Work & Energy: Introduction to Work & Energy

Work & Energy Introduction to Work & Energy: Work is energy transferred by a force (W = F ᐧ d or Fdcosθ → this is a dot product) and is in units of Joules (J) which is simply Nm or m2kg/s2 The cosθ is there because the only component of the force that does work is the one that lies along the same direction as displacement (the perpendicular component does NO work) If work a positive then the force is giving the object energy (force points in same direction as displacement), if work is negative then that force is trying to take away energy from that object (force points in opposite direction as displacement) Energy is the ability to do work It seems kind of circular, but that’s because they ARE related to one another There is a brilliant sort of relation between work and kinetic energy shown in this video (8:31) 1 Kinetic energy is the amount of work needed in order to get an object from rest to its current velocity (Ek = 2 𝑚𝑣 2 ) Potential energy is the potential to do work (Ep = mgh) and doesn’t have energy due to motion like an object with kinetic energy would Work Energy Principle simply states that Wnet = ΔEK Remember, if something moves with constant velocity then W is 0 because there was no ΔEK of the object Introduction to Springs & Hooke’s Law: Relationship between the amount of force applied to a spring and its compression is actually linear (within reasonable tolerance) Hooke’s Law: F = -kx (where k is the spring constant for that particular spring) → this equation gives the restorative force showing the direction of the force vector with regards to the spring) Potential Energy Stored in a Spring: Work for a spring is simply the area under the curve of a F vs. x (displacement) graph and therefore follows the formula W = 1 2 - 𝑘𝑥 2 Total work necessary in order to compress the spring by a distance of x Remember, centripetal acceleration is 𝑎! = "2 # (can use this equation in order to find the speed at the top of a loop) You can always find the work done by a force on an object if you know the energy that the force gives or takes away from the object - - Conservative Forces: Conservative forces are any force where the work done by that force only depends on the initial and final positions of the object (path independent) and therefore conserve mechanical energy (Ek + EP) Examples include gravitational force, spring force, An example of a nonconservative force is friction and air resistance (since its path is important in determining its work) Also, it’s important to know that conservative forces have potential energy associated with them while nonconservative forces do not This basically means that nonconservative forces can not be transferred back and forth from U and K Power: Power measures the rate at which someone/thing does work 𝑃 = - $ % (units are in Watts or J/s) This only gives average power since you would need calculus in order to give the instantaneous power If power is constant the entire time, then average power and instantaneous power are equal to one another If you know the instantaneous velocity, then you can figure out the instantaneous power by using 𝐹 = 𝐹𝑣𝑐𝑜𝑠𝜃 Introduction to Mechanical Advantage: Fulcrum is where the lever pivots and the mass is the object sitting on the lever If you have a lever, you can push twice as force for half as much force in order to move an object with double the amount of force (mechanical advantage is the factor of which you are using less force → such as using 5N to move an object of 10N, MA = 2 &'#!( '& '*+(!% and if you use 20N to move an object of 10N, MA = ½ → 𝑀𝐴 = &'#!( ,-(. %' /'"( %ℎ( '*+(!% = - 0! 0" ) Mechanical advantage is also proportional to the ratio between the two differences on either side of the fulcrum and can be summed up as F1d1=F2d2 and is actually related to the moment of inertia (cross product) For inelastic collisions, you can use conservation of momentum (p = mv) Also for finding MA of a ramp, do 𝑀𝐴 = ℎ12'%(3,-( ℎ(45ℎ%