thus storing more potential energy, and will also have a greater kinetic energy as it returns to its original state.

5. What factors can affect the amount of energy conserved in a spring system?

The amount of energy conserved in a spring system can be affected by factors such as the initial height from which the block is dropped, the mass of the block, and the stiffness of the spring. Friction or air resistance can also play a role in the conservation of energy in a spring system.

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