1. Physics “Forces and the Laws of Motion”

2. "Forces" u kinematics - the study of motion without regard to the forces causing the motion u dynamics - the study of forces which cause motion u force - the product of a body's mass and any acceleration acting on the body

3. Types of Forces u 1. Electric Forces -- forces caused by the interaction of electrons. Most forces we deal with are electric. For example, when you push an object you are creating electric forces between the electrons in your hand and the electrons in the object. Mechanical and frictional forces are electrical forces. u 2. Gravitational forces -- The force of attraction between masses. Gravitational forces are the weakest of all forces. But gravitational forces act over very long distances.

4. Types of Forces u 3. Magnetic forces -- forces produced by moving electric charges. Magnetic forces are closely related to electric forces but the relationship is not completely understood at present. u 4. Nuclear forces -- forces within the nucleus which hold particles together. Nuclear forces are the strongest of the known forces but they act over the shortest distances. u 5. Weak Interaction forces -- the forces which is believed to cause atoms to break apart.

5. Vector Addition: Graphical Method u A vector requires magnitude and direction. u Magnitude is indicated by the length of the arrow representing the vector. u Direction is simply the direction of the arrow. u Vectors are always drawn head to tail. u The result of a series of vectors is measured from the tail of the first vector to the head of the last vector drawn.

6. Sample Problem u A plane flies 300km N, turns and flies 400km E. What is the displacement of the plane from its starting position? u Remember, displacement is a vector requiring both magnitude and direction. u Solve this problem graphically.

7. Solution u 1. Consider the magnitude of the vectors and your sketching area and develop a scale for drawing the diagram. u 2. Draw the vectors using the " head to tail " method being careful with the magnitude and direction. u 3. Measure the length ( Magnitude ) of the resultant and use a protractor to find the angle between the initial vector and the resultant. u 4. Express your answer indicating both magnitude and direction. The direction should have both degrees and the general direction.

8. Vector Operations Mathematical Method u c 2 = a 2 + b 2 u sin x = opp/hyp u cos x = adj/hyp u tan x = opp/adj u A man walks 3m N and 4m E. Find the resultant vector of his walk.

9. Resolving Vectors Into Components u It is possible to regard a single vector as two perpendicular components; i.e., two vectors acting at a 90 0 angle to each other. u This is useful in determining the most efficient angle for force application in many areas such as pushing lawn mowers, hanging signs, pulling sleds, etc. u You will see as we work problems in this area that you increase or decrease the angle of application of forces automatically simply because it "feels" right.

10. Example u A boy pulls on a sled with a force of 80N. If the angle of the rope with the ground is 30 0, find the horizontal component ( that force which is actually causing horizontal motion). u Find the vertical component of the applied force (that force which is used to overcome friction). friction - the opposition to motion u What general statement can be made concerning the angle of applied force? u As the angle of the applied force increases, the horizontal force _____________? u Find the component velocities of a helicopter traveling 95km/h at an angle of 35 0 with the ground.

11. Adding Vectors That Are Not Perpendicular u law of cosines - c 2 = a 2 + b 2 - 2ab cos C u law of sines - a/Sin A = b/ Sin B = c/ SinC u A hiker walks 25.5km from her base camp at 35 0 south of east. On the second day, she walks 41.0km in a direction 65 0 north of east, at which point she discovers a forest ranger’s tower. Determine the magnitude and direction of her resultant displacement between the base camp and the ranger’s tower. u Page 121, 1-4

12. Changes in Motion Changes in Motion u 1. A net force will change the state of motion of an object. u 2. Forces can be exerted through long distances. u 3. Forces always occur in pairs. u 4. In each pair of forces, one acts opposite the other.

13. Units System Mass Acceleration Force SI kg m/s 2 N- kg m/s 2 cgs g cm/s 2 dyne-g cm/s 2 Avoirdupois slug ft/s 2 lb-slug ft/s 2 Forces are vectors, the product of a vector and a scalar.

14. Newton's Laws of Motion u Newton's First Law of Motion ( Law of Inertia ) u An object at rest or in motion will remain so until acted upon by an outside (net) force. u inertia - the resistance of a body to change its state of motion.

15. Sample Problem u Derek left his physics book on top of a drafting table. The table is inclined at a 35 0 angle. Find the net external force acting on the book, and determine whether the book will remain at rest in this position.

16. Newton's Second and Third Laws of Motion u Newton's Second Law of Motion u When an unbalanced force acts on an object, the object will be accelerated. The acceleration will vary directly with the applied force and inversely with the mass of the object. u Equation: F = ma

17. Sample Problem u A 5.5kg watermelon is pushed across a table. If the acceleration of the watermelon is 4.2m/s 2 to the right, find the net external force exerted on the watermelon.

18. Newton's Third Law of Motion u For every action there is an equal and opposite reaction. u This is the law of interaction.

19. Everyday Forces u Mass depends on the amount of matter a body possesses. Weight depends on the distance an object is from the center of the earth. u A question for thought; If an object fell down a very deep hole, is there a point at which the object would become weightless? u F = maF w = mgF w = weight, g = 9.8 m/s 2, etc.

20. Sample Problems u Find the weight of a 2 kg object. u Find the mass of an object which weighs 49N.

21. Friction u Friction is the force which opposes the motion of two surfaces in contact. u Static friction is the force which opposes the start of motion. u Sliding friction is the force which opposes motion in progress. Sliding friction is much less than static friction. u Rolling friction is the force which opposes motion between a rolling object and the surface on which it rolls.

22. Coefficient of Friction u The ratio of the static frictional force,( F s ), to the force between two objects in contact, (F n ), is known as the coefficient of friction. The normal force, ( F n ), always acts perpendicular to the surfaces in contact. u F s   = ------- u F n

23. Sample Problem u A 24kg crate initially at rest on a horizontal surface requires a 75N horizontal force to set it in motion. Find the coefficient of static friction between the crate and the floor.

24. Sample Problem u A student moves a box of books by attaching a rope to the box and pulling with a force of 90.0N at an angle of 30.0 0. The box of books has a mass of 20.0kg, and the coefficient of kinetic friction between the bottom of the box and the sidewalk is 0.50. Find the acceleration of the box.

25. Experiment u You will be given a metal block and a wooden board to use as an incline. Use this material to determine the coefficient of static friction between the metal and the wood. u Your group will write one ppoc and be prepared to share the results with the class by giving a presentation.

26. Vocabulary Review u Terms u force u inertia u Newton’s 3 Laws of Motion u friction u Truths about forces