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Which has a greater Gravitational Energy?

  1. Apr 24, 2014 #1
    1. Imagine two objects, A and B, answer the questions that follow based on the conditions given.

    A= 500g, at 2m, B=1.0kg, at 1m

    a. Which has a greater Gravitational Energy? Why

    b. If they are both dropped, which would have a greater velocity impact? Why?

    c. If both are dropped onto a spring, which will store the greater energy?

    d. Which will cause the spring to compress more?




    2. Eg = mgh



    3. a. A=(.5kg)(9.8 N/kg)(2m) = 9.8 J

    B=(1kg)(9.8 N/kg)(1m) = 9.8 J

    b. They would both have the same velocity because they both have the same amount of gravitational energy.

    c. They will both store the same amount of energy.

    d. Both springs would compress the same.


    Hello everyone, I believe I did my calculations correct for part a, but I'm not positive about my answers on parts b, c, and d. Can someone tell me if I did this incorrectly? Thanks!
     
  2. jcsd
  3. Apr 24, 2014 #2

    Andrew Mason

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    Your answer to a., I assume, is that they both have the same gravitational energy. You should state that. c. and d. are correct.

    Your answer to b. is not correct. They both have the same kinetic energy just before impact. What is the expression for KE? (hint: it is in terms of mass and velocity). Work out your answer for v from that.

    AM
     
  4. Apr 24, 2014 #3
    So what you're saying is to use Ek=1/2mV^2? I do not understand how I am supposed to solve for EK (Kinetic Energy). If I want to find Ek, then I am missing the velocity component in order to figure out Ek. If I'm solving for velocity, then I'm missing the Ek piece. So I do not understand.


    And how do you know that they have the same kinetic energy?
     
  5. Apr 24, 2014 #4

    Andrew Mason

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    Energy is conserved. There are only two forms of energy here: gravitational potential energy and kinetic energy. What a body loses in gravitational potential energy it gains in kinetic energy. You can also think of gravity as doing work on the body so the work done (Force x distance = (mg) x h) must equal the change in kinetic energy. So if it starts with 0 velocity (0 KE), you can determine its kinetic energy by: -ΔPE = -mgΔh = ΔKE = .5mv2 - 0. You can work out the speed, v, from that.

    AM
     
    Last edited: Apr 24, 2014
  6. Apr 24, 2014 #5
    I still do not understand...If PE (Gravitational Energy) and KE are equal to eachother, then that means KE will equal 9.8J. Considering that both objects have 9.8J as their gravitational energy, then if I plug 9.8 J into KE, both objects come out to be 4.4 m/s. What am I missing?
     
  7. Apr 24, 2014 #6
    Well, if you look at the equations a little more closely, you'll notice something peculiar.

    Say you are given two different masses at two different heights like you are in this situation. Without using any numbers, you can see why these two things will not be going the same speed.

    So, the maximum kinetic energy for both of these objects at different heights is basically when the height is zero, because all of your energy will then be coming from the kinetic energy alone.

    Setting up your equations for two different objects of two different masses, you'll get:

    $$m_{1}gh_{1} = 1/2m_{1}v^2$$
    $$m_{2}gh_{2} = 1/2m_{2}v^2$$

    Without plugging in any numbers, you might notice that your masses in both cases just end up cancelling out. So, what does this tell you? It tells you that ending the velocity after falling a certain distance is completely independent of the mass of the object, and has EVERYTHING to do with the specific height.

    So, in your case,
    $$v_{1} = \sqrt{2gh_{1}}$$ and
    $$v_{2} = \sqrt{2gh_{2}}$$


    This makes sense from a real world standpoint. If you were to drop two balls from the same height, but they both had drastically different masses, they would hit the ground at the same time if air resistance is not taken into account. In your result, it would make no sense
     
  8. Apr 24, 2014 #7
    So if I plug numbers into those equations, Object A would be 6.26 m/s and Object B would be 4.43 m/s...making Object A with the higher velocity?
     
  9. Apr 25, 2014 #8

    haruspex

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    Yes.
     
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