How is energy lost to heat calculated?

[AddversitY]

Energy Lost to Heat ~ Spring (Solved)

Homework Statement

--->What is the energy lost to heat?<---

spring mass = 15g = .015kg
spring constant = 220 J/m^2
spring is compressed 5cm (.05m) then released to achieve maximum height of 102 cm (1.02 m)

Homework Equations

U = .5(k)(x)^2 where U is the potential energy of a spring, k is the spring constant, and x the compression length.

K=.5(m)(v)^2 where K is kinetic energy, m is a mass, and v is velocity

Ug = mgy where Ug is gravitational potential energy, m is a mass, g is gravity, y is height in y direction

ME (Mechanical Energy) = Kinetic Energy K + Potential Energy (Ug)

The Attempt at a Solution

Ok, I understand that this is a Conservation of Energy question. I don't know how to go about it.

I need to find energy lost to heat.

U = .5(220J/m^2)(.05m)^2
= 0.275 Joules <--Spring potential energy

At it's highest point...Kinetic Energy = 0 and Potential Energy is at its greatest.

Ug= mgy
= (.015kg)(9.81m/s^2)(1.02m)
= .15J

_______

This is where I'm lost, would anybody mind pointing me in the correct direction?

 

[altamashghazi]

Homework Statement

--->What is the energy lost to heat?<---

spring mass = 15g = .015kg
spring constant = 220 J/m^2
spring is compressed 5cm (.05m) then released to achieve maximum height of 102 cm (1.02 m)

Homework Equations

U = .5(k)(x)^2 where U is the potential energy of a spring, k is the spring constant, and x the compression length.

K=.5(m)(v)^2 where K is kinetic energy, m is a mass, and v is velocity

Ug = mgy where Ug is gravitational potential energy, m is a mass, g is gravity, y is height in y direction

ME (Mechanical Energy) = Kinetic Energy K + Potential Energy (Ug)

The Attempt at a Solution

Ok, I understand that this is a Conservation of Energy question. I don't know how to go about it.

I need to find energy lost to heat.

U = .5(220J/m^2)(.05m)^2
= 0.275 Joules <--Spring potential energy

At it's highest point...Kinetic Energy = 0 and Potential Energy is at its greatest.

Ug= mgy
= (.015kg)(9.81m/s^2)(1.02m)
= .15J

_______

This is where I'm lost, would anybody mind pointing me in the correct direction?

as mechanical energy is conserved. so no energy is lost as heat.

 

[AddversitY]

Heat is counted as energy...

 

[cepheid]

In this problem, are you saying that the compressed spring, after being released, *jumps into the air* and reaches a height of 1.02 m?

If so, then you basically have the answer. If mechanical energy had been conserved, then all of the initial elastic potential energy stored in the spring ought to have been converted into gravitational potential energy when the spring reached its max height.

However, the gravitational potential energy at max height is clearly less than the initial elastic potential energy that was stored.

So the difference must have been dissipated as heat.

 

[AddversitY]

In this problem, are you saying that the compressed spring, after being released, *jumps into the air* and reaches a height of 1.02 m?

If so, then you basically have the answer. If mechanical energy had been conserved, then all of the initial elastic potential energy stored in the spring ought to have been converted into gravitational potential energy when the spring reached its max height.

However, the gravitational potential energy at max height is clearly less than the initial elastic potential energy that was stored.

So the difference must have been dissipated as heat.

That easy!? Haha, thank you!