{"id":2027,"date":"2020-12-18T09:44:21","date_gmt":"2020-12-18T04:14:21","guid":{"rendered":"https:\/\/cbselibrary.com\/?p=2027"},"modified":"2020-12-18T11:39:28","modified_gmt":"2020-12-18T06:09:28","slug":"potential-energy","status":"publish","type":"post","link":"https:\/\/cbselibrary.com\/potential-energy\/","title":{"rendered":"How Do You Find The Potential Energy"},"content":{"rendered":"
Potential Energy:<\/strong>\u00a0Thus the energy<\/a> possessed by a body by virtue of its position or change in shape is known as potential energy. It is obvious that a body may possess energy even when it is not in motion<\/a>.<\/p>\n Expression for Potential Energy: <\/strong><\/p>\n Mechanical Energy of a Freely Falling Body:<\/strong> Example 1.\u00a0<\/strong>What will be the potential energy of a body of mass 2 kg kept at a height of 10 m ? Example 2.\u00a0<\/strong>In lifting a mass of 25 kg to a certain height 1250 J energy is utilized. Calculate to what height it has been lifted ? (Take g = 10 m\/s2<\/sup>) Example 3.<\/strong> During a physical exercise, Samad, with a mass of 75 kg, is lifted to a height of 2.1 m. Idris, with a mass of 46 kg, is lifted to a height of 3.2 m. Example 4.<\/strong> A lift with its passengers has a total mass of 1350 kg. Calculate the gravitational potential energy gained by the lift by moving upwards to a height of 25 m. [g = 9.8 m s-2<\/sup>J] What Is\u00a0Potential Energy Potential Energy:\u00a0Thus the energy possessed by a body by virtue of its position or change in shape is known as potential energy. It is obvious that a body may possess energy even when it is not in motion. Expression for Potential Energy: Gravitational potential energy is the energy of an object because … Read more<\/a><\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[404],"tags":[759,797,795,785,758],"yoast_head":"\n\n
\n<\/li>\n
\nDisplacement, s = h
\nWork done, W = F x s = mgh<\/li>\n
\nEp\u00a0<\/sub>= mgh<\/li>\n<\/ol>\nInter conversion of Potential Energy and Kinetic Energy<\/h3>\n
\nAssume, a body of mass m is at rest at a height h from the earth’s surface, as it starts falling, its velocity after travelling a distance x (point B) becomes v and its velocity on the earth’s surface is v’.
\nMechanical energy of the body at point A:
\nEA<\/sub>\u00a0= Kinetic energy + Potential energy
\nEA<\/sub>\u00a0= m(0)2<\/sup> + mgh
\nEA<\/sub>\u00a0= mgh \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u2026\u2026\u2026 (i)
\nMechanical energy of the body at point B:
\nEB<\/sub> = \\(\\frac { 1 }{ 2 }\\) mv2<\/sup> + mg (h \u2013 x) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u2026\u2026..(ii)
\n
\nMechanical energy of the body at point C:
\nEC\u00a0<\/sub> = \\(\\frac { 1 }{ 2 }\\) m (v’)2<\/sup> + mg \u00d7 0
\nEC<\/sub> = \\(\\frac { 1 }{ 2 }\\) m (v’)2<\/sup> \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u2026\u2026..(iv)
\nUse: EA<\/sub>\u00a0= EB<\/sub> = EC<\/sub>
\nHence, when a body falls freely, its mechanical energy will be constant. That means, the total energy of the body during free fall, remains constant at all positions. However, the form of energy keeps on changing at all points during the motion.
\n<\/p>\nPotential Energy<\/strong> Example Problems With Solutions<\/strong><\/h2>\n
\nSolution: \u00a0\u00a0<\/strong>\u00a0The potential energy is given by
\nU = mgh
\nHere, m = 2 kg; g = 10 m\/s2<\/sup>; h = 10 m
\n\u2234 U = 2 \u00d7 10 \u00d7 10 = 200 J<\/p>\n
\nSolution: \u00a0\u00a0<\/strong>In lifting a mass through a height h the work done is given by
\nU = mgh
\nHere, U = 1250 J; g = 10 m\/s2<\/sup>; m = 25 kg
\n\u2234 1250 = 25 \u00d7 10 \u00d7 h
\nor h = 5 m<\/p>\n
\n
\nWhich of the two boys has gained more gravitational potential energy? [g = 9.8 m s-2<\/sup>]
\nSolution:<\/strong>
\nFor Samad;
\nGravitational potential energy,
\nEp\u00a0<\/sub>= 75 x 9.8 x 2.1
\n= 1543.5 J
\nFor Idris;
\nGravitational potential energy,
\nEp<\/sub>\u00a0= 46 x 9.8 x 3.2 P
\n= 1442.6 J
\nTherefore, Samad has gained more gravitational potential energy.<\/p>\n
\nSolution:<\/strong>
\nMass, m = 1350 kg; Height, h = 25 m Therefore,
\nGravitational potential energy,
\nEp<\/sub>\u00a0= mgh
\n= 1350 x 9.8 x 25 = 330 750 J<\/p>\n","protected":false},"excerpt":{"rendered":"