# Kinematics - spring + friction

1. Jan 10, 2010

### nahanksh

1. The problem statement, all variables and given/known data
http://online.physics.uiuc.edu/cgi/courses/shell/common/showme.pl?courses/phys211/oldexams/exam2/fa09/fig8.gif [Broken]
A small block having a mass of 2 kg is in contact with an ideal spring of relaxed length 1 m and spring constant k = 100 N/m . The spring is compressed to a length of 0.5 m. The block is released from rest at x = 0.5 m. At x = 1 m the mass leaves the spring and comes to rest at x = 2 m. Throughout its entire motion the block slides on a rough surface with a coefficient of kinetic friction μk .

Q1) The maximum acceleration of the block occurs the instant the block begins to move.
True/False

Q2) What is the coefficient of kinetic friction of the surface?

2. Relevant equations

3. The attempt at a solution

For the first question, i thought the acceleration is at maximum when the spring is about to move(at x=0.5m)... 'cause i thought the friction force will be exerted after this point reducing the acceleration...
What's wrong in my thought?

And, for the second question, i tried to get the velocity when x=1m using energy-conservation theorem, and i got m*v2 = k*x2 and hence v = 3.53

Now i used the constant acceleration formula, the final velocity is zero, and initial v = 3.53,
a= $$\mu$$mg/2 and the displacement = 1.

But then i got the answer as 0.62 which is wrong....

What's wrong in here?

I think its related to hooks law ( F =-kx )