University:
Eastern Kentucky University
Course:
PHY 131 | College Physics I
Academic year:

2021
Views:

296

Pages:

2
Author:

do3ran7ut

Work and Work-Energy Theorem Work Work is defined as the scalar product of force and displacement. Work is done when a non-zero net force acts on a moving object. If a force F moves an object over a distance d, work can be found by using the formula: F θ F θ d W = F id If F and d are parallel, the work is W = F d . If they are not parallel, then the work is W = F d cos θ . From this formula, one can conclude that for the work to be done, the following conditions must be met: • The object must move (i.e. d ≠ 0). A force can be exerted on an object with no work done, e.g. pushing on a wall, holding up 100 lb, etc. • If F and d are perpendicular, no work is done (cos θ = 0). For example, carrying something is not work because the angle between the force (upwards) and displacement (horizontal) is equal to 0. • The SI unit of work is Joule (J), and 1 J = 1 N x 1 m. • If the angle between force and displacement is less than 900, cos θ >0, and the work is positive. If 90o < θ < 180o, cos θ <0, and the work is negative. Friction always does negative work because it always acts in the direction opposite (180o) to the motion of the object. Work either changes the velocity of an object or counteracts the work done by an opposing force. For example, if a car is moving at a constant speed, the engine does work on the car to counteract the work done by friction in the opposite direction. If an object is moving with constant velocity, the net force acting on it is zero. In this case, the net amount of work done on it must also be zero (Wnet=Fnetd). Energy Energy is one of the most fundamental concepts of Physics. It is a very abstract concept that does not have a single definition. Energy is a characteristic of a system. Energy in a system gives it the capability to perform some operation. When work is done on a system or by a system, the energy of the system changes. In other words, the system gains or loses energy through the process of work. If positive work is done, the system gains energy. If work is negative, the system loses energy. If no work is done, the total energy of the system does not change. There are many types of energy. Kinetic energy (K or Ek) is the energy of motion. It depends only upon the square of the speed and the mass of the object. 1 2 K = mv 2 Work - Energy Theorem An object is moving with an acceleration a over a distance d. Then according to the formula, v 2f = vi2 + 2 a d : F v 2f = vi2 + 2( ) d . m vi vf F Solving for F d gives Fd = m 2 (v f − vi2 ) 2 d The work done on the object W is given by W =Fd = m 2 1 1 (v f − vi2 ) = mv 2f − mvi2 = K f − K i 2 2 2 Or, we can rewrite it as W = K f − Ki = ΔK This is the kinetic energy–work theorem: The change of kinetic energy of a body is equal to the work of all the forces acting upon it. F