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Kinetic Energy and Total Mechanical Energy

  1. Jul 23, 2009 #1
    1. The problem statement, all variables and given/known data

    A 1.90 kg rock is released from rest at the surface of a pond 1.00 m deep. As the rock falls, a constant upward force of 3.80 N is exerted on it by water resistance. Let y=0 be the bottom of the pond.

    a) what is the rock's kinetic energy at the surface and at the bottom of the pond (after sinking 1m)?
    b) what is the total mechanical energy of the system at the surface and at the bottom of the pond (after sinking 1m)?

    2. Relevant equations

    mgh
    k = 1/2mv^2?

    3. The attempt at a solution

    a) So I know the initial kinetic energy is obviously 0, that part I got correct. But the second part is tricky because I can't seem to apply 1/2mv^2 because I can't figure out how to find its velocity.

    b) I got the first part correct on this one also, the total mechanical energy at the surface is just mgh which equals 18.62 but I can't find out the total mechanical energy of the system when the rocks sinks to the bottom without knowing the rocks kinetic energy at that point.

    I hope that is clear enough for someone to tackle ;)
     
  2. jcsd
  3. Jul 23, 2009 #2

    jgens

    User Avatar
    Gold Member

    Write out an energy balance equation. Initially you have only potential energy. After releasing the rock that energy goes into kinetic energy and work done by the drag force from the water. Using this, you can solve for the kinetic energy.
     
  4. Jul 24, 2009 #3
    You need to use the 'Work-Energy Theorem' (which is the formal way of saying what jgens just said).

    Total Energy is a lot like money: you can save it (conserve it) or spend is (use it to do work). You can think of the work done by any non-conservative force (like friction, or in this case, water resistance) as a 'tax' you have to pay. Just like when you go into McDonald's and order something off the 'Dollar menu'. You can't really buy anything if you only have one dollar - you must start with enough to buy the food PLUS pay the tax.

    In your problem, you start with a certain amount of energy (E1). You are right in assuming this E1 is made up of some combination of Kinetic Energy (KE1) and Potential Energy (PE1). Use this energy just like money at the McDonald's - some will go into 'E2' (the potential plus kinetic energy at the pond's bottom), and some will be used to pay the 'tax' ('lost' to the work F*dr done by water resistance).

    The Work-Energy Theorem says:

    E1 = E2 + 'Tax', where the tax you pay to friction in this case is - Fresistive * r

    Now substitute KE1 + PE1 for E1, and KE2 + PE2 for E2, and you should be able to solve for KE2. From there, it's just a simple substitution to solve for v2, using the equations you've listed for PE and KE.
     
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