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Chapter_7

# Chapter_7 - Chapter 7 Kinetic Energy and Work In this...

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Chapter 7 Kinetic Energy and Work In this chapter we will introduce the following concepts: Kinetic energy of a moving object Work done by a force Power In addition, we will study the work-kinetic energy theorem and apply it to solve a variety of problems This is an alternative approach to mechanics. It uses scalars such as work and kinetic energy rather than vectors such as velocity and acceleration. Therefore it is simpler to apply. (7-1)

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m m Kinetic Energy: We define kinetic energy for an object of mass m and speed v 2 2 mv K = The SI unit for K is joule (symbol: J =kg m 2 / s 2 ). An object of mass m = 1kg that moves with speed v = 1 m/s has a kinetic energy K = 0.5J Work : (symbol W) If a force F is applied to an object of mass m , the object can accelerate and increase its speed v and kinetic energy K , or decelerate and decrease its kinetic energy. We account for these changes in K by saying that F has transferred energy W to or from the object: If energy is transferred to the object ( K increases ), positive work is done by F on the object ( W = K > 0). If energy is transferred from the object ( K decreases ), negative work is done by F on the object ( W = K < 0) (7-2) ?
m m Consider a bead of mass that can move without friction along a straight wire along the -axis. A force applied at an angle to the wire is acting on the b m x F φ Finding an expression for Work : constant r ead We apply Newton's second law: We assume that the bead had an initial velocity and after it has travelled a distance its velocity is . We apply the third equation of kinematics with c = x x o F ma v d v r r r ( 29 2 2 2 2 2 2 onstant acceleration: 2 2 2 cos 2 2 2 2 , The in kinetic energy cos 2 2 Thus the work done the force the bead - = - = = = = = = - = o x x o x x i o f f i v v a d F m m m m v v a d d F d F d m m m K v K v K K Fd W φ φ by on change is given by: cos = = x W F d Fd φ cos = W Fd φ W F d = r r (7-3)

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W = F d cos φ How to make non-zero W? Force>0 Distance>0 Angle φ is NOT 90 degrees N W f k F The SI unit for W is joule (N m = kg m 2 / s 2 = J). A force of 1N that moves an object by 1 m does work 1J
A F r B F r C F r m m The unit of is the same as that of (i.e. The above expression for work only applies when is We assume that the moving object is point-like 0 if 0 9 jo e ) 0 ul s , < < ° N con o s te 1 : Note tant 2 : Note 3 : W K F W φ 0 if 90 180 If several forces act on a body, there are two methods to calculate the net work First, calculate the work done by each force: = , = , and < ° < < ° Net Wo Method 1 : : rk net A A B B d W W W F W d F W φ r r r r First, c = . Then determine alculate . Then determine = + + = + + = Method 2 : C C net A net A B C net net B C F F F d W W W W W F F d F r r r r r r r r cos = W Fd φ W F d = r r (7-4)

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m m We have defined work as . We represent the change in kinetic energy as: . The equation fo the r - = - f i f i K K K K K work - kinetic energy theorem Work-Kinetic Energy Theorem f i net K K K W = - = Change in the kinetic net work done on = energy of a particle the particle
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