Chapter 6 Applications of Newtons Laws What keeps

Chapter 6 Applications of Newton’s Laws What keeps Leo in his seat when the train stops?

Units of Chapter 6 • Frictional Forces • Strings and Springs • Translational Equilibrium • Connected Objects • Circular Motion

6 -1 Frictional Forces

Kinetic Friction Kinetic friction: the friction experienced by surfaces sliding against one another

Static Friction

Real-World Physics – Tires use Static Friction!

Static Friction (6 -2) where (6 -3) The static frictional force is also independent of the area of contact and the relative speed of the surfaces.

Concep. Test 6. 4 Friction on a frictionless truck bed. 1) the force from the rushing air pushed it off When the truck accelerates 2) the force of friction pushed it off forward, the box slides off 3) no net force acted on the box the back of the truck 4) truck went into reverse by accident A box sits in a pickup truck because: 5) none of the above

Concep. Test 6. 4 Friction on a frictionless truck bed. 1) the force from the rushing air pushed it off When the truck accelerates 2) the force of friction pushed it off forward, the box slides off 3) no net force acted on the box the back of the truck 4) truck went into reverse by accident A box sits in a pickup truck because: 5) none of the above Generally, the reason that the box in the truck bed would move with the truck is due to friction between the box and the bed. If there is no friction, there is no force to push the box along, and it remains at rest. The truck accelerated away, essentially leaving the box behind!!

Concep. Test 6. 5 Antilock Brakes Antilock brakes keep the car wheels from locking and skidding during a sudden stop. Why does this help slow the car down? 1) mk > ms so sliding friction is better 2) mk > ms so static friction is better 3) ms > mk so sliding friction is better 4) ms > mk so static friction is better 5) none of the above

Concep. Test 6. 5 Antilock Brakes Antilock brakes keep the car wheels from locking and skidding during a sudden stop. Why does this help slow the car down? 1) mk > ms so sliding friction is better 2) mk > ms so static friction is better 3) ms > mk so sliding friction is better 4) ms > mk so static friction is better 5) none of the above Static friction is greater than sliding friction, friction so by keeping the wheels from skidding, the static friction force will help slow the car down more efficiently than the sliding friction that occurs during a skid.

Example • Leo goes down a playground slide that is inclined at an angle of 24. 5˚ below the horizontal. Find his acceleration given that the coefficient of kinetic friction between the child and the slide is 0. 375

6 -2 Strings and Springs

6 -2 Strings and Springs

Concep. Test 6. 1 a Tension I You tie a rope to a tree and you 1) 0 N pull on the rope with a force of 2) 50 N 100 N. What is the tension in the rope? 3) 100 N 4) 150 N 5) 200 N

Concep. Test 6. 1 a Tension I You tie a rope to a tree and you 1) 0 N pull on the rope with a force of 2) 50 N 100 N. What is the tension in the rope? 3) 100 N 4) 150 N 5) 200 N The tension in the rope is the force that the rope “feels” across any section of it (or that you would feel if you replaced a piece of the rope). Since you are pulling with a force of 100 N, that is the tension in the rope. Follow-up: How hard is the tree pulling?

Concep. Test 6. 1 b Tension II Two tug-of-war opponents each 1) 0 N pull with a force of 100 N on 2) 50 N opposite ends of a rope. What is the tension in the rope? 3) 100 N 4) 150 N 5) 200 N

Concep. Test 6. 1 b Tension II Two tug-of-war opponents each 1) 0 N pull with a force of 100 N on 2) 50 N opposite ends of a rope. What is the tension in the rope? 3) 100 N 4) 150 N 5) 200 N This is literally the identical situation to the previous question. The tension is not 200 N !! Whether the other end of the rope is pulled by a person, or pulled by a tree, the tension in the rope is still 100 N !!

Springs

6 -3 Translational Equilibrium When an object is in translational equilibrium, the net force on it is zero: (6 -5)

6 -3 Translational Equilibrium

Example • A picture hangs on the wall suspended by two strings, as shown in the figure. The tension in string 1 is 1. 7 N. – Find the tension in string 2 – Find the weight of the picture

Group Exercise • A spring with a force constant of 120 N/m is used to push a 0. 27 kg block of wood against a wall, as shown in the figure. (a) 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 0. 46.

6 -4 Connected Objects When forces are exerted on connected objects, their accelerations are the same.

6 -4 Connected Objects We treat each box as a separate system:

6 -4 Connected Objects If there is a pulley, it is easiest to have the coordinate system follow the string:

Announcements, 10/8 • Homework due Friday • Extra credit lecture: Today, right after class, Humanities auditorium – Remember to write up a 250 word essay about what you learned and what it meant to you. Do this soon – you don’t want to forget!

Example • Referring to the figure with masses shown, find the tension in the string connecting – m 1 and m 2 – m 2 and m 3. Assume the table is frictionless.

6 -5 Circular Motion An object moving in a circle must have a force acting on it; otherwise it would move in a straight line. The direction of the force is towards the center of the circle.

Centripetal Force This force may be provided by the tension in a string, the normal force, or friction, among others.

Concep. Test 6. 9 Tetherball In the game of tetherball, the struck ball whirls 1) Toward the top of the pole 2) Toward the ground a pole. In what 3) Along the horizontal component of the tension force direction does the net 4) Along the vertical component of the tension force on the ball point? 5) Tangential to the circle T W

Concep. Test 6. 9 Tetherball In the game of tetherball, the struck ball whirls 1) Toward the top of the pole 2) Toward the ground a pole. In what 3) Along the horizontal component of the tension force direction does the net 4) Along the vertical component of the tension force on the ball point? 5) Tangential to the circle The vertical component of the tension balances the weight The horizontal component of tension W T T provides the centripetal force that points toward the center of the circle. W

Concep. Test 6. 10 a Around the Curve I You are a passenger in a car, not wearing a seat belt. The car makes a sharp left turn. From your perspective in the car, what do you feel is happening to you? (1) You are thrown to the right (2) You feel no particular change (3) You are thrown to the left (4) You are thrown to the ceiling (5) You are thrown to the floor

Concep. Test 6. 10 a Around the Curve I You are a passenger in a car, not wearing a seat belt. The car makes a sharp left turn. From your perspective in the car, what do you feel is happening to you? The passenger has the tendency to continue moving in a straight line. From your perspective in the car, it feels like you are being thrown to the right, hitting the passenger door. (1) You are thrown to the right (2) You feel no particular change (3) You are thrown to the left (4) You are thrown to the ceiling (5) You are thrown to the floor

Concep. Test 6. 10 b Around the Curve II During that sharp left turn, you found yourself hitting the passenger door. What is the correct description of what is actually happening? (1) centrifugal force is pushing you into the door (2) the door is exerting a leftward force on you (3) both of the above (4) neither of the above

Concep. Test 6. 10 b Around the Curve II During that sharp left turn, you found yourself hitting the passenger door. What is the correct description of what is actually happening? (1) centrifugal force is pushing you into the door (2) the door is exerting a leftward force on you (3) both of the above (4) neither of the above The passenger has the tendency to continue moving in a straight line. There is a centripetal force, provided by the door, that forces the passenger into a circular path.

Centripetal Force The magnitude of the force is given by:

Banked Roads and Dips

Summary of Chapter 6 • Friction is due to microscopic roughness. • Kinetic friction: • Static friction: • Tension: the force transmitted through a string. • Force exerted by an ideal spring:

Summary of Chapter 6 • An object is in translational equilibrium if the net force acting on it is zero. • Connected objects have the same acceleration. • The force required to move an object of mass m in a circle of radius r is: