PHYS 218 sec Review Chap. 4 Newton’s laws of motion

2 Dynamics Studies the relationship of motion to the forces that cause it, i.e., the origin of the motion. Newton’s (three) laws of motion Classical Mechanics (Newtonian Mechanics) Contributions from Copernicus Brahe Kepler Galilei etc Modern Physics RelativityQuantum Mechanics

3 Force & Interactions Force: an interaction between two bodies or between a body and its environment. (There is no force without source.) A force is a vector quantity. Contact force : a force which involves direct contact between two bodies  Normal force exerted on an object by any surface with which it is contact always acts perpendicular to the surface of contact  Friction force exerted on an object by any surface with which it is contact acts parallel to the surface in the direction that opposes sliding  Tension force pulling force exerted by a stretched rope or cord on an object to which it is attached Long-range force : a force which acts even when the bodies are separated by empty space  Gravitational force which gives weight. Macroscopic concept

4 Superposition of forces Any number of forces applied at a point on a body have the same effect as a single force equal to the vector sum of the forces Just as you have learned about vector algebra Unit of force N: Newton See slide number 7 for details.

5 Newton’s first law of motion A body acted on by no net force moves with constant velocity (which may be zero) and zero acceleration. Important concepts Inertia: the tendency of a body to keep moving once it is set in motion a property of a body Equilibrium: when a body is either at rest or moving with constant velocity Therefore, it is moving in a straight line with constant speed

6 Inertial frame of reference Inertial frame See Chap. 3 Inertial frame of reference: A reference frame where Newton’s first law is valid. If a frame is accelerating, it is not an inertial frame. But if a frame is moving with a constant velocity with respect to an inertial frame, it is also an inertial frame. Inertial frame Non-inertial frame Inertial frame

7 Newton’s second law of motion Experimental observation Magnitude of the net force is proportional to the magnitude of the acceleration of the object You can write this relation to an equation by using a proportionality constant, m m is called mass; in fact, this defines mass This defines the unit of force: Newton (N) 1 Newton: the amount of force that gives an acceleration of 1 m/s 2 to a body of 1kg.

8 Inertial mass Newton’s 2nd law gives a way to measure masses. Suppose you have two objects with masses m 1 and m 2. Assume that you know the mass m 1, then you can measure m 2 by applying a constant net force to both objects. Masses determined in this way are called inertial masses.

9 Using Newton’s Second Law Newton’s 2 nd law is written as a vector equation. Consider all forces and write the net force in component form. Then each component satisfies Newton’s 2 nd law. Only external forces should be considered. The above form of Newton’s 2 nd law is valid only when the mass m is constant. Newton’s laws are valid only within an inertial frame. ma is not a force. It is the result of the force applied. Therefore, it should not appear in free-body diagrams.

10 Mass and weight Weight of a body: the gravitational force that the earth exerts on the body This is the force that makes the body accelerate downward. This force should be considered in most problems in Chap. 4 and 5. A body with mass m have weight of which magnitude w is given by w: magnitude of weight, always positive g: gravitation acceleration constant, always positive Therefore, if you choose upward as your positive y-direction, since weight directs always downward, you have –mg for weight. Weight also provides a way to measure masses, Gravitational mass Mass: scalar quantity

11 Newton’s third law of motion If body A exerts a force on body B (this is an action), then body B exerts a force on body A (this is a reaction). These two forces have the same magnitude but are opposite in direction IMPORTANT! These two forces act on different bodies! action-reaction pair Solve examples and problems in the textbook.