Work done in lifting mass m a distance h = W When you release the spring, you can deliver thisĪmount of energy to a mass m, so: mvf^2 =. Work the spring can now deliver W = ( Conservative Force) The spring is said to contain When you compress the spring a distance x, the work done to compress the spring = With or without motion, objects can have PotentialĮxamples: Object (Mass) at top of a buildingįor mechanical systems - best to think of this type of energy as "energy ofįor spring, we do work compressing the spring - once compressed, spring ready toĭeliver the energy back by accelerating a mass and giving it KE. Since we take a, ± does not give direction. = xo ) and let go, what is final KE and v? Work done by F on mass, WĬhange in KE = KEf - KEi = mvf^2 + 0. IF we use object and compress spring this same distance (xf Spring compress in bringing the mass to rest?Ī spring exerts F proportional to x in both compression and extension (for reasonableĬhange in KE = KEf - KEi = 0 - mvo^2. It comes into contact with a spring with force constant k. Ī mass m is moving in a straight line at velocity vo. įor linear force, F= kx, Area under curve from 0 to x f =. X 2 = W total = S F i D x i = area under curve!! (C word = integral of F from x 1 to x 2 ) and D KE = W total. Where Fi is the average force over that interval: Suppose F acting on a mass m depends on x e.g., F = kx We divide x (a) What is the work done by gravity on the car?į grav = mg D y = 24 m Force and displacement in same direction (down).į grav = F net because gravity is only force acting on car. Suppose a car of mass 1200 kg falls vertically a distance of 24 m (starting from rest (Net work done = change in kinetic energy If W is positive, KE increases IF W is negative, KE decreases. The mechanical work done on the object = the change in kinetic energy. (would get same result for non-constant F and a). Work done through the distance s, W = Fs = mas.ĭuring the deceleration, v 2 = v o2 + 2as or as = 1/2(v 2 - v o2 ) The force required to slow down the bullet is F = ma, where a is the deceleration. Suppose a "bullet" of mass m moving at v o mushes into a block of soft clay and experiences a constant force F Moving objects can do work (bowling ball displaces pins hammer pushes in nail carĬreams cow) energy of motion = kinetic energy. Mechanical Energy: traditional definition = the ability to do work. Work keeping a satellite in circular orbit above earth: Need more Twinkies to keep going)-in terms of mechanical work performed: ZIP!įorce not in same direction as displacement:
IF d = 0: Pushing against an immovable object, W = 0.īoth cases body uses chemical energy for muscles to exert these forces (you get tired, = 0! Carrying a weight corresponds to W = 0. Units of W = Newton-meters (N-m) 1 N m = 1 Joule. If F|| is the component of along, then the WORK done by, W, is given by W = F|| x d = dot product of the two vectors and. Unbalanced force applied to an object, and let be a resulting displacement. Simple Concepts Involving Work and Energy
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