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# Physics 151 week five notes PHYC 151 001

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This 3 page Class Notes was uploaded by Breanab on Sunday February 14, 2016. The Class Notes belongs to PHYC 151 001 at University of New Mexico taught by Dr. Dave Cardimona in Winter 2016. Since its upload, it has received 67 views. For similar materials see General Physics in Physics 2 at University of New Mexico.

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Date Created: 02/14/16

Chapter 5: Applying Newton's laws 5.1 Equilibrium When the net force on an object is zero. (Newton’s First Law) EXAMPLE 5.1: Forces supporting an orangutan An orangutan weighing 500 N hangs from a vertical vine. What is the tension in the vine? EXAMPLE 5.4: Tension in towing a car o A car with a mass of 1500 kg is being towed at a steady speed by a rope held at a 20 angle. A friction force of 320 N opposes the car's motion. What is the tension in the rope? 5.2 Dynamics and Newton's Second Law There IS a net force, and it produces an acceleration. There are two basic types of problems in mechanics: (1) Use information about forces to find acceleration, then use kinematics to determine motion (i.e., F = ma, then one of the 4 equations containing ‘a’) (2) Use information about motion to determine acceleration, then solve for unknown forces (reverse of above) EXAMPLE 5.5: Putting a golf ball A golfer putts a 46 g ball with a speed of 3.0 m/s. Friction exerts a 0.020 N retarding force on the ball , slowing it down. Will her putt reach the hole, 10m away? EXAMPLE 5.6: Towing a car with acceleration Acar with a mass of 1500 kg is being towed by a rope held at a 20 angle. A friction force of 320 N opposes the car's motion. What is the tension in the rope if the car goes from rest to 12 m/s in 10 s? 5.3 Mass and Weight Mass and weight are not the same thing, but they are related. Mass is an intrinsic property of an object; it has the same value wherever the object may be and whatever forces might be acting on it. It describes the amount of matter in the object. Weight, on the other hand, is a force. Specifically, it is the gravitational force exerted on an object by a planet. Weight is a vector, and the vector’s direction is always straight down. In freefall, the only force acting on an object is the force of gravity, i.e., it’s weight. Newton’s Second Law then states: F net F g w = m a freefall Galileo said all objects fall at the same rate, regardless of weight. Therefoae, = g for any object. freefall Therefore: Fg= m g (weight = mass times acceleration of gravity) “Apparent Weight”: How heavy you ‘feel’. This is what a scale reads when you stand on it. What if you were in an elevator … If a > 0 (accelerate upwards), you feel heavier. a F net= FN– F =gm a If a < 0 (accelerate downwards), you feel lighter. If a = 0 (constant speed, possibly 0), you feel your normal weight. F N FN= m (g + a) What if a = – g ?? F = 0 and you feel weightless. F N g EXAMPLE 5.8: Apparent weight in an elevator Sanjay’s mass is 70 kg. He is standing on a scale in an elevator that is moving at 5 m/s. As the elevator stops, the scale reads 750 N. Before it stopped, was the elevator moving up or down? How long did the elevator take to come to rest? 5.4 Normal Forces EXAMPLE 5.9: Normal force on a pressed book A 1.2 kg book lies on a table. The book is pressed down from above with a force of 15 N. What is the normal force acting on the book from the table below? 5.5 Friction There are two kinds of friction: static and kinetic. They NEVER act at the same time!! The direction of the friction force vector is opposite the direction of motion, or attempted motion. The magnitude is: static kinetic 0 < fs< fsmax= m s N fk= µkF N (Here we assume that kinetic friction is independent of speed.) When static, all forces add to zero (Newton’s First Law) – since nothing is moving. When kinetic, depends on if object is moving at constant speed or accelerating. µ is always greater thanµ s k [REMEMBER: µs and µk are NOT the frictional forces, fsand fkare the forces!!] STOP TO THINK 5.5: Rank from largest to smallest, the size of the friction forces EXAMPLE 5.11: Finding the force to slide a sofa Carol wants to move her 32 kg sofa to a different room. She places slippery disks witµk = 0.08 under the sofa feet. She pushes the sofa at a steady 0.4 m/s across the floor. How much force does she apply to the sofa? Counter to intuition, it is static friction that pushes you forward when you walk! If kinetic friction were involved, you would be slipping and sliding, not walking forward … 5.6 Drag X 5.7 Interacting Objects EXAMPLE 5.15: Pushing two blocks As shown in the figure to the right, a 5 kg block A is pushed with a 3 N force. In front of this block is a 10 kg block B. The two blocks move together. What force does block A exert on block B? 5.8 Ropes and Pulleys A massless string or rope "transmits" a force undiminished from one end to the other: If you pull on one end of a rope with forcF , the other end of the rope pulls on what it's attached to with aFf, and the tension within the rope equals the magnitude of the force pulling on the rope. F F T F T F CONCEPTUAL EXAMPLE 5.16: Pulling a rope Above on the left, a student pulls horizontally with a 100 N force on a rope attached to a wall. Above on the right, two students pull on opposite ends of a rope with 100 N each. Is the tension in the second rope larger, smaller. or the same as that in the first? The tension in a massless string is unchanged by passing over a massless, frictionless pulley. TACTICS BOX 5.3: Working with ropes and pulleys For massless ropes or strings and massless, frictionless pulleys: • If a force pulls on one end of a rope, the tension in the rope equals the magnitude of the pulling force. • If two objects are connected by a rope, the tension is the same at both ends. • If the rope passes over a pulley, the tension in the rope is unaffected. Problem 74. Two blocks are connected by a Problem 76. The 100 kg block in the figure takes string as in the figure. What is the upper block’s 6 s to reach the floor after being released from acceleration if the coefficient of kinetic friction rest. What is the mass of the block on the left? between the block and the table is 0.2? INTEGRATED EXAMPLE 5.20: Stopping distances A1500 kg car is traveling at a speed of 30 m/s when the driver slams on the brakes and skids to a halt. Determine the stopping distance if the car is traveling on a level road where the coefficient of kinetic friction between rubber and concrete is 0.80.

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