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.
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
This system consists of Earth and a tomato h vo
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
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,
• • the