1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Homework Problem about the Work-Energy Theorem

  1. Nov 22, 2007 #1
    [SOLVED] Homework Problem about the Work-Energy Theorem

    Please help! This is my first year of taking physics and Im really confused....

    A puck on a shuffleboard decreases in speed from 1.0 m/s to .20 m/s while traveling 4.0 m. What is the coeffecient of kinetic friction between the puck and the board?

    I think that the equations we have to use to solve this would be....

    w= [tex]\frac{1}{2}[/tex]m[tex]V_{1}^{2}[/tex]-[tex]\frac{1}{2}[/tex]m[tex]V_{o}^{2}[/tex]



    w = [tex]\frac{1}{2}[/tex]k[tex]d^{2}[/tex]

    k= [tex]\frac{1}{2}[/tex]m[tex]V^{2}[/tex]

    First : I was thinking about using the equation w= [tex]\frac{1}{2}[/tex]m[tex]V_{1}^{2}[/tex]-[tex]\frac{1}{2}[/tex]m[tex]V_{o}^{2}[/tex] to solve for work, then substitute the work value in for w=Fd then somehow put it in the equation [tex]F_{f}[/tex]=[tex]\mu[/tex][tex]F_{N}[/tex] . Then I got extremely confused...and I realized that I don't have the mass of the puck to put into the first equation.

    Second try: So, I decided to use w = [tex]\frac{1}{2}[/tex]k[tex]d^{2}[/tex] but in order to find out the k (spring constant) value, I need to use the equation k= [tex]\frac{1}{2}[/tex]m[tex]V^{2}[/tex]...which again, I dont have the mass for.

    Third try...I was going to use the equation F=kd to figure out F and then substitute it in for w in w=Fd and then solve for m in w= [tex]\frac{1}{2}[/tex]m[tex]V_{1}^{2}[/tex]-[tex]\frac{1}{2}[/tex]m[tex]V_{o}^{2}[/tex]
    . But I don't have the k again!!

    And now, I'm out of ideas...please help me...thank you! :) I hope this question makes sense....and my tries...if not, let me know and I'll try to fix them up! Thanks again!
  2. jcsd
  3. Nov 22, 2007 #2


    User Avatar
    Homework Helper

    Find the retardation of the body by using kinematic equatuon. Retarding force = m*a and normal reaction = mg. Plug it in the equation to get coefficient kinetic friction
  4. Nov 22, 2007 #3
    Try this

    Force of friction is given by:

    [tex]F_{f}[/tex] = [tex]\mu[/tex] N [1]

    Solving for [tex]\mu[/tex] we have

    [tex]\mu[/tex] = [tex]\frac{F_{f}}{N}[/tex] [2]

    The normal force N is given by:

    N = mg [3]

    Substituting [3] into [2] we have:

    [tex]\mu[/tex] = [tex]\frac{F_{f}}{mg}[/tex] [4]

    The force of friction is also defined by:

    [tex]F_{f}[/tex] = ma [5]

    where a is the deceleration and m is the mass of the puck. We also know given a distance and a constant acceleration (or deceleration in this case) that the acceleration is equal to the following (see: http://library.thinkquest.org/10796/ch3/ch3.htm ):

    a = [tex]\frac{(V_{f}^{2} - V_{i}^{2})}{2d}[/tex] [6]

    Substituting [6] into [5] we have:

    [tex]F_{f}[/tex] = [tex]\frac{m(V_{f}^{2} - V_{i}^{2})}{2d}[/tex] [7]

    and finally substituting [7] into [4] we have:

    [tex]\mu[/tex] = [tex]\frac{(V_{f}^{2} - V_{i}^{2})}{2dg}[/tex]
    Last edited by a moderator: Apr 23, 2017
  5. Nov 23, 2007 #4
    photonsquared, I used your method to solve the problem....it made sense to me and this is the answer that I got [tex]\mu_{k}[/tex]= .0122. Is there anyway you could tell me if this is correct? Thank you very much for your help! :smile:
  6. Nov 23, 2007 #5
    That is the same value I calculate. The reason you don't need the mass of the puck is because the masses cancel out when you substitute eqn 7 into 4. Hope this helps.
  7. Nov 23, 2007 #6
    Ok thank you very much photonsquared! :) Thanks rl.bhat for your response!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook