Law of conservation of energy and springs.

[firezap]

Homework Statement

see the 2 image attachments.

Homework Equations

law of conservation of energy
Fs = -kx
Eg = mgh
Ek = 1/2mv^2
Es = 1/2kx^2

The Attempt at a Solution

i have no idea.

 

[rude man]

How about energy conservation as the mass oscillates back & forth?
.

 

[firezap]

i found this answer online. can i trust this solution or is it wrong?

 

[rude man]

i found this answer online. can i trust this solution or is it wrong?

I'm sorry, I can't read it.

But it's a simple problem if you keep total (potential plus kinetic) energy constant as the mass oscillates.

 

[Nickie]

I can provide some clarification and explanation on the topic of the law of conservation of energy and springs. The law of conservation of energy states that energy cannot be created or destroyed, it can only be transformed from one form to another. In the case of a spring, when it is compressed or stretched, it stores potential energy in the form of elastic potential energy. This energy is then released as kinetic energy when the spring returns to its original shape.

The equation Fs = -kx represents Hooke's Law, where Fs is the force exerted by the spring, k is the spring constant, and x is the displacement from the equilibrium position. This equation shows that the force exerted by a spring is directly proportional to the displacement from its equilibrium position.

When discussing the potential energy of a spring, we use the equation Es = 1/2kx^2, where Es is the elastic potential energy, k is the spring constant, and x is the displacement from the equilibrium position. This equation shows that the potential energy of a spring is directly proportional to the square of its displacement.

In the case of a spring being dropped or released from a certain height, we can also consider the potential energy due to gravity, Eg = mgh, where Eg is the gravitational potential energy, m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object. This potential energy is converted into kinetic energy as the spring falls, which can be calculated using the equation Ek = 1/2mv^2, where Ek is the kinetic energy and v is the velocity of the object.

In summary, the law of conservation of energy applies to the system of a spring, where the potential energy stored in the spring is converted into kinetic energy and vice versa. This can be seen through the equations and the relationship between the various forms of energy. I hope this helps in your understanding of the topic.