Potential Energy and Conservation gy of Energy Chap.7 位能與能量守恆

 8-2 Work and Potential Energy (功與位能)  8-3 Path Independence of Conservative Forces (保守力與 83 路徑無關)  8-4 Determining Potential Energy Values (決定位能值) 84  8-5 Conservation of Mechanical Energy (力學能守恆)  8-6 Reading a Potential Energy Curve (解讀位能曲線) 86  8-7 Work Done on a System by an External Force (外力對 系統作功) )  8-8 Conservation of Energy (能量守恆)

8-2 Work and Potential Energy (功與位能)
 The tomato (番茄) is thrown upwards with initial speed vo at point A.  Under the action of the gravitational force (重力) it slows down and stops completely at point B.  Then the tomato falls back and by the time it reaches point A B its speed has reached the original value vo.  D i th trip from A to B the gravitational During the t i f t th it ti l force (重力) Fg does negative work h W1 = -mgh. h vo  Energy is transferred by Fg from the kinetic energy (動能) of the tomato to the gravitational f h h i i A potential energy U of the tomato-earth system.

vo

 During the trip from B to A the transfer is reversed. The work W2 done by Fg is positive ( W2 = mgh ) ).  The gravitational force transfers energy from the gravitational potential energy U of the tomato earth system tomato-earth to the kinetic energy of the tomato.  The change in the potential energy U is defined as: g p gy

U  W
 This system consists of Earth and a tomato h vo

B

vo A

 Consider the mass m attached to a spring (彈簧) of spring constant (彈性係數) k as shown in the figure figure.  The mass is taken together with the spring as the system we wish to study.  The mass is given an initial speed (起始速度) B A k vo at point A. A m  Under the action of the spring force (彈力) it slows down and stops completely at point B B A which corresponds to a spring compression x.  Then the mass reverses the direction of its motion and by the time it reaches point A its speed has reached the original value(原始速度) vo.

 During the trip from A to B the spring force (彈力) Fs does negative work W1 = -kx2/2 /2.  Energy is transferred by Fs from the kinetic energy of the mass to the potential energy U of the mass-spring system. mass spring  During the trip from B to A the transfer is reversed. The work W2 done by Fs is positive ( W2 = kx2/2 ). y p )  The spring force transfers energy from the p potential energy U of the mass-spring gy p g B A k system to the kinetic energy of the mass. m

U  W

A

B

 Consider a system that consists of a block (積木) of mass m and the floor on which it rests.  The block starts to move on a horizontal floor with initial speed vo at point A. p p  The coefficient of kinetic friction (動摩擦係數) between the floor and the block is μk.  The block will slow down by the kinetic friction fk and will stop at point B after it has traveled a distance d.  During the trip from point A to point B the frictional force has done work Wf = - μkmgd.  The frictional force transfers energy from the kinetic energy of the block to a type of energy called thermal energy.  Thi energy transfer cannot b reversed. This t f t be d d
A fk m vo fk B m x

Potential Energy (位能)
 Potential energy is the energy associated with the configuration of a system of objects that exert forces on each other  There are many forms of potential energy, including:
– – – – Gravitational (重力) G it ti l Electromagnetic (電磁) Chemical (化學) Nuclear (原子核)

 The energy storage mechanism is called potential energy  A potential energy can only be associated with (有關聯) specific types of forces  Potential energy is always associated with a system of two or more interacting objects

Conservative and Nonconservative Forces (保守力 與非保守力)
Let us list the key elements of the two situations we just discussed: 1. The system consists of two or more objects. 2. A force acts between a particle-like object (tomato or block) in the system and the rest of the system. 3. When the system configuration changes,
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