# Ground Rules. PC1221 Fundamentals of Physics I. Force. Zero Net Force. Lectures 9 and 10 The Laws of Motion. Dr Tay Seng Chuan

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1 PC1221 Fundamentals of Physics I Lectures 9 and 10 he Laws of Motion Dr ay Seng Chuan 1 Ground Rules Switch off your handphone and pager Switch off your laptop computer and keep it No talking while lecture is going on No gossiping while the lecture is going on Raise your hand if you have question to ask Be on time for lecture Be on time to come back from the recess break to continue the lecture Bring your lecturenotes to lecture 2 Force Forces can cause a change in the velocity of an object his is because a force can causes an acceleration he net force is the vector sum of all the forces acting on an object A net force is also called the total force, resultant force, or unbalanced force Zero Net Force When the net force is equal to zero: he acceleration is equal to zero he velocity is constant Equilibrium occurs when the net force is equal to zero he object, if at rest, will remain at rest If the object is moving, it will continue to move at a constant velocity 3 4

2 Classes of Forces Contact forces involve physical contact between two objects Field forces act through empty space No physical contact is required Fundamental Forces Gravitational force Between two objects Electromagnetic forces Between two charges Nuclear force Between subatomic particles Weak forces Arise in certain radioactive decay processes 5 6 More About Forces A spring can be used to calibrate the magnitude of a force Forces are vectors, so you must use the rules for vector addition to find the net force acting on an object Newton s First Law If an object does not interact with other objects, it is possible to identify a reference frame in which the object has zero acceleration his is also called the law of inertia It defines a special set of reference frames called inertial frames, We call this an inertial frame of reference 7 8

3 Inertial Frames Newton s s First Law Alternative Statement Any reference frame that moves with constant velocity relative to an inertial frame is itself also an inertial frame A reference frame that moves with constant velocity relative to the distant stars is the best approximation of an inertial frame We can consider the Earth to be such an inertial frame inertial frame constant velocity inertial frame In the absence of external forces, when viewed from an inertial reference frame, an object at rest remains at rest and an object in motion continues in motion with a constant velocity Newton s s First Law describes what happens in the absence of a force It tells us that when no force acts on an object, the acceleration of the object is zero 9 10 Inertia and Mass Which string will be broken? he tendency of an object to resist any attempt to change its velocity is called inertia Mass is that property of an object that specifies how much resistance an object exhibits to changes in its velocity 11 A B 100 kg If we pull string B downward slowly, which string will be broken or both will be broken? Why? What if we pull string B downward at very fast speed, which string will be broken or both? Why? 12

4 More About Mass Mass is an inherent property of an object Mass is independent of the object s surroundings Mass is also independent of the method used to measure it Mass is a scalar quantity he SI unit of mass is kg Mass vs. Weight Mass and weight are two different quantities Weight is equal to the magnitude of the gravitational force exerted on the object Weight will vary with location Newton s s Second Law When viewed from an inertial frame, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass Force is the cause of the change in motion. he change in motion is measured by the acceleration Algebraically, ΣF = m a More About Newton s Second Law ΣF is the net force his is the vector sum of all the forces acting on the object Newton s Second Law can be expressed in terms of 3 components: ΣF x = m a x ΣF y = m a y ΣF z = m a z 15 16

5 Units of Force Gravitational Force he gravitational force, F g, is the force that the earth exerts on an object his force is directed toward the center of the earth Its magnitude is called the weight of the object Weight = F g = mg More About Weight Because weight is dependent on g, the weight varies with location g, and therefore the weight, is smaller at higher altitudes Weight is not an inherent property of the object Gravitational Mass vs. Inertial Mass In Newton s Laws, the mass is the inertial mass and measures the resistance to a change in the object s motion In the gravitational force, the mass is determining the gravitational attraction between the object and the Earth Experiments show that gravitational mass and inertial mass have the same value 19 20

6 Newton s s hird Law If two objects interact, the force F 12 exerted by object 1 on object 2 is equal in magnitude, and opposite in direction, to the force F 21 exerted by object 2 on object 1 F 12 = - F 21 Note on notation: F AB is the force exerted by A on B Newton s hird Law, Alternative Statements Forces always occur in pairs A single isolated force cannot exist he action force is equal in magnitude to the reaction force and opposite in direction One of the forces is the action force, the other is the reaction force It doesn t matter which is considered the action and which the reaction he action and reaction forces must act on different objects and be of the same type Action-Reaction Examples, 1 Which direction is the vehicle moving? he force F 12 exerted by object 1 on object 2 is equal in magnitude and opposite in direction to F 21 exerted by object 2 on object 1 F 12 = - F (i) he fan on vehicle is switched off but a fan on the left of the vehicle is switched on. (ii) he fan on vehicle is switched on and the sail is removed (the fan on the left is switched off). (iii) he fan on vehicle is switched on and the sail is attached (the fan on the left is switched off). 24

7 Action-Reaction Examples, 2 he normal force (table on monitor) is the reaction of the force the monitor exerts on the table Normal means perpendicular to the surface he action (Fig, Earth on monitor) force, i.e. the weight of monitor, is equal in magnitude and opposite in direction to the reaction force Applications of Newton s Law Assumptions Objects can be modeled as particles Masses of strings or ropes are negligible When a rope attached to an object is pulling it, the magnitude of that force,, is the tension in the rope Objects in Equilibrium If the acceleration of an object that can be modeled as a particle is zero, the object is said to be in equilibrium Mathematically, the net force acting on the object is zero F = 0 F x = 0and F = 0 y Equilibrium, Example 1a A lamp is suspended from a chain of negligible mass he forces acting on the lamp are the force of gravity (Fig) the tension in the chain () Equilibrium gives F = 0 F = 0 y g = F g 27 28

8 Equilibrium, Example 1b If the chain is hooked on ceiling, the chain exerts a force of on the ceiling On the ceiling the force acted on the chain is also Equilibrium, Example 2 Let the mass of the traffic light be m. We have mg = 3 3 = 1 sin (37 ) + 2 sin (53 ) mg Objects Experiencing a Net Force If an object that can be modeled as a particle experiences an acceleration, there must be a nonzero net force acting on it. Newton s Second Law, Example 1a hree Forces acting on the crate: A tension, the magnitude of force he gravitational force, Fig he normal force, n, exerted by the floor Ignore friction at the moment

9 Newton s Second Law, Example 1b Apply Newton s Second Law in component form: F = = ma x F = n F = 0 n = F Solve for the unknown(s) If is constant, then a is constant and the kinematic equations can be used to describe the motion of the crate x y g g 33 Note About the Normal Force he normal force is not always equal to the gravitational force of the object For example, in this case y and F = n F F = 0 g n = Fg + F Normal force (n) may also be less than the weight (Fig ). How? Use air cushion! ie a string on the book and pull it up! Etc. 34 Inclined Planes Forces acting on the object: he normal force, n, acts perpendicular to the plane he gravitational force, F g, acts straight down Choose the coordinate system with x along the incline and y perpendicular to the incline Replace the force of gravity with its components mg sinө = ma mg cosө = n What if Ө =0? 35 Example. A van accelerates down a hill, going from rest to 30.0 m/s in 6.00 s. During the acceleration, a toy (m = kg) hangs by a string from the van's ceiling. he acceleration is such that the string remains perpendicular to the ceiling. Determine (a) the angle and (b) the tension in the string. Answer: mg Ө 36

10 Example. A 5.00-kg object placed on a frictionless, horizontal table is connected to a cable that passes over a pulley and then is fastened to a hanging 9.00-kg object, as in Figure. Find the acceleration of the two objects and the tension in the string. Answer: mg = 9 a 9 x 9.8 = 9 a 88.2 = 9 a --- (1) = 5 a --- (2) Substitute (2) in (1) a = 9 a 14 a = 88.2 a = 6.3 m/s 2 Forces of Friction When an object is in motion on a surface or through a viscous medium, there will be a resistance to the motion his is due to the interactions between the object and its environment his resistance is called the force of friction mg = 5 a = 5 x 6.3 = 31.5 N Forces of Friction, cont. Forces of Friction, final Friction is proportional to the normal force f s µ s n and ƒ k = µ k n hese equations relate the magnitudes of the forces, they are not vector equations he force of static friction is generally greater than the force of kinetic friction he coefficient of friction (µ) depends on the surfaces in contact n push f s = µ s n mg he direction of the frictional force is opposite to the direction of motion and parallel to the surfaces in contact he coefficients of friction are independent of the area of contact n push as = µ s n mg 39 40

11 Static Friction Static friction acts to keep the object from moving If F increases, so does ƒ s If F decreases, so does ƒ s ƒ s µ s n where the equality holds when the surfaces are on the verge of slipping Called impending motion Kinetic Friction he force of kinetic friction acts when the object is in motion Although µ k can vary with speed, we shall neglect any such variations ƒ k = µ k n Friction in Newton s Laws Problems Friction is a force, so it is included in the ΣF in Newton s Laws he rules of friction allow you to determine the direction and magnitude of the force of friction Friction Example, 1 he block is sliding down the plane, so friction acts up the plane his setup can be used to experimentally determine the coefficient of friction µ = tan θ For µ s, use the angle where the block just slips For µ k, use the angle where the block slides down at a constant speed 43 44

12 Example. wo blocks connected by a rope of negligible mass are being dragged by a horizontal force F. Suppose that F = 68.0 N, m 1 = 12.0 kg, m 2 = 18.0 kg, and the coefficient of kinetic friction between each block and the surface is (a) Draw a freebody diagram for each block. (b) Determine the tension and the magnitude of the acceleration of the system. Example. Each of this toy bus s two sets of wheels, front or back, can be locked so that they are no longer free to roll. Given that the coefficient of rolling friction is greater than that of sliding, which set of wheels should be locked (front two, or back two) if we want the car to travel smoothly down the incline plane? Answer: Is locking the front wheels the right place? Why? Is locking the back wheels the wrong place? Why? Answer: Rolling friction Sliding friction Sliding friction Rolling friction 47

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