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: Potential elastic energy problem in an incline

  1. Oct 19, 2005 #1
    Question
    A [tex]20.0[/tex] kg package is released on a [tex]50 ^\circ[/tex] incline, [tex]4.50 m[/tex] from a long spring with force constant [tex]150[/tex] N/m that is attached at the bottom of the incline. The block hits the spring, compresses the spring, and finally bounds back. The coefficient of kinetic friction between the package and the incline is [tex]\mu_k = .20[/tex]. The mass of the spring is negligible

    1. Calculate the maximum compression of the spring by the block.

    2. How far does the block rebound back along the incline?

    For the first part, I used work done by nonconservative force (W_nc) = [tex]E_f - E_i[/tex].

    This translates into [tex]-f_k(d+x) = (1/2)(k)(x^2) - (mg)(d+x)(sin(\Theta))[/tex].
    Plugging in known values, noting that x is the unknown results in: [tex]-(.20)(20.0)(9.80)(cos(50 ^\circ)(4.50 + x)=(1/2)(150)(x^2) - (20)(9.80)(4.50+x)(sin(50 ^\circ)[/tex].

    Evaluating, [tex]-25.2(4.5+x)=75x^2 - 150(4.5+x)[/tex]
    [tex]0=75x^2 - 124.8(4.5+x)[/tex]
    [tex]x_1 = 3.69[/tex] m.

    Is this procedure correct?

    2. [tex]K_1 + U_1 + W_n = K_2 + U_2[/tex]
    [tex]W_n=U_2 - U_1[/tex].
    [tex]-25.2x = (20.0)(9.80)(xsin(50 ^\circ) - (1/2)(150)(3.69)^2[/tex]
    [tex]-25.2x=150x - 1021[/tex]
    [tex]1021=175.2x[/tex]
    [tex]x=5.83[/tex] m

    Is this procedure correct?
     
    Last edited: Oct 19, 2005
  2. jcsd
  3. Oct 19, 2005 #2
    Both seem fine to me!
     
  4. Oct 20, 2005 #3
    Thanks!

    I checked today and they were correct.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook




Loading...
Similar Threads for Potential elastic energy Date
Elastic Potential Energy Jun 18, 2017
Elastic and gravitational potential energy Nov 15, 2016
Motion with elastic potential energy and other forces May 30, 2016
[Mechanics] Tension in bungee jumping Apr 24, 2016