- #1

MigMRF

- 15

- 0

- Homework Statement
- A box of mass m is placed on a treadmill. The box is connected to a stationary wall to the left via. a sping. The dynamic coeffecient of friction between the box and the treadmill is mu_k and the sping constant is k. The treadmill moves to the right. How far will it stretch the spring (assuming it is unstreched before we start)

- Relevant Equations
- Newtons laws, Energy conservation

First i show the sketch of the setup:

My first attempt was just to balance out the forces on the box. On the sketch below i have shown the situation where the spring is stretched distance L.

In this situation we get the equations:

Which when solved leads to

All good. I then looked at the proposed solution. Here they instead looked at the conservation of energy, saying that the work done by the friction should equal the stored potential energy of the spring:

Which then leads to:

I can't really see why the two methods do not yield the same result and why my solution is incorrect. Any suggestions?

My first attempt was just to balance out the forces on the box. On the sketch below i have shown the situation where the spring is stretched distance L.

In this situation we get the equations:

Which when solved leads to

All good. I then looked at the proposed solution. Here they instead looked at the conservation of energy, saying that the work done by the friction should equal the stored potential energy of the spring:

Which then leads to:

I can't really see why the two methods do not yield the same result and why my solution is incorrect. Any suggestions?