Forces & the Laws of Motion

1. Forces & the Laws of Motion Chapter 4

2. 4.1 Changes in Motion • Objectives: • Explain how force affects the motion of an object • Distinguish between contact forces and field forces • Interpret and construct free-body diagrams

3. Force • What is a force? • A push or pull that can change the motion of an object • What is the SI unit for force? • The newton (N) • One newton is the force required to accelerate a 1-kg mass at 1 m/s2 • 1N = 1 kg·m/s2 1N = 0.225 lbf • 1lbf = 4.448 N

4. Forces act through contact or at a distance • Contact forces: • Forces that affect an object through physical contact with another object • Example: a baseball bat hitting a baseball • Field forces: • Forces that affect an object without physical contact • Examples: gravitational, magnetic, and electrostatic forces

5. Field Theory • Explains how forces can affect an object without physical contact • Explanation of field forces… • An object affects the space surrounding it so that a force is exerted on other objects in that space. • The “field” is the region of space in which the force is exerted • Example: magnetic field

6. Electrostatic Forces • Example of a field force • Stream of ethanol is attracted to an electrically charged probe

7. Force Diagrams • Force is a vector • Force diagrams: • Diagram the objects involved in a situation and the forces acting on the objects • Free-body diagrams: • Diagram the forces acting on a single object • i.e. diagram the object “free” from influence of other objects and their forces

8. Representing Forces • Force is a vector • Free-body diagrams illustrate forces acting on an object isolated from its surroundings

9. Free-body Diagrams • Free-body diagrams are diagrams used to show the relative magnitude and direction of all forces acting upon an object in a given situation • Represent object as a box with forces originating from center of box

10. Example of a Free-Body Diagram

11. Common Forces in Force Diagrams • Applied force Fapp • Weight Fg (mg) • Normal force FN ┴ to surface • Friction Ff • Air resistance Fair • Tension Ftens • Spring force Fspring

12. Force Equilibrium • Force equilibrium • All forces “cancel” • No net force acting on an object • Can an object in force equilibrium be in motion?

13. 4.2 Newton’s First Law:Law of Inertia • Galileo noted that things tend to slide further on smoother surfaces • Concluded that an object would slide forever on a perfectly smooth surface in the absence of any applied force • This led to Newton’s First Law of Motion

14. Newton’s First Law of Motion:Inertia • An object at rest remains at rest, and an object in motion continues in motion in a straight line, with a constant velocity, unless acted upon by a net external force • Inertia: the tendency of an object to maintain its state of motion • When net force on an object is zero, acceleration is zero (∆v/∆t= 0)

15. Newton’s First Law of Motion • An object at rest remains at rest, and an object in motion continues in motion with a constant velocity unless acted upon by a net external force • A net force is required to change the state of motion of an object • Net external force • Resultant force produced from combination of all forces acting on an object

16. Net External Force • Typical external forces: gravity (weight = mg) = 22N normal force ┴ to surface = 18N push/pull =0 friction = 11N • A book is left on a drafting table with an incline of 35˚ • Identify forces acting on the book & calculate Fnet (sum of x & y components)

17. Forces Acting on Inclined Planes • FN, normal force, surface acting on object • Fg, weight = mg • Fgx, component of g, ║ to surface • Fgy, component of g ┴ surface • Ff, friction

18. Calculating Net External Force • Identify variables & select equation • Draw free-body diagram and apply coordinate system • Calculate x & y components of all vectors • Calculate x & y components of the resultant Fnet (Fx, Fy) • Calculate net external force (Fnet)

19. Inertia • Inertia is tendency of an object to maintain its state of motion unless acted upon by a net force • Mass is a measurement of inertia • ↑ mass → ↑ inertia • As the same speed, a rolling car is more difficult to stop than a rolling basketball

20. Equilibrium • The state of a body in which there is no change in motion • Net force acting on a body is zero

21. 4.3 Newtons 2nd & 3rd LawsLearning objectives • Describe acceleration of an object in terms of its mass and the net external force acting on it • Predict direction & magnitude of acceleration caused by a known net external force • Identify action-reaction force pairs • Explain why action-reaction pairs do not result in equilibrium

22. Newtons 2nd Law • The acceleration of an object is directly proportional to the net external force acting on the object and inversely proportional to the mass of the object • a = ΣFnet /m , where Σ means “sum of” • ΣFnet = ma

23. Conceptual Question A grain truck filled with soy beans accelerates along the highway at 0.50 m/s2. If the driving force on the truck remains the same, what happens to the acceleration of the truck if soybeans leak from it at a constant rate? Answer: The loss of soy beans is a decrease in mass. Since a = ΣFnet /m , acceleration increases.

24. Newton’s 3rd Law • "For every action, there is an equal and opposite reaction." equal magnitude and opposite direction • In every interaction, there is a pair of forces acting on the two interacting objects. • Action-reaction force pairs: equal in magnitude, but opposite in direction.

25. Action-Reaction Force Pairs • Since force pairs are equal in magnitude, but opposite in direction, why do they not result in equilibrium? • Because they act on different objects. • If equal but opposite forces acted on the same object, there would be equilibrium, i.e. no net force.

26. 4.4 Everyday Forces • Weight Force of gravity acting on a mass Fg = mg W = mg Fw = mg • Normal Force contact force exerted by one object on another in a direction ┴ surface of contact • Friction contact force that opposes motion…. opposes applied force

27. Weight & Normal Force • Fg = mg • Always ┴surface of earth • Directed toward center of earth • FN = Fgcos (θ) • Always ┴surface of contact • Always opposes Fg

28. Identify Forces Acting on Inclined Planes • FN, normal force, surface acting on object • Fg, weight = mg • Fgx, component of g, ║ to surface • Fgy, component of g ┴ surface • Ff, friction

29. Force of Friction • Ff opposes applied force • Static friction Ffs …. force exerted by environment on motionless body to resist applied force • Kinetic friction Ffk …. force exerted by environment on moving object to resist applied force • Ffs > Ffk • Depends on surfaces in contact…. Types and smoothness • Proportional to FN

30. Static vs. Kinetic Friction

31. Relationship of Ff and Fn • Ff is proportional to FN • Proportionality constant is the coefficient of friction, μ • μ = Ff/ FN • Depends on types of surfaces in contact • Depends on static or kinetic friction μs = Fs / FN μk = Fk/ FN

32. Problem 4C • A crate of mass 24 kg is set in motion on a horizontal surface with a horizontal force of 75 N. Find the coefficient of static friction, μs • μs = Fs / FN • = Fs / mg • = 75 N / (24 kg x 9.81 m/s2) • = 0.32

33. Coefficients of Friction(Approximate)

34. Role of Surface in Friction • Static friction increases with increasing force until overcome • Kinetic friction is less than the maximum static friction

35. Frictional & Applied Force

36. Fn Fn Fa Fa Fay Fk Fk Fax Fg Fg