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!

Calculating the acceleration and kinetic energy of a bucket in a pulley system

  1. Nov 12, 2009 #1
    1. The problem statement, all variables and given/known data

    A well pulley is constructed from wooden cylinder with a mass of 5 kg and a radius of 10 cm and a light handle. The bucket filled with water is hanging on the rope coiled to the cylinder has a mass of 7 kg.
    - With how much acceleration does the bucket move if the handle breaks; the pulley is spinning with no friction?
    - How much is the kinetic energy of the bucket after it falls for 1 m?

    2. Relevant equations

    F=ma
    KE= mv²/2
    PE= mgh

    3. The attempt at a solution

    First part: With how much acceleration does the bucket move if the handle breaks; the pulley is spinning with no friction?

    m(1)= 5 kg, m(2)= 7 kg, g= 10 m/s²

    (m(1) + m(2))*a= m(2)g
    a= m(2)g / (m(1) + m(2)
    a= 5.8 m/s²

    ARE MY CALCULATIONS CORRECT?

    Second part: How much is the kinetic energy of the bucket after it falls for 1 m?

    KE= PE
    mv²/2= mgh
    v= sqrt(2gh)
    v= 4.47 m/s

    KE= mv²/2= 69.9 J

    Are my calculations correct?

    Thank you helping!
     
  2. jcsd
  3. Nov 12, 2009 #2

    rl.bhat

    User Avatar
    Homework Helper

    The equation for acceleration is wrong. Check it.
     
  4. Nov 13, 2009 #3
    Do I have to take into the consideration inertia and the torque of the pulley (I know the radius and the mass of the pulley) and develop it from there?:confused:

    What about the second part? Is it correct?

    Thank you for helping!
     
    Last edited: Nov 13, 2009
  5. Nov 13, 2009 #4
    There is torque acting on the cylinder because of the tension in the rope.
     
  6. Nov 13, 2009 #5
    Please, can you give a hint how to apply the torque into the calculations? I'm really confused!?

    I tried it like this:

    For the bucket:
    m(1)a= m(1)g - T

    For the pulley:
    Iα= Tr

    I= 1/2m(2)r² and α= a/r

    1/2m(2)r²*a/r = Tr → 1/2m(2)r= T

    For the system:
    1/2m(2)a + m(1)a = m(1)g -T + T
    a= m(1)g / (m(1) + 1/2m(2))
    a= 7 m/s²

    I really need help with solving this problem. Thank you for helping!
     
  7. Nov 13, 2009 #6
    Yes.

    Now for the second part you just replace g with your new a.
     
  8. Nov 13, 2009 #7
    :biggrin: Thank you very much!:biggrin:

    So the correct answer is: 49 J
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Calculating the acceleration and kinetic energy of a bucket in a pulley system
Loading...