Need help on a energy question: Hockey puck sliding across the ice

[sky]

Homework Statement

A 0.18 kg hokey puck is placed against a horizontal spring compressing it 15cm. The spring has a spring constant k = 37 and shoots the puck sideways along the ice. If the friction force between the puck and ice is 1.77N how far will the puck travel after leaving the spring before coming to a stop?

Relevant Equations

Ein = Eout
Uspring = Wspring
(1/2)kx^2 = Ffriction * x

I first attempted to do Ein = Eloss + Eout because the equation had friction in it but in the answer key they set it as the energy was conserved by doing Ein = Eout, why is it conserved when the puck comes to a stop which means energy was lost? I thought the equation should have been Uspring = Wspring + Ffriction because energy wasn't conserved.

 

[PeroK]

Homework Statement: A 0.18 kg hokey puck is placed against a horizontal spring compressing it 15cm. The spring has a spring constant k = 37 and shoots the puck sideways along the ice. If the friction force between the puck and ice is 1.77N how far will the puck travel after leaving the spring before coming to a stop?
Relevant Equations: Ein = Eout
Uspring = Wspring
(1/2)kx^2 = Ffriction * x

I first attempted to do Ein = Eloss + Eout because the equation had friction in it but in the answer key they set it as the energy was conserved by doing Ein = Eout, why is it conserved when the puck comes to a stop which means energy was lost? I thought the equation should have been Uspring = Wspring + Ffriction because energy wasn't conserved.

Please show your calculation. Mechanical energy is not conserved, so you must be misunderstanding the answer key.

 

[sky]

Here are the files (white is answer key):

 

[sky]

Please show your calculation. Mechanical energy is not conserved, so you must be misunderstanding the answer key.

I don't know why the images didn't load the first time but hopefully you can see this:

 

[PeroK]

In your solution, you have a force of 1.77 (N) in the middle of an energy equation!

 

[PeroK]

The answer keys says "use energy to solve". This does not mean that the mechanical energy of the puck is conserved.

 

[sky]

The answer keys says "use energy to solve". This does not mean that the mechanical energy of the puck is conserved.

By setting Ein to Eout and making the equation Us = Wf why doesn't that imply conservation of energy? I always thought you had to include an E loss to the equation as well to show that the mechanical energy wasn't conserved. Where did the Eloss go in this case?

 

[PeroK]

Where did the Eloss go in this case?

Mechanical energy was lost to friction.

You perhaps need to learn the difference between conservation of energy and conservation of mechanical energy. Total energy is always conserved.

 

[sky]

Ah that makes sense, thank you!

 

[PeroK]

Note that at the start all the energy is in the elastic PE of the spring. And at the end all that energy has been lost to friction. So, in terms of magnitudes, these two must be equal.