# Spring - Kinematics

1. Jan 11, 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*v^2 = k*x^2 and hence v = 3.53

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

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

What's wrong in here?

Last edited by a moderator: May 4, 2017
2. Jan 11, 2010

### Fightfish

The spring still exerts a force on the block during the 0.5m to 1m period and thus continues to supply it with energy.
Your energy conservation equation is wrong because it fails to account for energy loss due to friction during the initial period.

3. Jan 11, 2010

### jegues

Spring energy = Kinetic energy of uncompressed spring + change in thermal energy