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    An artificial satellite orbiting the earth in very thin atmosphere loses its energy gradually due to dissipation against atmospheric resistance however small. Why then does its speed increase progressively as it comes closer and closer to the earth?

    For a satellite orbiting the earth, the necessary centripetal force is applied by gravitational pull.

    That is, 



     

    Retarding torque is applied by the air friction. Hence, there is a decrease in the angular momentum. Therefore, the speed increases.

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    Answer

    The potential energy function for a particle executing linear simple harmonic motion is given by V(x) =kx2/2, where k is the force constant of the oscillator. For k = 0.5 N m-1, the graph of V(x) versus x is shown in Fig. 6.12. Show that a particle of total energy 1 J moving under this potential must ‘turn back’ when it reaches x = ± 2 m.

    Here,   space space straight V left parenthesis straight x right parenthesis space equals space 1 half kx squared
    where              space space space space straight k equals 1 half straight N divided by straight m
                    Here,   where                                   ?
                 Total energy of particle E = 1J
          Since at extreme position total energy is potential energy,
    ∴                space space space space space space straight V equals 1 half kx squared equals 1 straight J
    or                   straight x equals plus-or-minus square root of 2 over straight k end root equals plus-or-minus square root of 4
    or                   <pre>uncaught exception: <b>mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied</b><br /><br />in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56<br />#0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>
    Hence the results.



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    Answer carefully, with reasons:
    In an elastic collision of two billiard balls, is the total kinetic energy conserved during the short time of collision of the balls (i.e. when they are in contact)?
    No, kinetic energy during the short time of collision of balls is converted into potential energy.
    212 Views
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    The casing of a rocket in flight burns up due to friction. At whose expense is the heat energy required for burning obtained? The rocket or the atmosphere?

    In case of rocket, heat energy required for burning is at the cost kinetic energy of rocket.

    Due to air friction the kinetic energy is converted into heat energy which burns up the rocket.
    184 Views
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    Answer carefully, with reasons:
    Is the total linear momentum conserved during the short time of an elastic collision of two balls?
    Yes, because during the collision there is no external force on the colliding bodies. Hence, according to the law of conservation of linear momentum, the total linear momentum of the system will remain conserved.
    187 Views
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