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Physics Newton’s Laws of Motion Newton’s Laws of Motion 4.1 Objectives Explain Newton’s first law of motion. Explain Newton’s second law of motion. Explain Newton’s third law of motion. Solve problems in mechanics involving: ¾ Know when to apply the 1st, 2nd, and 3rd Law. ¾ Determine the mass, acceleration, and/or net force for a set of given information in a word problem. ¾ The weight of an object in accelerating objects. ¾ The normal force of an object. object ¾ Use kinematic equations from Uniform motion unit to determine: ¾ Acceleration ¾ Velocity ¾ Displacement Newton’s Laws of Motion 4.2 1 Newton’s First Law or Law of Inertia ¾ “Every body continues in its state of rest or of uniform motion in a straight line unless acted on by a net ( b l (unbalanced) d) external t l fforce to t change h th thatt state.” t t ” ¾ Example: The case of passengers traveling in a car being thrown forward when the brakes are applied suddenly, as in the following figure. Newton’s Laws of Motion 4.3 Newton’s First Law (cont.) Newton’s First law talks about following concepts: ¾ States that an object moving in a frictionless, airless environment continues to move forever with a uniform velocity. ¾ States that force is required to change the velocity of a body arising as a result of the interaction of bodies with each other. ¾ States that only observers in a reference frame that does not accelerate can apply Newton’s laws. Newton’s Laws of Motion 4.4 2 Newton’s Second Law “The acceleration of a body is proportional to the net force acting on it and is in the direction of the net force.” acceleration = Force / mass If F, a, and m represent the force, acceleration, and mass, respectively, the relationship between the three entities can be written as, aןF for constant m, or a ן1/m for constant F, or F=ma “ ” ןmeans proportional Newton’s Laws of Motion 4.5 Two Special Forces The following are two special forces: ¾ Weight, g , FG : The force with which the Earth’s g gravitational force pulls the object. ¾ Weight always acts down. ¾ Weight is not mass. ¾ Weight, force of gravity, is mass times gravity. ¾ Gravity g, is 9 Gravity, 9.8 8 m/s2 The force of gravity, FG, acting on an object of mass, m, is equal to mass times acceleration, which is given by: FG = m g Newton’s Laws of Motion 4.6 3 Two Special Forces(cont.) ¾ Normal Force: The perpendicular force exerted by a surface on the object when an object presses against the surface surface. The following figure displays the normal force, FN, exerted by the table on the book. FN FG = mg FN FG = mg Newton’s Laws of Motion 4.7 Two Special Forces(cont.) ¾ Normal Force: The perpendicular force exerted by a surface on the object when an object presses against the surface surface. The following figure displays the normal force, FN, exerted by the table on the book. FN FN FG = mg Newton’s Laws of Motion FG = mg 4.8 4 Newton’s Third Law “For every action, there is an equal and opposite reaction.” Forces occur in p pairs. You cannot p push on an object j without being pushed back by the object. Action-Reaction Pairs: If you press your hand against the wall, as shown in the figure, you feel that the wall also pushes your hand back with the same force. Newton’s Laws of Motion 4.9 Accelerating Elevators Following are the types of accelerating elevators: ¾ Elevator Moving with Constant Velocity: As displayed in the following figure, if the object is placed on the horizontal platform of a weighing scale, the weight that the scale will indicate will correspond to mg as shown below. ¾ At a constant velocity, a = 0 m/s2 Fnet = m a = m (0 m/s2) = 0 N Fnet = FN – FG 0 = FN – F G FN FN = ? FG = mg Newton’s Laws of Motion 4.10 5 Mass Mass is an INVARIANT!!! What does this mean? The mass of an object remains i th the same any where in the universe. Newton’s Laws of Motion 4.11 Accelerating Elevators (cont.) ¾ Elevator Accelerating Upward: The following figure, displays the weight of an object placed on the horizontal surface of an elevator that is accelerating. accelerating ¾ Determine what the scale will read. ¾ The scale will read the normal force. ¾ Find the normal force FNET = ma FNET = FN – mg FN – mg = ma FN = mg + ma Newton’s Laws of Motion FN (ma) mg FN = ? 4.12 6 Accelerating Elevators (cont.) ¾ Elevator Accelerating Downward: If an object is placed in the elevator accelerating downward, the weight of the object is FN, which is less than mg, mg the force due to gravity, gravity as in the following figure. ¾ Determine what the scale will read. ¾ The scale will read the normal force. ¾ Find the normal force FNET = -ma ma FNET = FN – mg FN – mg = -ma FN = mg – ma FN (-ma) mg FN = ? Newton’s Laws of Motion 4.13 Freebody Diagrams – Examples No Angles A fish is hanging on a scale in an elevator (it could happen). Draw a freebody diagram and write the net force equations for fish for the following scenarios. a) The elevator starting to accelerate up. Newton’s Laws of Motion 4.14 7 Freebody Diagrams – Examples No Angles A fish is hanging on a scale in an elevator (it could happen). Draw a freebody diagram and write the net force equations for fish for the following scenarios. b) The elevator moving up at a constant speed. Newton’s Laws of Motion 4.15 Freebody Diagrams – Examples No Angles A fish is hanging on a scale in an elevator (it could happen). Draw a freebody diagram and write the net force equations for fish for the following scenarios. c) The elevator coming to a stop at the top of the ride. Newton’s Laws of Motion 4.16 8 Summary 1. Newton’s first law of motion states that a body continues in its state unless acted on by an external force to change that state. 2 2. Forces arise due to the interaction between bodies bodies. 3. Newton’s second law of motion states that the net force on a body is equal to mass times the acceleration of the body. 4. In the SI system, the unit of force called the Newton, is defined as the force required to accelerate a mass of 1 kg by 1 m/s2. 5. Newton’s third law of motion states that for every action, there is an equal and opposite reaction. 6. The weight, FG, of a body is the force of gravity on a body. 7. Normal force, FN, is a contact force exerted by a surface on an object. The normal force is perpendicular to the surface. 8. The normal force or scale reading of an object varies when the object is measured in an accelerating elevator. Newton’s Laws of Motion 4.17 9