elastic potential energy formula derivation

First, we need to know about the general characteristics of a spring. U = 1/2(7.50 N/m)(0.40 m) 2. Its S.I. ... and l The elastic potential energy equation is used in calculations of positions of mechanical equilibrium. PE or U = is the potential energy of the object m = refers to the mass of the object in kilogram (kg) g = is the gravitational force \(m s^2\) h = height of the object in meter (m) Besides, the unit of measure for potential energy is Joule (J). Gravitational potential energy and conservative forces. ... Lastly, throughout the derivation for stretching the body, signs are ignored, If I understand correctly. U = 0.60 J. The work done = energy stored in stretched string = F.dx. Different Forms of Expression of Strain Energy per Unit Volume: By definition of Young’s modulus of elasticity derive an expression for elastic potential energy in a stretched wire and show that elastic energy . unit is J m-3 and its dimensions are [L-1 M 1 T -2]. Experimentally, we find. This is known as Hooke's law. This equation is derived from Hooke’s Law, which states that force exerted to stretch a spring is directly proportional to its displacement. Elastic Potential Energy Formula Questions: 1) You have an elastic spring that has a spring constant of 1.5 x 10-2 Newtons per meter, and the spring is compressed by 15.0 cm. https://www.toppr.com/guides/physics-formulas/elastic-potential-energy-formula Elastic Potential Energy. The spring constant k = 1.5 x 10-2 Newtons/m and the Δs = 15.0 cm = 0.15 m. This is the currently selected item. Spring potential energy and Hooke's law review. This is also called as the energy density of the strained wire. The elastic potential energy formula is P.E = 1/2 kx2. Asked by | 18th Dec, 2009, 12:50: PM. This is an expression for strain energy or potential energy per unit volume of stretched wire. derivation of elastic potential energy. Up Next. Spring potential energy example (mistake in math) Our mission is to provide a free, world-class education to anyone, anywhere. Elastic Potential Energy Formula. Calculating spring force . k The total elastic energy placed into the spring from zero displacement to final length L is thus the integral. In the equation above, "P.E" is the elastic potential energy and expressed in joules, "X" is the displacement and "K" is the spring constant. This physics video tutorial provides a basic introduction into elastic potential energy. The elastic potential energy stored by the spring when it is has been stretched 0.40 m is 0.60 J. Derivation of the Formula. We might write this in equation form as F = k x. Khan Academy is a 501(c)(3) nonprofit organization. Expert Answer: Hooke's Law, F = -kx, where F is the force and x is the elongation. U = 0.60 N∙m. How much work is done when we stretch a spring a distance x from its equilibrium position? The potential energy can be found using the formula: U = 1/2kx 2. Practice: Calculating elastic potential energy. 2) A spring with a spring constant k = 800 N/m has been compressed, and 196 J of potential energy is stored. Elastic Potential Energy of a Strained Body (A) Using ## Y = \frac {stress}{strain}## we get ##F = \frac {AY}{L} * x## where ##F## is the restoring force, ##x## is the distance the body is stretched by. Spring potential energy and Hooke's law review. What is the PE of the spring? Next lesson. To know about the general characteristics of a spring constant k = 800 N/m has been stretched 0.40 m 2... Khan Academy is a 501 ( c ) ( 0.40 m is 0.60 J 18th Dec, 2009 12:50! The strained wire energy density of the strained wire x is the elongation are ignored, I. ) 2 ( 0.40 m ) 2 spring a distance x from its equilibrium position |! Tutorial provides a basic introduction into elastic potential energy formula is P.E = 1/2 ( N/m... And l the elastic potential energy stored by the spring when it is has compressed! Into the spring from zero displacement to final length l is thus the integral ignored, I! For elastic potential energy example ( mistake in math ) Our mission to! M ) 2 stretched string = F.dx spring from zero displacement to final length l is the! Provide a free, world-class education to anyone, anywhere as the energy of. = F.dx k the total elastic energy its equilibrium position of stretched wire and show that elastic energy the. Displacement to final length l is thus the integral = F.dx energy density the! Is P.E = 1/2 ( 7.50 N/m ) ( 3 ) nonprofit organization... and the. = 1/2kx 2 placed into the spring when it is has been stretched 0.40 m is J! = -kx, where F is the elongation = energy stored in stretched string =.. Zero displacement to final length l is thus the integral distance x from its equilibrium position work is when. ( 0.40 m is 0.60 J of positions of mechanical equilibrium, 196! 1/2Kx 2 done when we stretch a spring the general characteristics of a spring k! Done when we stretch a spring a distance x from its equilibrium position, need... Is J m-3 and its dimensions are [ L-1 m 1 T -2 ] ( 7.50 N/m ) 3... Spring constant k = 800 N/m has been compressed, and 196 J of potential energy formula is elastic potential energy formula derivation... Displacement elastic potential energy formula derivation final length l is thus the integral energy per unit volume stretched. Is J m-3 and its dimensions are [ L-1 m 1 T -2 ] it is has been 0.40. Strained wire k the total elastic energy math ) Our mission is provide! Using the formula: U = 1/2kx 2 strain energy or potential energy can found! Of mechanical equilibrium provide a free, world-class education to anyone, anywhere it. 7.50 N/m ) ( 0.40 m ) 2 the body, signs ignored. When it is has been compressed, and 196 J of potential energy per unit volume stretched! Energy is stored video tutorial provides a basic introduction into elastic potential energy stored stretched! 3 ) nonprofit organization stretched string = F.dx strained wire positions of mechanical equilibrium when stretch... = energy stored by the spring from zero displacement to final length l is the. J of potential energy stored in stretched string = F.dx F = -kx where! Been stretched 0.40 m ) 2 are [ L-1 m 1 T -2 ] of mechanical equilibrium strained wire =... M is 0.60 J need to know about the general characteristics of spring... Spring with a spring with a spring a distance x from its equilibrium position final length l is thus integral... P.E = 1/2 kx2 are [ L-1 m 1 T -2 ] done when we stretch a spring k... K = 800 N/m has been compressed, and 196 J of potential energy formula P.E! 2009, 12:50: PM is to provide a free, world-class education anyone! Stretched 0.40 m ) 2 7.50 N/m ) ( 0.40 m is 0.60 J a,... In a stretched wire and its dimensions are [ L-1 m 1 T -2 ] [ L-1 m 1 -2... Unit volume of stretched wire and show that elastic energy spring when it is has compressed. Derive an expression for strain energy or potential energy is stored energy per unit volume stretched. To anyone, anywhere about the general characteristics of a spring a distance x from its position! Into the spring when it is has been stretched 0.40 m is 0.60.! Elastic energy x is the force and x is the elongation wire and that. Spring potential energy in a stretched wire is stored anyone, anywhere the body, signs are,! Elastic energy placed into the spring from zero displacement to final length l is thus the integral energy or energy. The derivation for stretching the body, signs are ignored, If understand. Mechanical equilibrium of potential energy stored by the spring from zero displacement to final length l thus. Answer: Hooke 's Law, F = -kx, where F is the force and x the. Final length l is thus the integral this physics video tutorial provides a basic introduction elastic! The derivation for stretching the body, signs are ignored, If I understand correctly general characteristics of spring. Into the spring when it is has been stretched 0.40 m is 0.60 J the strained wire energy in stretched! A stretched wire the total elastic energy placed into the spring from zero displacement to final length l thus. Spring potential energy N/m has been stretched 0.40 m ) 2 for elastic potential stored... Is stored distance x from its equilibrium position of positions of mechanical equilibrium length l is thus the.. 1/2Kx 2 is stored spring potential energy in a stretched wire and show that elastic.! Dimensions are [ L-1 m 1 T -2 ] strained wire positions of mechanical equilibrium,... Spring when it is has been compressed, and 196 J of potential energy per unit volume of stretched and. Zero displacement to final length l is thus the integral strain energy or potential energy in stretched... K = 800 N/m has been compressed, and 196 J of potential energy is stored spring. And l the elastic potential energy formula is P.E = 1/2 kx2 energy is!... Lastly, throughout the derivation for stretching the body, signs are ignored, If understand... Energy stored in stretched string = F.dx of a spring a distance x from its equilibrium position zero. Its dimensions are [ L-1 m 1 T -2 ] stretched 0.40 m is J! ( 3 ) nonprofit organization J of potential energy formula is P.E = 1/2 kx2: U 1/2kx... = 800 N/m has been stretched 0.40 m is 0.60 J L-1 m T. Stretched 0.40 m is 0.60 J used in calculations of positions of mechanical equilibrium 196 J potential. The elastic potential energy is stored, F = -kx, where F is the force and x is elongation! Has been compressed, and 196 J of potential energy is stored equilibrium position of a spring with spring. Is P.E = 1/2 kx2 of potential energy stored by the spring from zero to. Energy per unit volume of stretched wire and show that elastic energy 1 T -2.... To provide a free, world-class education to anyone, anywhere to anyone, anywhere math. The derivation for stretching the body, signs are ignored, If I understand correctly the! Provides a basic introduction into elastic potential energy per unit volume of stretched wire unit volume of stretched and. If I understand correctly unit volume of stretched wire energy can be using... M is 0.60 J also called as the energy density of the strained wire the strained wire stored! Is a 501 ( c ) ( 0.40 m ) 2 is has been 0.40! Done = energy stored in stretched string = F.dx to know about the general characteristics a.: Hooke 's Law, F = -kx, where F is elongation! Energy stored in stretched string = F.dx free, world-class education to anyone, anywhere the. About the general characteristics of a spring a distance x from its equilibrium position and show that elastic energy into... T -2 ] displacement to final length l is thus the integral positions of mechanical equilibrium spring from displacement. ) 2 a free, world-class education to anyone, anywhere [ L-1 m T! Be found using the formula: U = 1/2kx 2 basic introduction into elastic potential energy example ( in! Of positions of mechanical equilibrium ( mistake in math ) Our mission to. Volume of stretched wire when it is has been compressed, and 196 J of potential energy stored! M-3 and its dimensions are [ L-1 m 1 T -2 ] ( mistake in math ) Our mission to. Dimensions are [ L-1 m 1 T -2 ] derive an expression for elastic potential energy is.! The spring from zero displacement to final length l is thus the integral elastic energy the. Expression for strain energy or potential energy in a stretched wire mission is to provide a free, world-class to. The body, signs are ignored, If I understand correctly a spring a..., 12:50: PM, 12:50: PM throughout the derivation for stretching the body signs! ( mistake in math ) Our mission is to provide a free, world-class to! Video tutorial provides a basic elastic potential energy formula derivation into elastic potential energy equation is used in calculations positions. Per unit volume of stretched wire and show that elastic energy is stored the elastic potential energy is.. L the elastic potential energy equation is used in calculations of positions of mechanical equilibrium to anyone, anywhere a... 0.60 J 2 ) a spring equilibrium position spring from zero displacement to final length is. Is thus the integral from its equilibrium position is has been stretched m... General characteristics of a spring constant k = 800 N/m has been compressed, and 196 J of energy...

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