Potential energy of a spring

• emeraldempres
In summary, a spring with a force of 790 N and a displacement of 0.135 m has a potential energy of 31.5 J when a mass of 62.0 hangs vertically from it. To find the potential energy, the spring constant k was first calculated to be 585.85, and then used in the equation U_s = 0.5kx^2, where x is the displacement. This value can also be found by using Newton's second law and solving for the displacement of the object hanging from the spring.

emeraldempres

A force of 790 N stretches a certain spring a distance of 0.135 m. What is the potential energy of the spring when a mass of 62.0 hangs vertically from it?

I thought starting with finding the spring constant k would be good and i got it to be 585.85. i then plugged it into the potential energy equation u= .5(k)(x)^2 where x is the displacement. I got the new displacement by setting up a porportional equation and the new x was .104 m.

All the answers look correct except for k.

when i calculated k this is what i did

Spring Force(790 N) = (k)(distance(.135m))
and isolated the variable.

what did i do wrong?

790 is the force in Newtons and i divided it by .135 which is the distance the weight on the spring made the spring stretch, the answer was 5851.85

emeraldempres said:
790 is the force in Newtons and i divided it by .135 which is the distance the weight on the spring made the spring stretch, the answer was 5851.85
Ok. You wrote
585.85
Everything else is fine.

Another way to find the displacement would be to set up Newton's second law as well.

$$mg+(-k\Delta y=0) \Rightarrow \Deltay=\frac{mg}{k}$$

Then plug back into the potential energy of the spring. $$U_{s}=\frac{1}{2}ky^2$$

does that help me with finf=ding the potnetial energy?

sorry,i meant does that help me with finding the potential energy?

Yes. The potential energy of a spring is just a formula unless you want to find the total change in potential energy = gravitational potential energy + potential energy of the spring.

konthelion said:
Another way to find the displacement would be to set up Newton's second law as well.

$$mg+(-k\Delta y=0) \Rightarrow \Deltay=\frac{mg}{k}$$

Then plug back into the potential energy of the spring. $$U_{s}=\frac{1}{2}ky^2$$

using the mg/k equation gave me 1.03 m as my displacement but that does not sound right if the force 0f 709 only gave a displacement of .135 m

Actually you would get ~.1038 =~ .104m which is the distance you're trying to find.

You've already found k, you need to find the distance y(the distance that the object stretches the spring, hence why I used Newton's 2nd law). There are two distances in this problem., one is already given, the other(the distance that the mass is stretching the string so that you can find the potential energy of the spring)is the one you're trying to find.

thank you so much for your help. i am doing my home work online and my summer school teaher gave us a homework assignment due each night of the weekend but is unavailable himself to answer questions. i got the answer though 31.5 J

What is potential energy of a spring?

Potential energy of a spring is the energy stored in a spring when it is compressed or stretched from its equilibrium position.

What factors affect the potential energy of a spring?

The potential energy of a spring is affected by its spring constant, which is a measure of its stiffness, and the displacement from its equilibrium position.

How is the potential energy of a spring calculated?

The potential energy of a spring can be calculated using the equation PE = 1/2kx^2, where k is the spring constant and x is the displacement from the equilibrium position.

What is the relationship between the potential energy of a spring and its displacement?

The potential energy of a spring is directly proportional to the square of its displacement from the equilibrium position. This means that as the displacement increases, the potential energy also increases.

What are some real-life examples of potential energy of a spring?

Springs are used in many everyday objects, such as car suspension systems, pogo sticks, and door hinges. These all rely on the potential energy stored in the spring to function.