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Newton’s Laws Newton-1: Law of Inertia • Newton’s First Law • An object subject to no external forces is at rest or moves with a constant velocity if viewed from an inertial reference frame. – If no net forces act, there is no acceleration. F net 0 a 0 Newton 2 Cart Demo Newton 2 Slide 3 Minimizing Friction • One way to minimize friction is to float objects on a cushion of air. You will use an air track in lab this week. • Any horizontal force exerted on the cart is the net force acting on the cart. Acceleration vs Force • Experiments show that Acceleration is proportional to force F1 a1 2 F1 2a1 Acceleration vs Mass • Acceleration is inversely proportional to mass M a1 2M 1 a1 2 Newton-2 • Combining these two observations gives F F a and by an appropriate choice of units a m m Or, more familiarly, Units: Mass has SI units of kg, and acceleration has SI units of m/s2. The SI unit of force is: 1 newton = 1 N = 1kg m/s2. Newton-2 (Second Law of Motion) Fnet a m The Unit Newton • Newton’s 2nd law says a = Fnet / m • So Fnet = ma by algebra 1N 1kg m / s 2 • 1 Newton of force is the amount of force necessary to accelerate 1 kg at 1 m/s/s • This is why 1 kg weighs 9.8 N on Earth, because the acceleration due to gravity on earth (g) is 9.8 m/s/s Example: Accelerated Mass m1 A net force of 3.0 N produces an acceleration of 2.0 m/s2 on an object of unknown mass. What is the mass of the object? F (3.0 N) m1 = 2 1.5 kg a1 (2.0 m/s ) Newton 2 Practice The skater’s mass is 25 kg. Force Mass Acceleration 100 N 200 N 10 m/s/s Complete the table below for a 50 N resistance force. Force Acceleration 50 N 100N 200 N Friction: force that resists motion • force between the surfaces of two objects • Examples: sliding friction, air resistance • Friction acts in the direction opposite to motion Friction Example • A force of 5 N is used to drag a 1 kg object across the lecture table at a constant velocity of 1 m/s. What is the friction force opposing the motion? – What is the acceleration of the object? • Velocity constant – acceleration = 0 – What is the net force on the object? • Acceleration = 0 Fnet = 0 – What is the force of friction opposing the motion? 5N FN = 10 N Ff = 5 N 5N Fg = 10 N Friction Example • A force of 5 N is used to drag a 1 kg object across the lecture table at a constant velocity of 1 m/s. What is the friction force opposing the motion? – What is the force of friction opposing the motion? •5N • Now a force of 13 N is applied to the object. What is its acceleration? FN = 10 N • Fnet = 13 N – 5 N = 8 N • a = Fnet/m = 8 N/1 kg = 8 m/s2 13 N Ff = 5 N Fg = 10 N Kinematics & Dynamics Combo You are stranded in space, away from your spaceship. Fortunately, you have a propulsion unit that provides a constant net force F for 3.0 s. You turn it on, and after 3.0 s you have moved 2.25 m. If your mass is 68 kg, find F. x x0 v0t 1 at 2 1 at 2 2 2 2 x 2(2.25 m) a 2 0.50 m/s 2 t (3.0 s) 2 a 0.50 m/s 2 Fnet ma (68 kg)(0.50 m/s 2 ) 34 N Since there is only one force, we call that direction positive x and only worry about magnitudes. In which direction does the object accelerate? 1. a. 2. b. 3. c. 74% 4. d. 5. e. 19% 6% 0% 0% 1 2 3 4 5 In which direction does the object accelerate? 1. a. 2. b. 100% 3. c. 4. d. 5. e. 0% 0% 0% 0% 1 2 3 4 5 Example: Three Forces Moe, Larry, and Curley push on a 752 kg boat, each exerting a 80.5 N force parallel to the dock. (a) What is the acceleration of the boat if they all push in the same direction? (b) What is the acceleration if Moe pushes in the opposite direction from Larry and Curley as shown? Fnet1 FM FL FC 3(80.5 N) 241.5 N a1 Fnet1 / m (241.5 N) / (752 kg) 0.321 N/kg 0.321 m/s 2 Fnet 2 FM FL FC 80.5 N a2 Fnet 2 / m (80.5 N) / (752 kg) 0.107 m/s 2 Astronaut Checkpoint 1 Suppose you are an astronaut in outer space giving a brief push to a spacecraft whose mass is bigger than your own. Compare the magnitude of the force you exert on the spacecraft, Force on spacecraft by astronaut, to the magnitue of the force exerted on you by the spacecraft, Force on astronaut by spacecraft , while you are pushing. A. Force on astronaut by spacecraft = Force on spacecraft by astronaut B. Force on astronaut by spacecraft > Force on spacecraft by astronaut C. Force on astronaut by spacecraft < Force on spacecraft by astronaut Astronaut Checkpoint 2 Suppose you are an astronaut in outer space giving a brief push to a spacecraft whose mass is bigger than your own. Compare the magnitude of the force you exert on the spacecraft, Force on spacecraft by astronaut, to the magnitude of the force exerted on you by the spacecraft, Force on astronaut by spacecraft , while you are pushing. A. acceleration of astronaut = acceleration of spacecraft B. acceleration of astronaut > acceleration of spacecraft C. acceleration of astronaut < acceleration of spacecraft Newton’s Third Law of Motion Forces always come in pairs, acting on different objects: If Object 1 exerts a force F on Object 2, then object 2 exerts a force –F on Object 1. These forces are called action-reaction pairs. Newton’s Third Law of Motion Some action-reaction pairs: Contact forces: The force exerted by 12 N one box on the other is 3 kg 1 kg different depending on which one you push. Boxes 1 and 2 rest on a 12 N 3 kg frictionless surface. 1 kg What is the acceleration in each case? Fnet a What is the force m between the boxes in 12 N each of the cases? a 3m s 2 4kg Contact forces: The force exerted by one box on the other is different depending on which one you push. 12 N Boxes 1 and 2 rest on a frictionless 3 kg 1 kg surface. What is the force between the boxes in each of the cases? In the first case: find the net force on mass 1 12 N Fnet ma 3 kg 3 m s 2 3 kg 1 kg Fnet 9 N this is the force on 1 by 2Fnet 12 N F2,1 Since there is no friction, Alternatively, you could analyze mass 2 3 N 12 N F2,1 Fnet ma 1kg 3 m s 2 F2,1 12 N 3N Fnet 3 N Mass 2 also has the applied force of F2,1 9 N 12 N acting in the opposite direction. Contact forces: The force exerted by one box on the other is different depending on which one you push. Boxes 1 and 2 rest on a frictionless 3 kg 1 kg12 N surface. What is the force between the boxes in each of the cases? In the second case: find net force on mass 2 Fnet ma 1kg 3 m s 12 N 2 3 kg 1 kg Fnet 3 N this is the force on 2 by 1 Since there is no friction, Fnet 12 N F1,2 Or as before, mass 1 could be analyzed . 9 N 12 N F1,2 Fnet ma 3 kg 3 m s 2 F1,2 12 N 9 N Fnet 9 N Mass 1 also has the applied force of F1,2 3 N 12 N acting in the opposite direction. Freefall • The ratio of weight (F) to mass (m) is the same for all objects in the same locality • Therefore, their accelerations are the same in the absence of air resistance. In a vacuum, a coin and a feather fall equally, side by side. Would it be correct to say that equal forces of gravity act on both the coin and the feather when in a vacuum? 77% 1. Yes 2. No 23% 1 2 In a vacuum, a coin and a feather fall equally, side by side. Would it be correct to say that equal forces of gravity act on both the coin and the feather when in a vacuum? 1. Yes 2. No NO! These objects accelerate equally not because the forces of gravity on them are equal, but because the ratios of their weights to masses are equal. Non-Freefall The Effect of Air Resistance • Force of air drag on a falling object depends on two things. – the frontal area of the falling object—that is, on the amount of air the object must plow through as it falls – the speed of the falling object; the greater the speed, the greater the force • As an object falls through air, the force of air resistance on it increases as its speed increases Terminal Speed v vs t 120 100 80 speed 60 40 20 0 0 10 20 30 40 50 time • When the force of air resistance is equal to the force of gravity on an object, it no longer accelerates. This speed is called terminal velocity. Terminal Speed • The heavier parachutist must fall faster than the lighter parachutist for air resistance to cancel his greater weight. Golf Ball & Styrofoam Ball • A stroboscopic study of a golf ball (left) and a Styrofoam ball (right) falling in air. The air resistance is negligible for the heavier golf ball, and its acceleration is nearly equal to g. Air resistance is not negligible for the lighter Styrofoam ball, which reaches its terminal velocity sooner. A skydiver jumps from a high-flying helicopter. As she falls faster and faster through the air, does her acceleration increase, decrease, or remain the same 90% 1. It increases 2. It decreases 3. It remains the same Acceleration decreases because the 7% 3% net force on her decreases. Net force is equal to her weight minus her air 1 2 3 resistance, and since air resistance increases with increasing speed, net force and hence acceleration decrease. Newton 2 Slide 34

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