Fundamentals of Physics School of Physical Science and Technology Mechanics (Bilingual Teaching) 张昆实 School of Physical Science and Technology Yangtze University

Chapter 6 Force and Motion-II 6-1 Friction 6-2 Properties of Friction 6-3 The Drag Force and Terminal speed 6-4 Uniform Circular Motion

6-1 Friction Friction: When a force tends to slide a body along a surface, a frictional force from the surface acts on the body. The frictional force is parallel to the surface and directed so as to oppose the sliding. It is due to bonding between the body and the surface. If the body does not slide, the frictional force is a static frictional force . If there is sliding, the frictional force is a kinetic frictional force .

6-2 Properties of Friction When a dry and unlubricated body presses against a surface, a force attempts to slide the body along the surface, the frictional force has: Property1. If the body does not move, then the static frictional force and the component of that is parallel to the surface balance each other. Property2. The magnitude of has a maximum velue : is the coefficient of static friction If , the body begins to slide. (6-1)

6-2 Properties of Friction Property3. If the body begins to slide along the surface, the magnitude of the frictional force rapidly decreases to a value is the coefficient of kinetic friction. The coefficient and are dimensionless and must be determined experimentlly. 漆安慎书 :P75 table 3.2 (6-2)

6-3 The Drag Force and Terminal speed When there is a relative motion between air ( or some other fluid ) and a body, the body experiences a drag force that opposes the relative motion and points in the direction In which the fluit flows relative to the body. The magnitude of is related to the relative speed by an experimentlly determined drag coefficient C according to (6-14) (6-14)

6-3 The Drag Force and Terminal speed (6-14) Where is the air density; is the effective cross-sectional area of the body ( the area of a cross section taken perpendicular to the velocity ). The drag coefficient C can vary with the variation of , For simplicity, take it as a constant.

6-3 The Drag Force and Terminal speed (6-14) Falling body During the falling, Newton’s second law for a vertical y axis: If the body falls long enough, eventually equals the body’s speed no longer increases. (6-15)

6-3 The Drag Force and Terminal speed If the body falls long enough, eventually equals the body’s speed no longer increases. The body then falls at a constant speed, called the terminal speed Find : (6-15) terminal speed (6-16)

6-3 The Drag Force and Terminal speed Skydiving

6-3 The Drag Force and Terminal speed Group Skydiving

6-4 Uniform Circular Motion ★ Uniform circular Motion : ( Section 4-7 ) A particle travel around a circle or a circular arc at constant (uniform) speed , it is said to be in Uniform circular Motion. The body has a centripetal acceleration. direction: toward the center of the circle; magnitude: (4-32) Example: Fig.6-9 , P107 A centripetalforce accelerates a body by changing the direction of the body’s velocity without changing the body’s speed.

6-4 Uniform Circular Motion ★ From Newton’s second law and (4-32) (magnitude of centripetal force) The directions of the centripetal acceleration and force are not constant, they vary continuously so as to always point toword the center of the circle along a radial axis . The positive direction of the axis is radially outward, but the acceleration and force vectors point radially inward. Sample problem 6-9 : P110