LECTURE 12 FRICTION, STRINGS & SPRINGS. Instructor: Kazumi Tolich

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1 LECTURE 12 FRICTION, STRINGS & SPRINGS Instructor: Kazumi Tolich

2 Lecture 12 2! Reading chapter 6-1 to 6-4! Friction " Static friction " Kinetic friction! Strings! Pulleys! Springs

molecules/atoms of one surface to these of another in close contact.

3 Origin of friction 3!! The origin of friction is electromagnetic attraction force between molecules/atoms of one surface to these of another in close contact. The microscopic contacting surface area increases when the normal force increases due to the flattening of the tips. Polished steel surface

4 Static friction 4! Static friction is the frictional force that prevents surfaces in contact from sliding.! The direction of the static friction is anti-parallel to the force trying to slide the object relative to the surface.

5 Static friction: 2 5! While the object is not sliding on a surface, the magnitude of the static friction equals the magnitude of the force trying to slide the object until it reaches the maximum value given by f s,max = µ s N! µ s is the coefficient of static friction (dimensionless).! N is the magnitude of the normal force by one surface on the other. f s FBD of the block N F mg

6 Clicker question: 1

7 7 Clicker question: 2

8 Kinetic friction 8! Kinetic friction is the frictional force that opposes sliding motion.! The direction of the kinetic friction is anti-parallel to the velocity of the sliding object relative to the surface.! The magnitude of the kinetic friction is given by f k = µ k N! µ k is the coefficient of kinetic friction (dimensionless).! N is the magnitude of the normal force by one surface on the other.! Kinetic friction is independent of the relative speed of the surfaces or the area of contact between the surfaces.

9 Static vs. kinetic frictions 9! For any given contacting surfaces, µ k is usually less than or equal to µ s.! You have to push harder to get an object to begin sliding than to keep it sliding at constant speed. f s,max = µ s N f k = µ k N

10 Demo 1 10! Incline with Sliding Blocks (with Tacky Wax)! Demonstration of various surfaces with different coefficients of static friction.! Coefficient of static friction can be measured by the maximum angle without the block sliding. +y N BR +x θ θ f s BR W BE θ Max static friction: f s BR, max = µ s N BR in x-dir: f s BR, max cosθ N BR sinθ = 0 in y-dir: N BR cosθ + f s BR, max sinθ W BE = 0 µ s = tanθ

11 Example: 1 11! A 0.11-kg hockey puck whose initial speed was 6.0 m/s slides on the ice for 15.0 m before it stops. a) What was the magnitude of the frictional force on the puck during the sliding? b) What was the coefficient of friction between the puck and the ice?

12 Tension in strings 12! In a rope dangling from a ceiling, tension is the greatest at the ceiling due to the weight of the rest of the rope dangling below.! If the mass of the rope can be neglected, the tension is the same throughout the rope.

13 Frictionless massless pulleys 13! The force exerted by the frictionless massless pulley on the rope is always a normal force.! A normal force has no component tangent to the rope, so it cannot produce a change in the magnitude of tension.! N

Frictionless massless pulleys: 2 14! If the pulley axis is not accelerating, the net force on the pulley axis is zero.! Right pulley: The weight, W, is pulling the pulley axis down.

14 Frictionless massless pulleys: 2 14! If the pulley axis is not accelerating, the net force on the pulley axis is zero.! Right pulley: The weight, W, is pulling the pulley axis down. Two tensions (of the same magnitude, W/2) are pulling up the pulley axis.! Left pulley: Two tensions (of the same magnitude, W/2) are pulling down the pulley axis. The support is pulling up the pulley axis with force W.

15 Demo 2 15! Load on Removable Incline! Demonstration of various forces acting on an object and the net force acting on it.

the mechanical laws of uniform acceleration motion. For m 1 :! F 1 net = m 1!

16 Demo 3 16! Atwood s Machine! Atwood's machine was invented in 1784 by George Atwood as an experiment to verify the mechanical laws of uniform acceleration motion. For m 1 :! F 1 net = m 1! a T m 1 g = m 1 a T = m 1 ( a + g) T m 1 g T m 2 g For m 2 :! F 2 net = m 2! a T + m 2 g = m 2 a T = m 2 ( g a) ( ) ( ) g a = m m 2 1 m 2 + m 1

17 Demo 4! Force Board! Demonstration of forces and net force.

18 Clicker question: 3

19 Example: 2 19! A lamp hangs vertically from a cord in a descending elevator. The elevator has a deceleration of a = 2.4 m/s 2 before coming to a stop. a) If the tension in the cord is T = 89 N, what is the mass of the lamp? b) What is the tension in the cord when the elevator ascends with an upward acceleration of 2.4 m/s 2?

20 Spring force 20! Force exerted by a compressed or stretched spring obey Hook s law. F x = kx! - : the direction of force is opposite from the displacement of the end of the spring. This type force is called restoring force.! k: force constant for stiffness of the spring! x: the displacement of the end of the spring.

21 Example: 3 21! A spring with a force constant of k = 120 N/m is used to push a 0.27-kg block of wood against a wall, as shown. Find the minimum compression of the spring needed to keep the block from falling, given that the coefficient of static friction between the block and the wall is µ s = 0.46.

22 22 Clicker question: 4

23 Example: 4 23! Two blocks are connected as shown on a horizontal table with the coefficient of kinetic friction µ = The right string is pulled to the right with a force T 2 = 65.0 N. m 1 = 12.0 kg and m 2 = 24.0 kg. a) What is the acceleration of the system? b) What is the tension, T 1? T 1 T 2 m 1 m 2

LECTURE 12 FRICTION & SPRINGS. Instructor: Kazumi Tolich

LECTURE 12 FRICTION & SPRINGS. Instructor: Kazumi Tolich LECTURE 12 FRICTION & SPRINGS Instructor: Kazumi Tolich Lecture 12 2 Reading chapter 6-1 to 6-2 Friction n Static friction n Kinetic friction Springs Origin of friction 3 The origin of friction is electromagnetic