Transcript Lecture 3
NEWTON’S LAWS OF MOTION Review Equations for Motion Along One Dimension x vave t x dx v lim t 0 t dt v aave t v dv a lim t 0 t dt Review Motion Equations for Constant Acceleration • 1. v v0 at • 2. x x0 v0t 12 at2 • 3. v2 v02 2ax • 4. vave v v0 2 Dynamics vs Kinematics So far we’ve been studying kinematics, we’ve been describing how things move. We were only concerned with a particles position, velocity or acceleration. But why do things move? What gives objects motion? What is Force? What is Force? Force is either a push or a pull. It is an interaction between two bodies. Force is a vector. It has both magnitude and direction. When force is a result of two objects touching, we call that a contact force. Aside from that there are also long-range forces or field forces Examples of Contact Forces Normal Force Frictional Force Tension Force Examples of Field Forces Gravitational Force Magnetic Force Electric Attraction Fundamental Forces Gravitational Forces – weakest of the four forces Electromagnetic Forces – force between electrically charged particles. Weak Nuclear Forces – responsible for some nuclear phenomena like beta decay Strong Nuclear Forces – only holds inside an atomic nucleus. Superposition of Forces Throwing a basketball into the hoop What are the forces involved? Superposition of Forces Throwing a basketball into the hoop What are the forces involved? Force of your hand on the ball Force of gravity (i.e. weight) Superposition of Forces If we can add forces, we can also separate a force into its components! A Ax Ay Ax A cos Ay A sin Examples Young and Freedman 4.4 A man is dragging a trunk up a loading the loading ramp of a mover’s truck. The ramp has a slope angle of 20.0o, and the man pulls upward with a force F, who’s direction makes an angle of 30o with the ramp. (a) How large a force F is necessary for the component Fx parallel to the ramp to be 60.0 N? (b) How large will the component Fy perpendicular to the ramp then be? Isaac Newton Born January 4, 1643 (December 25, 1642 under old calendar) He was a physicist, mathematician, astronomer, natural philosopher, alchemist and theologian. Considered by many to be the “greatest scientist who ever lived”. He published the “Philosophiæ Naturalis Principia Mathematica” in 1687 which laid the foundations for classical mechanics. He also invented calculus Isaac Newton – lesser known facts Was a religious nut He published more papers on scripture than science. He poured over the bible looking for secret codes. He also poured a lot of effort into alchemy and the philosophers stone Isaac Newton – questionable facts Invented the cat door (pet door) Apple hitting Newton on the head Principia was written due to a bet Christopher Wren was with some astronomers when he bet 40 shillings (around 4,000 php now) that no one could explain elliptical orbits. It took Newton years to find the answer so he didn’t get any money. But he expanded his answers and published Principia. Included in Principia are the Three Laws of Motion First Law of Motion Lets examine an object at rest If there are no forces acting on it the object what will happen to the object? If the sum of forces on an abject equal zero, what will happen to the object? First Law of Motion Lets examine an object in motion If there are no forces acting on it the object what will happen to the object? If the sum of forces on an abject equal zero, what will happen to the object? First Law of Motion Every object continues in its state of rest or of uniform velocity as long as no net force acts on it. Inertia – the tendency of an object to maintain its state of rest or uniform motion Law of inertia A body is in equilibrium if F 0 But wait If you’re in a decelerating car, your body gets thrown forward, but there is no net force acting on you!!! Inertial Frames of Reference Frames of reference where First Law of Motion holds Frames fixed on the Earth can be considered to be inertial frames of reference Frames of reference travelling at constant velocity relative to another inertial frame are also inertial frames (a=0). Mass Mass is usually defined as quantity of matter an object has. We need to be a bit more specific here Mass is a measure of inertia of an object. Uses SI unit kg Mass vs Weight Mass and weight are used interchangeably in everyday language In physics, mass and weight are different Mass is the measure of inertia. It is an intrinsic property of matter. No matter where you are, or where the observer is, your mass will be the same. Weight is the force of gravity on an object. Your weight will be different here than on the moon or in space. Young and Freedman 4.20 An astronauts pack weighs 17.5N on earth and 3.24N on an asteroid. (a) what is the acceleration due to gravity on the asteroid? (b) what is the mass of the pack on the asteroid? What happens then if net Force is not equal to 0 F 0 F Newton’s Second Law of Motion The acceleration of an object is directly proportional to the net force acting on it and indirectly proportional to its mass. The direction of the acceleration is in the direction of the net force acting on the object. F a m F ma Force We now define the Newton 1 Newton is the amount of force needed to accelerate a 1kg object by 1m/s2 1N=1kg m /s2 It is the SI unit for Force Force We now define the Newton 1 Newton is the amount of force needed to accelerate a 1kg object by 1m/s2 1N=1kg m /s2 It is the SI unit for Force Pull of the earth is a force Weight has SI unit of N Example What average force is required to stop an 1,100 kg car in 8.0 s if the car is travelling at 95 km/h Example F ma We have mass, we need acceleration v0 95 km h 26.389m s v 0ms t 8.0s Example v v0 at v v0 a t 0 26.389 a 8 a 3.298m s 2 F ma F (1100kg )(3.298 F 3,600N m s2 ) Newton’s Third Law of Motion Force is an interaction between two objects It always comes in pairs Newton’s Third Law of Motion Whenever one object exerts a force on a second object, the second exerts an equal force in the opposite direction on the first. FAonB FBonA Newton’s Third Law of Motion To every action there is an equal but opposite reaction Remember the action and reaction forces are acting on different objects FAonB FBonA Horse and Cart Paradox Example Giancoli 4-19 A box weighing 77.0N is resting on a table. A rope tied to the box runs vertically upward over a pulley and a weight is hung from the other end. Determine the force the table exerts on the box if the weight on the other side of the pulley weighs (a) 30.0N (b) 60.0N (c) 90.0N 77N Example Force table exerts on the box is just normal force Normal Force = Weight of box on table 77N Application of Newton’s Laws Serway 5-18 A bag of cement weighs 325 N and hangs from three wires. Two of the wires make angles 60.0o and 25.0o with the horizontal. If the system is in equilibrium, find the tensions, T1, T2, T3 in the wires. Young & Freedman 5.10 A 1130 kg car is held in place by a light cable on a very smooth (frictionless) ramp. The cable makes an angle of 31.0o above the surface of the ramp. The ramp itself rises 25.0o above the horizontal. (a) find the tension in the cable. (c) How hard does the surface of the ramp push on the car? Giancoli 4-30 At the instant a race began a 65kg sprinter exerted a force of 720N on the starting block at an angle of 22o with respect to the ground. (a) What is the horizontal acceleration of the sprinter? (b) if the force was exerted for 0.32s with what speed did the sprinter leave the starting block? Serway 5-24 A 5.00 kg object placed on a frictionless, horizontal table is connected to a string that passes over a pulley and then is fastened to a hanging 9.00-kg object. Find the acceleration of the two objects and the tension in the string. Giancoli 4-34 Two masses each initially 1.80 m above the ground, and the massless fricitonless pulley is 4.8m above the ground. What maximum height does the lighter mass reach after the system is released? 4.80 m 2.2 1.80 m 3.2 Friction Results from contact between two surfaces. Parallel to the surface of contact. Always opposite to the relative motion of the two surfaces. Kinetic Friction Frictional force can be approximated to be proportional to normal force f k k N Where µk is the coefficient of kinetic friction Note: friction is not dependent on surface area Static Friction Force of friction that arises even when objects are not in relative motion. f s s N Where µs is the coefficient of Static friction k s Friction Graph Young & Freedman 5.30 A box of bananas weighs 40.0N and rests on a horizontal surface. µs=0.40 while µk =0.20. (a) if no horizontal force is being applied and the box is at rest, what is the friction force exerted on the box. (b) What is the magnitude of friction is a monkey exerts a force of 6.0 N on the box. (c) What is the minimum horizontal force the monkey needs to apply to start the box in motion? (d) What is the minimum horizontal force the monkey needs to keep the box in motion? (e) If the monkey applies a horizontal force of 18.0N what is the magnitude of friction force and the boxes acceleration. Young & Freedman 5.30 FN=40.0N (a) = 0 (b) max fs=0.4*40=16N => fs=6N (c) 16N (d) fk=0.2*40=8N (e) Fnet=ma=F-fk ma=18-8=10N a=10/m=10*9.8/40=2.45m/s2 Serway 5-44 Three objects are connected as shown. Table has µk =0.350. (a) determine the acceleration of each object in the system (b) Determine the tensions in the two chords. Serway 5-49 A block weighing 75.0N rests on a plane inclined at 25.0o to the horizontal. A force F is applied at 40.0o to the horizontal pushing it upward on the plane. If µs =0.363 and µk =0.156 (a) What is the minimum value of F to prevent the block from slipping down the plane. (b) what is the minimum value of F that will start the block up the plane. (c) What value of F will move the block up at constant velocity. Apparent Weight Tension in an elevator cable Elevator has a total mass of 800 kg. its moving downwards at 10 m/s but slows to a stop at constant acceleration for 25.0m. Find the tension T while the elevator is being brought to rest. Apparent Weight Elevator has a total mass of 800 kg. its moving downwards at 10 m/s but slows to a stop at constant acceleration for 25.0m. Find the tension T while the elevator is being brought to rest. A woman is on a scale while riding the elevator. Mass of the woman is 50.0 kg, what is the reading on the scale? Common Movie Mistakes Seat Work/Home Work (time dependent) A block with mass 15.0kg is placed on a frictionless inclined plane with slope 20.0o and is connected to a second block with mass 6.00kg hanging over a small, frictionless pulley. (a) Will the first block accelerate to the left or to the right? (b) What is the magnitude of the acceleration? 15kg 6kg Seat Work/Home Work (time dependent) A block with mass 15.0kg is placed on an inclined plane with slope 20.0o and is connected to a second block with mass 6.00kg hanging over a small, frictionless pulley. If µs= 0.300 and µk= 0.150 (a) Will the system accelerate? Why or why not? (b) If yes, what is the magnitude of the acceleration? 15kg 6kg