Chapter 3

1. Chapter 3 Newton's laws of motion

2. 3 .1 Force,weight,and gravitational mass Forces Kinematics describes motion, but does not explain why motion occurs. In order to explain the cause of motion, we must learn about Statics and Dynamics … and FORCES. mass Pushing force What is a Force? Friction force • a push or pull that one body exerts on another • Vector • the force causes a change in velocity, or an acceleration… Fkick • There are two types of forces that we can see • Contact Forces • At a distance forces Fgrav

3. Contact Force Forces in which the two interacting objects are physically in contact with each other. EXAMPLES Hitting - Pulling with a rope - Lifting weights - Pushing a couch Frictional Force - Tensional Force - Normal Force- Air Resistance Force Applied Force- Spring Force At A Distance Force (field force) • Forces in which the two interacting objects are not in physical contact with each other, but are able to exert a push or pull despite the physical separation. Example: Gravitational Force - Electrical Force - Magnetic Force- Nuclear Forces

4. Measuring Forces • Forces are measured in newtons (kg . m/s2). • Forces are measured using a spring scale.

5. N N What is meant by unbalanced force? If the forces on an object are equal and opposite, they are said to be balanced, and the object experiences no change in motion. If they are not equal and opposite, then the forces are unbalanced and the motion of the object changes. + • Are forces that results in an object’s motion being changed. • velocity changes (object accelerates) Fnet Fpull Ffriction W

6. Balanced Force • A force that produces no change in an object’s motion because it is balanced by an equal, opposite force. • no change in velocity The object shown in the diagram must beat rest since ther is no net force acting on it. FALSE! A net force does not cause motion. A net force causes a change in motion, or acceleration.

8. Example On a horizontal, frictionless surface, the blocks above are being acted upon by two opposing horizontal forces, as shown. What is the magnitude of the net force acting on the 3kg block? A. zero B. 2N C. 1.5 N D. 1N E. More information is needed.

9. Example : Example : 0 a=3.02 m / s

10. Weight Weight = Mass x Gravity The weight of an object is the gravitationalforce that the planet exerts on the object. The weight always acts downward, toward the center of the planet. SI Unit of Weight: Newton (N) • m: mass of the body (units: kg) • g: gravitational acceleration (9.8m/s2, • As the mass of a body increases, its’ weight increases proportionally

11. Weight • the force of gravity on an object W = mg W: weight (N) m: mass (kg) g: acceleration due to gravity (m/s2) MASS always the same (kg) WEIGHT depends on gravity (N)

12. Mass … • is a measure of how much matter there is in something -- usually measured in kilograms in science • causes an object to have weight in a gravitational field • A measure of the resistance of an object to changes in its motion due to a force (describes how difficult it is to get an object moving) • Scalar Note that mass is involved in the force of gravity! This is a separate property from that of inertia, so we give this property the name gravitationalmass.

13. Mass = Inertia – an object’s resistance to motion Would it be more difficult to pull an elephant or a mouse?

14. what is the weight of a 2 kg mass? • W = Fg = mxg = 2 kg x 9.8 m/s2 • = 19.6 N • What is the mass of a 1000 N person? • W = Fg = mxg • m = Fg/g = 1000 N / 9.8 m/s2 • =102 kg • A girl weighs 745 N. What is his mass m = F ÷ g m = (745 N) ÷ (9.8 m/s2) m = 76.0 kg

15. 3.3 Newton's first law Every object continues in a state of rest , or of uniform motion in a straight line , unless it is compelled to change that state by forces acting upon it. An equivalent statement of the first law is that : An object at rest will stay at rest, and an object in motion will stay in motion at constant velocity, unless acted upon by an unbalanced force. This, at first, does not seem obvious. Most things on earth tend to slow down and stop. However, when we consider the situation, we see that there are lots of forces tending to slow the objects down such as friction and air resistance.

16. “Law of Inertia” • Inertia • tendency of an object to resist any change in its motion • increases as mass increases

17. Inertia • Inertia is a term used to measure the ability of an object to resist a change in its state of motion. • An object with a lot of inertia takes a lot of force to start or stop; an object with a small amount of inertia requires a small amount of force to start or stop. • The word “inertia” comes from the Latin word inertus, which can be translated to mean “lazy.”

18. example • A railway engine pulls a wagon of mass 10 000 kg along a straight track at a steady speed. The pull force in the couplings between the engine and wagon is 1000 N. • A. What is the force opposing the motion of the wagon? • B .If the pull force is increased to 1200 N and the resistance to movement of the wagon remains constant, what would be • The acceleration of the wagon? • Solution • a) When the speed is steady, by Newton’s first law, the resultant force must be zero. • The pull on the wagon must equal the resistance to motion. So the force resisting motion is 1000 N. • b) The resultant force on the wagon is 1200 – 1000 = 200 N • By Equation

19. 3.5Newton’s Third Law of Motion • When one object exerts a force on a second object, the second object exerts an equal but opposite force on the first. • IdentifyingNewton’sthirdlawpairs • Each force has thesamemagnitude • Each force acts alongthesame line • but in oppositedirections • Each force acts at thesame time • Each force acts on a differentobject • Each force is of thesametype

20. 3rd Law According to Newton, whenever objects A and B interact with each other, they exert forces upon each other. When you sit in your chair, your body exerts a downward force on the chair and the chair exerts an upward force on your body. All forces come in action-reaction pairs Ex: feet push backward on floor, the floor pushes forward on feet

21. NO!!! • Problem: • How can a horse pull a cart if the cart is pulling back on the horse with an equal but opposite force? • Aren’t these “balanced forces” resulting in no acceleration? • Explanation: • forces are equal and opposite but act on different objects • they are not “balanced forces” • the movement of the horse depends on the forces acting on the horse

22. example a) Find the acceleration of a 20 kg crate along a horizontal floor when it is pushed with a resultant force of 10 N parallel to the floor. b) How far will the crate move in 5s (starting from rest)? Solution b) Distance travelled Δ X Δ X Δ X

23. example A 1kg stone fall freely from rest from a bridge. a -What is the force causing it to accelerate? b -What is its speed 4s later? c -How far has it fallen in this time? Solution The force causing it to fall is its weight. As it is falling with acceleration due to gravity b) c)

24. Action-Reaction Pairs • The hammer exerts a force on the nail to the right. • The nail exerts an equal but opposite force on the hammer to the left. • Single isolated force cannot exist • For every action there is an equal and opposite reaction

25. FG FR • Action-Reaction Pairs • The rocket exerts a downward force on the exhaust gases. • The gases exert an equal but opposite upward force on the rocket. Flying gracefully through the air, birds depend on Newton’s third law of motion. As the birds push down on the air with their wings, the air pushes their wings up and gives them lift.

26. Other examples of Newton’s Third Law • The baseball forces the bat to the left (an action); the bat forces the ball to the right (the reaction).

27. Define the OBJECT (free body) • Newton’s Law uses the forces acting ON object • N and Fg act on object • N’ and Fg’ act on other objects

29. Normal Force Is Not Always Equal to the Weight

30. 3.6 Newton’s Second Law F a m • Newton’s Second Law of Motion • The force F needed to produce an acceleration a is • The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. F = ma F F: force (N) m: mass (kg) a:acceleration (m/s2) 1 N = 1 kg ·m/s2 m

31. F m Newton’s Third Law • Action-Reaction Pairs • Both objects accelerate. • The amount of acceleration depends on the mass of the object. • Small mass  more acceleration • Large mass  less acceleration

32. F a m Newton’s Second Law F m F = ma F: force (N) m: mass (kg) a:acceleration (m/s2) 1 N = 1 kg ·m/s2

33. More about F = ma If you double the mass, you double the force. If you double the acceleration, you double the force. What if you double the mass and the acceleration? (2m)(2a) = 4F Doubling the mass and the acceleration quadruples the force. So . . . what if you decrease the mass by half? How much force would the object have now?

34. Equilibrium • The condition of zero acceleration is called equilibrium. • In equilibrium, all forces cancel out leaving zero net force. • Objects that are standing still are in equilibrium because their acceleration is zero. • Objects that are moving at constant speed and direction are also in equilibrium. • A static problem usually means there is no motion.

36. Example : a2

37. example 8 How much force is needed to accelerate a 1,300 kg car at a rate of 1.5 m/s2? A- 867 N b 1,950 N c 8,493 N d 16,562 N F = m a or = 1300Kg x 1.5m/s2 F = 1950 N

38. Balancing Forces (Statics) • There are often situations where a number of forces are acting on something, and the object has no motion – it is STATIC or in EQUILIBRIUM or at rest. • This means the NET FORCE on the object is zero, or in other words the forces balance each other out. • ΣF = m a • a =0 • ΣF = 0 Objects in equilibrium (no net external force) also move at constant velocity In a two-dimensional problem, we can separate this equation into its two component, in the x and y directions: Σ Fx = 0 Σ Fy = 0

39. unbalanced Forces (Dynamics) • There are other situations where all the forces acting on something do not cancel each other out completely. • This means the NET FORCE on the object is not zero, the object will change its motion and accelerate proportional to the object’s mass. • ΣF = m a

40. The acceleration of an object is equal to the force you apply divided by the mass of the object.

41. If you apply more force to an object, it accelerates at a higher rate. • If an object has more mass it accelerates at a lower rate because mass has inertia.

42. What force would be required to accelerate • a 40 kg mass by 4 m/s2? F = ma F = (40 kg)(4 m/s2) F = 160 N • A 4.0 kg shot-put is thrown with 30 N of force. What is its acceleration? a = F ÷ m a = (30 N) ÷ (4.0 kg) a = 7.5 m/s2

43. Newton’s Second Law of Motion Note that this is a vectorequation, and should really be worked in component form: S Fx = max S Fy = may. We can now see that Newton’s First Law of Motion is really just a special case of his Second Law of Motion.

44. Example • A railway engine pulls a wagon of mass 10 000 kg along a straight track at a steady speed. The pull force in the couplings between the engine and wagon is 1000 N. • ) What is the force opposing the motion of the wagon? • ) If the pull force is increased to 1200 N and the resistance to movement • of the wagon remains constant, what would be the acceleration of the wagon? • Solution • a) When the speed is steady, by Newton’s first law, the resultant force must be zero. • The pull on the wagon must equal the resistance to motion. So the force resisting motion is 1000 N. • b) The resultant force on the wagon is 1200 – 1000 = 200 N • By Equation

45. Example

46. Example a) Find the acceleration of a 20 kg crate along a horizontal floor when it is pushed with a resultant force of 10 N parallel to the floor. b) How far will the crate move in 5s (starting from rest)? Solution Distance travelled

47. A 1kg stone fall freely from rest from a bridge. a -What is the force causing it to accelerate? b -What is its speed 4s later? c -How far has it fallen in this time? Solution The force causing it to fall is its weight. As it is falling with acceleration due to gravity

48. Example :

49. 3 . 7 the significance of Newton's laws of motion • 3 .7 some examples of Newton's laws • Make a diagram (conceptualize) • Categorize: no acceleration (at rest ) • accelerating object: • Isolate each object and draw a free body diagram for each object. Draw in all forces that act on the object. • Establish a convenient coordinate system. • Write Newton’s law for each body and each coordinate component.  set of equations. • Finalize by checking answers.

50. Free body diagram