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Another Energy Efficiency Equation Problem

  1. Nov 4, 2013 #1
    1. The problem statement, all variables and given/known data

    A golf club with 65 J of kinetic energy strikes a stationary golf ball with a mass of 46 g. The energy transfer is only 20% efficient. Calculate the initial speed of the golf ball.

    2. Relevant equations

    efficiency = E out/E in x 100%

    3. The attempt at a solution

    I found E in by: E in = E out/efficiency x 100% = 65 J/20 x 100% = 325 J
    But how could I find initial speed?
    I now have E out= 65 J, E in= 325 J, m= 46 g= 0.046 kg, and efficiency = 20%.
    I'm confused as to how I should tackle most of these efficiency problems...
     
  2. jcsd
  3. Nov 4, 2013 #2

    cepheid

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    There's a bunch of things wrong with this. First of all, Ein is 65 J. This is the input, because it's the energy that the golf club has before transferring some energy to the ball. The output is the energy that remains after the process has taken place. In other words, it's the energy that the ball has after being struck. Since the process is only 20% efficient, 80% of the 65 J are gone, and the ball only ends up with 20%.

    65 J * 0.2 = 13 J

    If you are wondering how I got that: Eout = Ein * efficiency.

    Now you know that the ball has 13 J of kinetic energy. So, what speed must it be going at? Hint: how does kinetic energy depend on speed? What is the mathematical expression for kinetic energy?
     
  4. Nov 4, 2013 #3

    Simon Bridge

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    You are told the Ein in the problem statement.

    cephied has all-but done the problem for you - I'll tackle the meta-question:
    You basically work this sort of problem backwards.
    Start with what you need to find. You know it's an energy problem, so what sort of energy do you need to know in order to find what you need ... then: where does it get that energy from?[1]

    You need to find the speed of the golf ball just after it has been struck.

    If you knew the KE of the golf ball, you could do this right?

    So where does the ball get it's KE from?

    So how would you find out the initial KE of the ball from the information provided?

    You've been doing conservation of energy problems before - like a block slides down a slope from height h, what is it's speed at the bottom of the slope? In those sorts of problems you always start with some statement about the initial energy (in this case, gPE = mgh) and then you'd assume all the energy goes into kinetic energy.

    In the efficiency problems, not all the energy gets transferred.
    That's all there is to it.[2]
    -------------------------------------------

    [1] Conversely, you may want to find some initial energy - in which case you ask "where does it's energy go."
    All conservation of energy problems are about what happens to the energy?

    [2] Oh - and getting comfy with percentages.
    "efficiency" e is a fraction: 0<e<1
    If the efficiency is quoted a p%, then e=p/100.
     
    Last edited: Nov 4, 2013
  5. Nov 4, 2013 #4
    The efficiency is basically how much of the energy is lost to other means like friction and heat, and how much energy is actually used to accomplish this goal.
     
  6. Nov 4, 2013 #5
    Ek = 1/2mv^2; so v = √2Ek/m
    Ok, I got the answer of 24m/s; Thank you so much!

    Helped my understanding of this topic by a LOT!!! Thank you all! :)
     
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