2.2 Forces. 2.2 Forces. Kari Eloranta Jyväskylän Lyseon lukio International Baccalaureate. October 31, Kari Eloranta

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1 Kari Eloranta 2015 Jyväskylän Lyseon lukio International Baccalaureate October 31, 2016 Kari Eloranta 2015

2 Newton s Laws of Motion 2.2 Newton s First Law of Motion Definition of Newton s First Law of Motion (Law of Inertia) An object at rest remains at rest, and an object in motion continues to move at constant speed along a straight line, unless acted upon by an unbalanced force. For example, a ball rolls on a floor along a straight line very easily, because the resistive forces on the ball are so small. Definition of inertial frame of reference An inertial frame of reference is a reference frame in which Newton s First Law is valid. An inertial frame of reference cannot be in accelerated motion. The laws of physics are valid as such in inertial reference frames only. Question. Is the observer in the physics class room in an inertial frame of reference?

3 Newton s Laws of Motion 2.2 Objects as Point Particles Often, we treat objects as point particles as if all the mass of the object would be concentrated at the centre of mass of the object. For homogeneous objects, the centre of mass is the middle point (point of symmetry). If you throw on extended object at an angle, the centre of mass of the object moves along a parabola. For example, see the flying kitten. Point particles do not have any dimensions. As a result, they cannot break, deform, or rotate.

4 Newton s Laws of Motion 2.2 Newton s Second Law of Motion Usually, several external forces act on an object. As an example, consider a book on a table. The weight W #» pulls the book towards the center of the Earth, and the normal reaction force exerted by the table on the book R #» pushes the book up. Since the forces are equal in magnitude, but opposite in direction, they cancel each other out. The net force Σ #» F is the vector sum of the external forces acting on an object. Definition of Newton s Second Law of Motion The net force is equal to the mass of the object multiplied by its acceleration. Any force on the object is a result of an interaction between the object and its surroundings.

5 Newton s Laws of Motion 2.2 Newton s Second Law of Motion Newton s Second Law as an Equation The net force is Σ #» F = m #» a (1) where m is the mass of the object and #» a the acceleration of the object. The data booklet reference does not use vector notation (F = ma). For the calculation of the net force we first have to find all the forces acting on the object. First, we identify distant interactions. If the object is electrically neutral, the only distant interaction is the gravitational interaction. The resulting force is the weight of the object #» G (force of gravity). Second, we identify contact interactions. The examples of contact forces include normal reaction force ( R #» ), solid friction (static and dynamic) F #» f, tension force T #» and buoyant force F #» b.

6 Newton s Laws of Motion 2.2 Newton s Third Law of Motion Definition of Newton s Third Law of Motion When two bodies interact, they exert equal but opposite forces on one another. #» F Moon on Earth #» F Earth on Moon Figure: According to Newton s Third Law of Motion the gravitational interaction between the Earth and Moon results in the equal but opposite forces on them.

7 Newton s Laws of Motion 2.2 Newton s Third Law of Motion Any force on an object is a result of interaction between two objects. As a result, forces come in pairs: one force on each object. Both objects feel the forces simultaneously if the force on the first object changes, the force on the second object changes exactly at the same moment. Force applied on the first object is always applied by the second object and vice versa. The force and reaction force act on different objects. Thus, they cannot cancel each other out. The force and reaction force are caused by the same interaction. For example, the weight of a book is caused by the gravitational interaction between the book and the Earth. The normal reaction force on the book is caused by the contact interaction between the book and table. As a result, normal force cannot be the reaction force to the weight.

8 Translational Equilibrium Translational Equilibrium Forces tend to accelerate, rotate and deform objects. From the Newton s First Law of Motion we know that if an object is at rest, there are no unbalanced forces acting on it. We say that the object is at translational equilibrium. The same would be true for a moving object at constant velocity. Translational Equilibrium An object is in translational equilibrium, when it is either at rest or moves at constant velocity along a straight line. Then, from Newton s Second Law of Motion, it follows that the net force acting on the object is Σ #» F = #» 0. (2)

9 Translational Equilibrium Free-body Diagrams To deduce the state of motion of an object, we need to determine the forces acting on it. In a free-body diagram the forces are represented by vectors acting on the object at a specific point of application. The length of a force vector represents the magnitude of the force and the arrowhead indicates the direction. The starting point of an vector arrow represents the point of application from which the force is exerted.

10 Friction 2.2 Solid Friction Whenever two bodies are in contact, friction opposes the relative motion of the bodies. For two ideal solid objects, the friction depends only on the material of the objects, not the surface area or relative speed. Static friction prevents objects from moving with respect to each other, and dynamic friction opposes the motion of sliding objects. Friction stems from intermolecular forces between interacting surfaces, and roughness of the materials involved. Overall, it is an extremely complicated phenomenon that remains to be only partially understood by physicists.

11 Friction 2.2 Static Friction Static Friction Friction between objects at rest with respect to each other is called static friction. Experiments have shown that fro two ideal solid objects the maximum value of static friction is proportional to normal reaction force #» R, and does not depend on the surface area of interacting objects. Static Friction Static friction F f between two solid surfaces is always less or equal than the maximum value of fully developed static friction, that is F f µ s R (3) where µ s is the coefficient of static friction of two surfaces, and R is the normal reaction force on a surface.

12 Friction 2.2 Dynamic Friction Dynamic Friction Friction between objects in contact, and in relative motion with respect to each other, is called dynamic (kinetic) friction. Experiments have shown that for ideal solid objects, the dynamic friction is independent of the relative speed and surface area. Dynamic Friction When two objects slide on one another, the dynamic friction between the objects is F f = µ d R (4) where µ d is the dynamic friction coefficient of two surfaces, and R is the normal reaction force on a surface. The dynamic friction depends on the material of interacting objects, and on the evenness of the surfaces.

13 Friction 2.2 Evolution of Static and Dynamic Friction N F f Static friction increases in a steady pull Static friction reaches maximum, and object starts moving at t = 6.2s. Dynamic friction equals the pulling force Figure: As a wooden block is pulled on a stony surface by gradually increasing the pulling force, the static friction increases until it reaches the maximum value (F f 9.0N = µ 0 R). When the block starts moving, the sliding friction opposes the motion (F f = 6.4N = µr). t s