4.4. Friction and Inclines

Transcription

1 4.4. Friction and Inclines

2 Frictional Forces Friction has its basis in surfaces that are not completely smooth. This roughness causes resistance to horizontal motion. Even smooth surfaces have a certain amount of roughness on the microscopic or atomic level.

3 Friction as a Reaction Pair Friction is a reaction force, and opposes the direction of motion. For instance, when you push a book horizontally across a table, the roughness between the two surface exerts a force on the table in the direction of motion. The table pushes back on the book with a force of equal magnitude and opposite direction i.e. opposite the direction of motion.

4 Friction Pros and Cons While friction is often something that we would like to reduce, it also is indispensable for many important tasks---like walking! When else is friction a pro or con?

5 Kinetic Friction Kinetic friction is the friction experienced by surfaces sliding against one another. This frictional force depends on the normal force:

6 Kinetic Friction The kinetic frictional force: 1. Is proportional to the normal force (~weight). 2. Is the same regardless of speed. 3. Is the same regardless of area of contact. How can we demonstrate these?

7 Kinetic Friction The kinetic frictional force is proportional to the normal force:

8 Kinetic Friction and Surface Area The fact that kinetic friction does not depend on the area of contact may seem surprising. For a given mass, when the area of contact is large, the normal force is spread out over a large area, giving a small normal force per unit area. As a result, the surfaces are not pressed as closely together, and the amount of resistance per area is less. Consequently the total amount of frictional force depends on mass (i.e. total normal force), but is independent of total surface area.

9 Example You slide a salt shaker across a table with an initial velocity of 1.15 m/s, and it comes to rest in m. What is the coefficient of kinetic friction between the shaker and the table?

10 Static Friction The static frictional force keeps an object from starting to move when a force is applied. The static frictional force has a maximum value, but may take on any value from zero to the maximum, depending on what is needed to keep the sum of forces zero.

11 Typical Coefficients of Friction Note the coefficients of friction depend on both material types.

12 Typical Coefficients of Friction Note static friction is generally greater than kinetic friction because objects in static contact have had opportunity to nestle and form bonds (adhesion).

13 Static Friction Where the maximum force of static friction is: Static friction is also a reaction to an applied force.

14 Static Friction The static frictional force increases as the applied force increases, until it reaches its maximum. Then the object starts to move, and the kinetic frictional force takes over.

15 Demonstration Hold a box against a wall. Why doesn t it fall? Make a body-force diagram.

16 Example 2 If a 2.80-kg mass just begins to make a 3.50-kg mass move, what must be the coefficient of static friction between the 3.50-kg mass and the table?

17 Friction on Inclines An object sliding down an incline has three forces acting on it: the normal force, gravity, and the frictional force. The normal force is always perpendicular to the surface. The friction force is parallel to it. The gravitational force points down. If the object is at rest, the forces are the same except that we use the static frictional force, and the sum of the forces is zero. The angle of the slope affects the frictional force.

18 Friction on Inclines

19 Example (AP)

20 Friction and Wheels Tires grip fast the road with static friction, not slip along the road with (lower) kinetic friction. Same with caterpillar treads, and shoes.

21 On Drive Wheels 1. A motor turns the axle and wheel clockwise. 2. Friction between the wheel and the ground exerts a force on the ground to the left. 3. The frictional force exerted by the ground on the wheel opposes the wheel s direction of motion. This force pushes the axle and wheel to the right.

22 On (Passive) Free Wheels 1. The car chassis pulls the axle and wheel to the right. 2. Friction between the nonrotating wheel and the ground exerts a dragging force on the ground to the right. 3. The frictional force exerted by the ground on the wheel opposes the non-rotating wheel s direction of motion. This force pushes the wheel to the left, causing rotation. 4. A major source of deceleration is the kinetic friction between the rotating axle and the chassis.

23 The Friction of Wheels For drive wheels, static friction pulls the rotating wheel forward. This force balances the force supplied by the engine. For free wheels, static friction keeps the wheel from slipping. However the resistance to motion is not the static friction 0 f s µ s N but rolling friction due to compression of the tire, and kinetic friction between the rotating axle and the chassis. Thus while static friction keeps wheels from slipping, the frictional resistance to acceleration by wheels is not that static friction.

24 Antilock Braking Systems (ABS) With ABS, the car s computer pumps the brakes to prevent the wheels from completely stopping, to avoid skidding. As static friction is greater than kinetic friction, this allows a shorter stopping distance.

25 Brakes Pads Because the frictional force does not depend on the area of contact, brake pads do not need to be large. Exception: The footprint of a tire does affect its rolling motion.

26 Air Resistance

27 On Force and Measurement How is time typically measured? Spring-driven and pendulum (gravity and weight) clocks Electric clocks: vibrations of a quartz crystal How is mass typically measured? By weight (force) How is acceleration typically measured? By force How is force typically measured? Spring displacement (Hooke s Law) Balance with a weight (gravity) Electrical: effect of strain on resistance or resonance; balance with an electromagnetic force

28 Contact Forces: Forces A push or pull by direct contact of objects; includes the normal force, tension, friction Field Forces that act at a distance: Gravity, attraction/repulsion of electric charges, attraction/repulsion of magnetic poles However, contact forces are actually electromagnetic forces on the atomic scale! So all forces are act-at-a-distance force pairs.

29 The Four Forces (Interactions) Gravity (attraction between masses) Electromagnetic Force (attraction/repulsion between unlike/like charges or poles) Strong Force (nuclear; bind neutrons and protons together) Weak Force (nuclear; apparent in radioactive beta decay of nuclei) Although recently the Electromagnetic and Weak Force are considered two different manifestations of the Electroweak Force.

30 Question You want to move a heavy box (given friction, at constant velocity) by pulling it with a rope. Is it easier (requires less force) to pull the rope horizontally or up at a particular angle?

31 Demos: Weighing a Hovering Magnet Cart with Fan and Sail 4.4 Clicker Questions