# Homework Help: Block can slide along a table where the coefficient of friction

1. Dec 12, 2004

### jbot2222

A 198g wood block is firmly attached to a very light horizontal spring, as shown in the figure below.

The block can slide along a table where the coefficient of friction is 0.287. A force of 23.1 N compresses the spring 17.7 cm. If the spring is released from this position, how far beyond its equilibrium position will it stretch on its first swing

the way i approached this:

1/2kx^2 - Ukmgx = 1/2mv^2 = UkmgD
where D is the distance it travels after acquiring kinetic energy.

however, there is something wrong with this approach and i cannot figure out what it is. please help!

2. Dec 12, 2004

### Andrew Mason

You are omitting the spring potential energy when the mass has extended to the distance D past the equilibrium position. This is provided by the original spring potential which also provides the work done against friction.

$$\frac{1}{2}k(x^2-D^2) =\mu_kmg(x+D)$$

AM