Applying Newton’s Laws Chapter 5 Applying Newton’s Laws

5 Applying Newton’s Laws Slide 5-2

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Reading Quiz Which of the following statements about mass and weight is correct? Your mass is a measure of the force gravity exerts on you. Your mass is the same everywhere in the universe. Your weight is the same everywhere in the universe. Your weight is a measure of your resistance of being accelerated. Answer: B Slide 5-5

Answer Which of the following statements about mass and weight is correct? Your mass is a measure of the force gravity exerts on you. Your mass is the same everywhere in the universe. Your weight is the same everywhere in the universe. Your weight is a measure of your resistance of being accelerated. Answer: B Slide 5-6

Reading Quiz The apparent weight of an object is the pull of gravity on the object. the object’s mass times the acceleration of gravity. the magnitude of the contact force that supports the object. the pull of gravity on an object that is accelerating upward. Answer: C Slide 5-7

Answer The apparent weight of an object is the pull of gravity on the object. the object’s mass times the acceleration of gravity. the magnitude of the contact force that supports the object. the pull of gravity on an object that is accelerating upward. Answer: C Slide 5-8

Reading Quiz The coefficient of static friction is smaller than the coefficient of kinetic friction. equal to the coefficient of kinetic friction. larger than the coefficient of kinetic friction. not discussed in this chapter. Answer: C Slide 5-9

Answer The coefficient of static friction is smaller than the coefficient of kinetic friction. equal to the coefficient of kinetic friction. larger than the coefficient of kinetic friction. not discussed in this chapter. Answer: C Slide 5-10

Reading Quiz The force of friction is described by the law of friction. the theory of friction. a model of friction. the friction hypothesis. Answer: C Slide 5-11

Answer The force of friction is described by the law of friction. the theory of friction. a model of friction. the friction hypothesis. Answer: C Slide 5-12

Equilibrium An object is in equilibrium when the net force acting on it is zero. In component form, this is The net force on each man in the tower is zero. Slide 5-13

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Example Problem A 100 kg block with a weight of 980 N hangs on a rope. Find the tension in the rope if the block is stationary. it’s moving upward at a steady speed of 5 m/s. it’s accelerating upward at 5 m/s2. Slide 5-15

Example Problem A wooden box, with a mass of 22 kg, is pulled at a constant speed with a rope that makes an angle of 25° with the wooden floor. What is the tension in the rope? Slide 5-16

Checking Understanding A rod is suspended by a string as shown. The lower end of the rod slides on a frictionless surface. Which figure correctly shows the equilibrium position of the rod? Answer: B Slide 5-17

Answer A rod is suspended by a string as shown. The lower end of the rod slides on a frictionless surface. Which figure correctly shows the equilibrium position of the rod? B Answer: B Slide 5-18

Example Problem A ball weighing 50 N is pulled back by a rope to an angle of 20°. What is the tension in the pulling rope? Slide 5-19

Using Newton’s Second Law Slide 5-20

Example Problem A sled with a mass of 20 kg slides along frictionless ice at 4.5 m/s. It then crosses a rough patch of snow which exerts a friction force of 12 N. How far does it slide on the snow before coming to rest? Slide 5-21

Example Problem Macie pulls a 40 kg rolling trunk by a strap angled at 30° from the horizontal. She pulls with a force of 40 N, and there is a 30 N rolling friction force acting on trunk. What is the trunk’s acceleration? Slide 5-22

Mass and Weight –w = may = m(–g) w = mg Slide 5-23

Apparent Weight Slide 5-24

Example Problem A 50 kg student gets in a 1000 kg elevator at rest. As the elevator begins to move, she has an apparent weight of 600 N for the first 3 s. How far has the elevator moved, and in which direction, at the end of 3 s? Slide 5-25

Example Problem Find the x- and y-components of w in each of these three coordinate systems. Slide 5-26

Example Problem A 75 kg skier starts down a 50-m-high, 10° slope on frictionless skis. What is his speed at the bottom? Slide 5-27

Example Problem Burglars are trying to haul a 1000 kg safe up a frictionless ramp to their getaway truck. The ramp is tilted at angle θ. What is the tension in the rope if the safe is at rest? If the safe is moving up the ramp at a steady 1 m/s? If the safe is accelerating up the ramp at 1 m/s2? Do these answers have the expected behavior in the limit θ → 0° and θ → 90°? Slide 5-28

Example Problem The same burglars push the 1000 kg safe up a 20° frictionless slope with a horizontal force of 4000 N. What is the safe’s acceleration? Slide 5-29

Static Friction fs max = µsn Slide 5-30

Kinetic Friction fk = µkn Slide 5-31

Working with Friction Forces Slide 5-32

Example Problem A car traveling at 20 m/s stops in a distance of 50 m. Assume that the deceleration is constant. The coefficients of friction between a passenger and the seat are μs = 0.5 and μk = 0.3. Will a 70 kg passenger slide off the seat if not wearing a seat belt? Slide 5-33

Drag An object moving in a gas or liquid experiences a drag force Drag coefficient. Depends on details of the object’s shape. “Streamlining” reduces drag by making CD smaller. For a typical object, CD 0.5. A is the object’s cross section area when facing into the wind. Drag depends on the square of the speed. This is a really important factor that limits the top speed of cars and bicycles. Going twice as fast requires 4 times as much force and, as we’ll see later, 8 times as much power. Density of gas or liquid. Air has a density of 1.29 kg/m3. Slide 5-34

Cross-Section Area Slide 5-35

Terminal Speed A falling object speeds up until reaching terminal speed, then falls at that speed without further change. If two objects have the same size and shape, the more massive object has a larger terminal speed. At terminal speed, the net force is zero and the object falls at constant speed with zero acceleration. Slide 5-36

Applying Newton’s Third Law: Interacting Objects Slide 5-37

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Example Problem Block A has a mass of 1 kg; block B’s mass is 4 kg. They are pushed with a force of magnitude 10 N. a. What is the acceleration of the blocks? b. With what force does A push on B? B push on A? Slide 5-39

Checking Understanding Which pair of forces is an action/reaction pair? The string tension and the friction force acting on A. The normal force on A due to B and the weight of A. The normal force on A due to B and the weight of B. The friction force acting on A and the friction force acting on B. Answer: D Slide 5-40

Answer Which pair of forces is an action/reaction pair? The string tension and the friction force acting on A. The normal force on A due to B and the weight of A. The normal force on A due to B and the weight of B. The friction force acting on A and the friction force acting on B. Answer: D Slide 5-41

Example Problem What is the acceleration of block B? Slide 5-42

Ropes and Pulleys Slide 5-43

Example Problem Block A, with mass 4.0 kg, sits on a frictionless table. Block B, with mass 2.0 kg, hangs from a rope connected through a pulley to block A. What is the acceleration of block A? Slide 5-44

Summary Slide 5-45

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Additional Example Problem A wooden box, with a mass of 22 kg, is pulled at a constant speed with a rope that makes an angle of 25° with the wooden floor. What is the tension in the rope? Slide 5-48