Elastic Potential- Acceleration with springs

In summary, the problem involves a 1.6kg mass suspended from a spring inside a stationary elevator. The spring stretches 12cm and then extends a further 12cm when the elevator accelerates upwards. The acceleration of the elevator can be found by using the equation Fy=may and solving for ay. To do this, the value of k needs to be found first, which is done by setting the initial force (kx-mg) equal to 0. After finding the value of k to be 130.666 N/m, the acceleration of the elevator is calculated to be 9.79999 m/s2.
  • #1
hsphysics2
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0

Homework Statement


A 1.6kg mass is suspended from a spring inside a stationary elevator. The spring stretches 12cm. The elevator now accelerates upwards, and the spring extends a further 12cm. What is the elevator's acceleration?


Homework Equations


Fy= may
Ue= 1/2 (kx2)

The Attempt at a Solution


I'm just not sure on the best way to start this question.
 
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  • #2
I would start with the first equation you provided. [itex]F_y = ma_y[/itex]. What's the acceleration ([itex]a_y[/itex]) in this problem? Where you can find a force on the system?
 
  • #3
Fy=may
kx-mg=may
ay=(kx-mg)/m

but k is not given...
 
  • #4
You need to find k first. What's the spring doing BEFORE the elevator starts moving?
 
  • #5
Fy=may
kx-mg=0
k=(mg)/x
k=1306.666 N/m

Fy=may
kx-mg=may
ay=(kx-mg)/m
ay=9.79999 m/s2
 
  • #6
I got a different value for k, could you double check it? My answer was a magnitude different.
 
  • #7
oops, so k=130.666 N/m
 
  • #8
Right, and you also know the distance so now would be a good time to find the potential.
 
  • #9
Looks to me like you're done. No need for the potential in this problem.
 
  • #10
Ah, yep. I was hasty.
 

1. What is elastic potential energy?

Elastic potential energy is the energy stored in a stretched or compressed elastic material, such as a spring. It is a type of potential energy that is the result of the deformation of an object.

2. How is elastic potential energy calculated?

The formula for calculating elastic potential energy is E = 1/2 kx², where E is the elastic potential energy, k is the spring constant and x is the displacement of the spring from its equilibrium position.

3. What is the relationship between spring constant and elastic potential energy?

The spring constant directly affects the amount of elastic potential energy stored in a spring. A higher spring constant means that the spring is stiffer and will require more force to stretch or compress, resulting in a higher amount of elastic potential energy.

4. Can elastic potential energy be converted into other forms of energy?

Yes, elastic potential energy can be converted into other forms of energy, such as kinetic energy, when the spring is released and returns to its equilibrium position. This is the basis for many devices that use springs, such as pogo sticks and trampolines.

5. How does acceleration affect elastic potential energy?

Acceleration is directly related to the amount of elastic potential energy stored in a spring. As the spring is stretched or compressed, the acceleration of the object attached to the spring increases, resulting in a higher amount of elastic potential energy being stored.

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