2.  Scalars are quantities that have magnitude only, such as › position › speed › time › mass  Vectors are quantities that have both magnitude and direction, such as › displacement › velocity › Acceleration › Forces

3.  Vector direction is the direction of the arrow, given by an angle.  This vector has an angle that is between 0 o and 90 o. A x 

4.  The best way to determine the magnitude (or size) of a vector is to measure its length.  The length of the vector is proportional to the magnitude (or size) of the quantity it represents.

6.  How fast your speed or velocity is changing in a particular time.  Units or  Accelerating › Velocity and Acceleration vectors in same direction  Decelerating › Velocity and acceleration vectors in opposite directions.

8. Review Newton’s Laws What is required to change an object’s motion? An UNBALANCED Force UNBALANCED Force = NET Force NET Force =  F (Sum of forces) What results if an unbalanced force is applied to an object? ACCELERATION Newton’s Second Law of Motion The acceleration of an object is proportional to the net force applied to the object and inversely proportional to the object’s mass.

10. Equation of Newton’s Second Law of Motion  F = ma Questions How do we know if we have an unbalanced force? If there is an unbalanced force, in what direction is it acting? Answer FREE-BODY DIAGRAM A vectors diagram of the forces acting on an object.

13.  Force that opposes motion between two materials sliding past one another. › Depends on the type of materials used › Can occur with fluids as well as solids  Air resistance  Water resistance

14.  Units › SI = Newton (N) › English = Pounds (lbs.)  Formula › F f =  F N › Friction is “F  N”

15.  Greek letter  (pronounced “mu”).  A ratio between the frictional force to the normal force › No units because it’s a ratio  Values depend on type of surface and type of friction. › metal on metal static friction (  s ) = 0.18 › metal on metal kinetic friction (  k ) = 0.15 › metal on wood kinetic friction (  k ) = 0.5  Large coefficients = large frictional forces  Small coefficients = small frictional forces

16. How to draw a Free Body Diagram (FBD) Rules 1.Draw an arrow representing the weight of the object. 2.Label the arrow F g. 3. Draw additional arrows in the appropriate directions to represent any forces acting on the object. The length of the arrows should be proportional to the quantity of the force.

17. FBD Rules (Continuted) 4.Label arrows with appropriate names, e.g.: 4.Force of Gravity, F g 5.Tension, F T 6.Normal, F N 7.Friction, F f 5.Remember, ONLY the arrows constitute the free body diagram (FBD), not the object.

18. Free-Body Diagram Construction Horizontal / Vertical Scenarios #1 A car is at Rest on a level road. Draw the Free- Body Diagram of the forces acting on the car. NO air resistances. F gravity F normal Forces are balanced, so example of Newton’s 1 st Law

19. Free-Body Diagram Construction #2 A car is driving on a level road at a constant velocity. Draw the Free-Body Diagram of the forces acting on the plane. Consider Air Resistance and friction. F gravity F normal F air F engine Forces are balanced again, another example of Newton’s 1 st Law F friction

20. Free Body Diagram Construction #3 A car is driving on a level road with an increasing velocity. Draw the Free-Body Diagram of the forces acting on the car. Consider Air Resistance. F gravity F normal F air F engine Forces are unbalanced, so example of 2 nd Law Acceleration F friction

21. Free Body Diagram Construction #4 A car is driving on a level road with an decreasing velocity. Draw the Free-Body Diagram of the forces acting on the car. Consider Air Resistance. F gravity F normal F air F engine Forces are also unbalanced, example of 2 nd Law Acceleration F friction

22. Example Problem 1 2 students pushed on a hockey goal that is situated in the middle of a hockey rink. Michael pushed with a force of 150 N to the west and Katie pushed with a force of 50 N to the north. A.) Draw a FBD for the situation first. B.) What was the magnitude and direction of resultant force?

23. Example Problem 2 Fred and Wilma push a stalled car at constant velocity along level ground. If Fred and Wilma push to the right with 550 N and 375 N respectively, what is the magnitude of the opposing force? Identify the opposing force. constant velocity means acceleration = 0 So  F = 0 F 1 + F 2 + ??? = 0 What would F 3 need to be so  F = 0?

24. Example Problem 3 Two forces are applied to a 10 kg block. Calculate the net force block on the block if F 1 equals 15 N and F 2 equals 30 N. A.) What is the block’s acceleration? F1F1 F2F2 10 kg B.) What is the Normal force for the block?

25. Example Problem 3 Two forces are applied to a 10 kg block. Calculate the net force block on the block if F 1 equals 15 N and F 2 equals 30 N. F1F1 F2F2 10 kg C.) If the box is sliding to the right what is the friction force? D.) Calculate the coefficient of friction (  ) for the box and the floor.