Physics Help Forum Kinetic/Potential Energies vs Distance --> Help needed please!

 Energy and Work Energy and Work Physics Help Forum

 Jun 16th 2009, 01:19 PM #1 Senior Member   Join Date: Mar 2009 Posts: 129 Kinetic/Potential Energies vs Distance --> Help needed please! PHYSICS 534 Can someone please explain Exam 2006 #10 to me? Any help would be greatly appreciated! Thanks in advance!
 Jun 16th 2009, 02:44 PM #2 Senior Member   Join Date: May 2009 Location: Mumbai,India Posts: 102 Answer is option A Kinetic Energy=1/2mv^2 where v is the velocity of the body at any instant. Now, using the equation of motion, v^2=2ax where x is the distance covered and a is the resultant acceleration of the object down the plane. clearly, KE has linear dependence with x so the graph of KE vs. Distance covered has to be a straight line. Now, PE of the object=mgh where h is the height of the object. we know that, h is proportional to the distance of the object from the ground ie h=k(l-x) where l is the total length of the plane while x is the distance covered k is a constant so PE=kmg(l-x) KE=max so PE is a line with negative slope while KE is a line with positive slope Now, as half of the PE is lost in heat,sound,etc. the value of KE has to be less than the max. value of the PE[its initial value when the object was on top] when the object reaches the ground. hence, A is the most appropriate option. Last edited by Akshay; Jun 16th 2009 at 03:00 PM.
 Jun 16th 2009, 02:58 PM #3 Senior Member   Join Date: Mar 2009 Posts: 129 Yes! Please explain! Last edited by s3a; Jun 16th 2009 at 03:13 PM.
 Jun 16th 2009, 03:45 PM #4 Senior Member   Join Date: Mar 2009 Posts: 129 Ok well I don't know some of the thing you said but from what I've understood: Ek = (1/2)(m)(v^2) and Eg = mgh (Kinetic and Gravitational) So I see how Eg = mgh, mass and gravity is constant while height is a variable and since gravity is negative, it'll make it a decreasing linear function. What I don't understand is how Ek = (1/2)(m)(v^2) is not a quadratic since velocity is what varies and it is a squared variable. The reason why I believe that velocity is the variable is because it is accelerating downwards on the ramp.
 Jun 17th 2009, 12:08 AM #5 Senior Member   Join Date: May 2009 Location: Mumbai,India Posts: 102 Yes, velocity does vary but the question asks the relationship between velocity and distance x because the square of the velocity is a linear function of x we know, that v^2=u^2+2ax since u=0 v^2=2ax hence KE=0.5mv^2=max so KE is an increasing linear function of x. it is the square of the velocity variable which is a linear function of x square of velocity however, is a quadratic function of time Last edited by Akshay; Jun 17th 2009 at 01:30 PM.

 Tags >, distance, energies, kinetic or potential, needed

 Thread Tools Display Modes Linear Mode

 Similar Physics Forum Discussions Thread Thread Starter Forum Replies Last Post Chris2093 Nuclear and Particle Physics 2 Nov 17th 2016 01:51 AM arangu1508 Energy and Work 2 Oct 20th 2015 11:28 AM noddy Energy and Work 5 Jan 3rd 2014 01:21 PM warrior90 Kinematics and Dynamics 2 Sep 18th 2010 08:27 AM s3a Kinematics and Dynamics 1 Mar 1st 2010 10:36 AM