Work_Energy_Power

 2013 Yeow Kok Han Page 1 WWoorrkk EEnneerrggyy PPoowweerr 11 IInnttrroodduuccttiioonn In physics, ‘work’ has a meaning different from normal everyday usage. In physics, w ork is a method of energy transfer. Doing positive work on a system means transferring energy into the system while doing negative work means transferring energy out of the system. Energy comes in many different forms - kinetic, potential, thermal, electromagnetic radiation - even mass is a form of energy as put forth by Einstein’s famous E = mc2 equation. Some of these energies are always in a state of flux or flow. Thus a system’s total energy can change because of work done or the energy flows. That naturally leads to the concept of power which is the rate of flow or transfer or transformation of energy. 22 WWoorrkk DDeeffiinniittiioonn ooff wwoorrkk Consider a box of mass m on a horizontal frictionless surface. In itially, the box wa s stationary. A constant force F applied on the box caused it to accelerate and acquire a final velocity v and KE = ½ mv2. Of the three forces acti ng on the box, the normal force N and the weight W do not contribute to the acceleration and gain in KE. Let’s work out the connection between F and the gain in KE:  F is a net force F = ma  F constant  a also constant. Straight line motion with constant a implies v2 = u2 + 2as  v2 = 2as since u = 0  v2 = 2(F/m)d   ½ mv2 = Fd The product Fd is the work done by F. Formally, work done WD is defined as follows BBaassiicc ccaasseess ooff wwoorrkk Case 1 - . F & d in same direction, WD = Fd. This case has been considered above. F & d are magnitudes. Case 2 - . F & d in opposite direction, WD =  Fd. In Fig. 2.2, F is to the left on a box with initial velocity v to the right, causing deceleration. The box loses KE and the work done by F is negative. Work done(scalar) by a force on a system is defined as the product of the force and the displacement in the direction of the force. Basic cases: 1 F & d in same direction, WD = Fd 2 F & d in opposite direction, WD =  Fd. 3 F & d are perpendicular, WD = 0 d N W F v Fig. 2.2 Work done by a force is defined as the product of the force and the displacement in the direction of the force. N W F d v Fig. 2.1

 2013 Yeow Kok Han Page 2 Case 3 - . F & d are perpendicular, WD = 0. Referring to Fig. 2.2, if F = N vertically upwards or F = W vertically downwards, it does not contribute to the change in KE of the box and WD = 0. GGeenneerraall ccaasseess ooff wwoorrkk In general, F can be at any angle to d . However, the force can always be resolved into a component parallel to d and another component perpendicular to d as shown in Fig. 2.3 and 2.4. The component perpendicular to d does no work (see basic case