Vertical mass less spring problem

In summary, the problem involves a 1.00 kg block being compressed against a vertical massless spring with a spring constant of 280 N/m. Using conservation of energy, we can determine that the block will travel a distance of 0.24 m from the maximum spring compression to the maximum height. However, in order to find the distance from the spring's equilibrium point, we need to subtract the initial compression distance of 0.13 m. This gives us a final answer of 0.11 m.
  • #1
squintyeyes
45
0
A 1.00 kg block is compressed a distance of x = 0.130 m against a vertical massless spring with spring constant 280 N/m. The block is released from rest. How far above the spring's equilibrium point does the block travel?

I used conservation of energy and got
0.5kx^2 + 0.5mv^2 + mgh = 0.5kX^2 + 0.5mV^2 + mgH
0.5(280)(0.13^2) + 0 + 0 = 0 + 0 + (1)(9.8)H
2.366 = 9.8H
H= 0.2414

This is marked wrong so i thn subtracted the initial 0.13 and it was still marked wrong.
Can anyone tell me why and how to do it? Please?
 
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  • #2
The 0.24 m that you found represents the distance from maximum spring compression to maximum height. As you suspected, you need to subtract from it the distance to the "spring's equilibrium point". Is that 0.13 m? I think not because it is the overall compression of the spring. When the 1 kg mass is placed on the spring and the system is at rest (equilibrium) that's the equilibrium point. So by what distance is the spring compressed when you place the 1 kg mass on it and you just let it sit there?
 

1. What is a vertical massless spring problem?

A vertical massless spring problem refers to a theoretical physics problem where a mass is attached to a spring that is hung vertically from a fixed point. The mass is subject to the forces of gravity and the spring's tension, and the problem typically involves finding the mass's position or motion at a given point in time.

2. What is the equation for a vertical massless spring?

The equation for a vertical massless spring is F = mg - kx, where F is the net force on the mass, m is the mass of the object, g is the acceleration due to gravity, k is the spring constant, and x is the displacement of the mass from its equilibrium position.

3. How do you solve a vertical massless spring problem?

To solve a vertical massless spring problem, you need to use Newton's second law of motion, F = ma, and the equation for a vertical massless spring, F = mg - kx. You can set up and solve a differential equation to find the position or motion of the mass at a given time.

4. What is the role of the spring constant in a vertical massless spring problem?

The spring constant, k, represents the stiffness of the spring and is a measure of how much force is required to stretch or compress the spring by a certain distance. In a vertical massless spring problem, the spring constant determines the strength of the spring's tension and plays a crucial role in the equation of motion for the mass.

5. What are some real-life applications of vertical massless spring problems?

Vertical massless spring problems have many real-life applications, such as in the design of suspension systems for vehicles, shock absorbers in buildings, and bungee jumping. They are also used in the study of seismology to model the motion of buildings during earthquakes.

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