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A box slides over friction and hits a spring

0 votes
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I've been struggling with these problems for days. 

A block is released from point A on a track 
ABCD as shown in the figure. Point A is 
higher than points B, C, and D. The track is 
frictionless except for a portion BC which has 
a coefficient of friction µ. The block travels 
down the track and hits the spring with spring 
constant k. 
The acceleration of gravity is 9.8 m/s^2. 

Here's the picture: 
http://4gp.tw/b029/1394047113958.jpg 

1. If the spring compresses 6 cm, find the 
coefficient of friction µ. 

2.For this value of µ, to what height (h′) will the 
block rise when it returns to point E ? 
Answer in units of m 

3.Suppose µ is changed. After releasing the 
mass m from point A, the mass travels over 
the rough portion of the track BC, bounces 
off the spring, and travels a distance 2.9 m 
part way back across the rough portion of the 
track to stop at point F . 
Under these conditions, what is the value 
of µ? 

I know I'm supposed to use (initial potential energy + initial kinetic energy + work done by friction = final potential energy + final kinetic energy) to solve them, but I'm not sure how to manipulate the equation. Thank you!

asked Mar 5, 2014 in Intro College Physics by Park3r20 (120 points)

1 Answer

0 votes

We do want to compare initial and final energies as you suggested above. 

To do so, we can note that in each of the situations mentioned (1, 2, and 3) the initial and final kinetic energies are zero \(U_i - W_{friction} = U_f \). Also, the initial potential energy is the same in each case: \( U_i = mgh \) and the final total energy will be all potential energy. The work done by friction will be \( W_{friction} = \mu N d \)

  1. \( mgh - \mu N d = \frac{1}{2}m \Delta x^2 \)
    Here, we are looking for \( \mu \) being given all of the other variables (m, g, h, d, and x).
  2. \( mgh - 2 \mu N d = mgh' \) 
    Here we are looking for h' being given all of the other variables.
  3. \( mgh - \mu N (d+x) = 0 \)
    Here we are looking for x.

 

answered Mar 10, 2014 by jcf1559 (2,140 points)
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