1. The Laws of Motion

2. Classical Mechanics Describes the relationship between the motion of objects in our everyday world and the forces acting on them Describes the relationship between the motion of objects in our everyday world and the forces acting on them Conditions when Classical Mechanics does not apply Conditions when Classical Mechanics does not apply very tiny objects (< atomic sizes) very tiny objects (< atomic sizes) objects moving near the speed of light objects moving near the speed of light

3. Forces Usually think of a force as a push or pull Usually think of a force as a push or pull Vector quantity Vector quantity May be contact or field force May be contact or field force

4. Fundamental Forces Fundamental Forces Interaction (force) Strength (compared to strong) Strong1 Electromagnetic1/100 Weak1/1,000,000 Gravitational1/10 43 Characteristics All field forces

5. Newton’s First Law An object at rest remains at rest and an object moving with some velocity continues with that same velocity, unless something exerts an unbalanced force on it An object at rest remains at rest and an object moving with some velocity continues with that same velocity, unless something exerts an unbalanced force on it Alternative statement of Newton’s 1 st Law Alternative statement of Newton’s 1 st Law When there are no external forces acting on an object, the acceleration of the object is zero. When there are no external forces acting on an object, the acceleration of the object is zero.

6. Inertia Is the tendency of an object to continue in its original state of motion Is the tendency of an object to continue in its original state of motion

8. Mass A measure of the resistance of an object to changes in its motion due to a force A measure of the resistance of an object to changes in its motion due to a force Scalar quantity, SI unit is kg Scalar quantity, SI unit is kg More mass, more inertia More mass, more inertia

10. Newton’s Second Law -1 The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. F and a are both vectors F and a are both vectors

11. 1) A constant Force acting on 2 different masses: Newton’s Second Law-2 mass Acceleration

12. 2) Different forces acting on 2 identical objects Force Acceleration

13. Newton’s Second Law - 3 mass Force 3) Different masses having the same acceleration

14. Units of Force SI unit of force is a Newton (N) SI unit of force is a Newton (N) US Customary unit of force is a pound (lb) US Customary unit of force is a pound (lb) 1 N = 0.225 lb 1 N = 0.225 lb 1N = weight of an apple 1N = weight of an apple 10 N ~ 1 kg 10 N ~ 1 kg

15. Weight The magnitude of the gravitational force acting on an object of mass m near the Earth’s surface is called the weight w of the object The magnitude of the gravitational force acting on an object of mass m near the Earth’s surface is called the weight w of the object W or F g = m g is a special case of Newton’s Second Law W or F g = m g is a special case of Newton’s Second Law Weight mass Slope = g (9.81m/s 2 on Earth)

16. More about weight Weight is not an inherent property of an object Weight is not an inherent property of an object mass is an inherent property (it doesn’t change) mass is an inherent property (it doesn’t change) Weight depends upon location Weight depends upon location Height above Earth’s surface Height above Earth’s surface You weigh less on Mt. Everest than at sea level You weigh less on Mt. Everest than at sea level What astronomical body you are on/ near What astronomical body you are on/ near You weigh less on the moon and more on Jupiter You weigh less on the moon and more on Jupiter

17. Translational Equilibrium All the forces on an object are balanced All the forces on an object are balanced The net force acting on the object is zero The net force acting on the object is zero F net = 0 F net = 0

18. Two cases of an object at equilibrium: Two cases of an object at equilibrium: An object is at rest An object is at rest An object is moving with a constant velocity (same speed, same direction) An object is moving with a constant velocity (same speed, same direction) Equilibrium cont.

19. Terminal Velocity Another type of friction is air resistance Another type of friction is air resistance Air resistance is proportional to the speed of the object Air resistance is proportional to the speed of the object When the upward force of air resistance equals the downward force of gravity, the net force on the object is zero When the upward force of air resistance equals the downward force of gravity, the net force on the object is zero The constant speed of the object is the terminal velocity The constant speed of the object is the terminal velocity

20. Newton’s Third Law If two objects interact, the force exerted by object 1 on object 2 (F 12 ) is equal in magnitude but opposite in direction to the force exerted by object 2 on object 1 (F 21 ) If two objects interact, the force exerted by object 1 on object 2 (F 12 ) is equal in magnitude but opposite in direction to the force exerted by object 2 on object 1 (F 21 ) Equivalent to saying a single isolated force cannot exist Equivalent to saying a single isolated force cannot exist

21. Newton’s Third Law cont. F 12 may be called the action force and F 21 the reaction force F 12 may be called the action force and F 21 the reaction force Actually, either force can be the action or the reaction force Actually, either force can be the action or the reaction force The action and reaction forces act on different objects The action and reaction forces act on different objects

22. Some Action-Reaction Pairs n and n’ n and n’ n is the normal force, the force the table exerts on the TV n is the normal force, the force the table exerts on the TV n is always perpendicular to the surface n is always perpendicular to the surface n’ is the reaction – the TV on the table n’ is the reaction – the TV on the table n = - n’ n = - n’

23. More Action-Reaction pairs F g and F g ’ F g and F g ’ F g is the force the Earth exerts on the object F g is the force the Earth exerts on the object F g ’ is the force the object exerts on the earth F g ’ is the force the object exerts on the earth F g = -F g ’ F g = -F g ’

24. Forces Acting on an Object Newton’s 3 rd Law uses the forces acting on an object Newton’s 3 rd Law uses the forces acting on an object n and F g are acting on the object n and F g are acting on the object n’ and F g ’ are acting on other objects n’ and F g ’ are acting on other objects

25. Newton’s Laws on an Elevator 1 2 3 4

26. Elevator Explanation Step 1: Step 1: Step 2: Step 2: Step 3: Step 3: Step 4: Step 4:

27. Applying Newton’s Laws Assumptions Assumptions Objects behave as particles Objects behave as particles can ignore rotational motion (for now) can ignore rotational motion (for now) Masses of strings or ropes are negligible Masses of strings or ropes are negligible Interested only in the forces acting on the object Interested only in the forces acting on the object can neglect reaction forces (via Newton’s 3 rd Law) can neglect reaction forces (via Newton’s 3 rd Law)

28. Free Body Diagram Identifies all the forces acting on the object(s) of interest Identifies all the forces acting on the object(s) of interest Weight- force of gravity, directed straight downward towards the center of the Earth Weight- force of gravity, directed straight downward towards the center of the Earth Normal- supporting force, directed perpendicular to surface the object is in contact with Normal- supporting force, directed perpendicular to surface the object is in contact with Friction- force that opposes motion, opposite direction of desired motion Friction- force that opposes motion, opposite direction of desired motion Tension- force on a cord, rope or wire Tension- force on a cord, rope or wire

29. Free Body Diagram examples Normal Force Weight Friction

30. Equilibrium Example – Free Body Diagrams

31. Inclined Planes Choose the coordinate system with x along the incline and y perpendicular to the incline (notice sine and cosine are reversed) Choose the coordinate system with x along the incline and y perpendicular to the incline (notice sine and cosine are reversed)

32. Hanging masses (pendulums) Notice sine and cosine are reversed because the angle is measured from the vertical Notice sine and cosine are reversed because the angle is measured from the vertical T cos  T sin 

33. More About Friction Friction is proportional to the normal force Friction is proportional to the normal force The force of static friction is greater than the force of kinetic friction The force of static friction is greater than the force of kinetic friction The coefficient of friction (µ) depends on the surfaces in contact The coefficient of friction (µ) depends on the surfaces in contact The coefficients of friction are nearly independent of the area of contact The coefficients of friction are nearly independent of the area of contact

35. Static Friction, ƒ s Static friction acts to keep the object from moving Static friction acts to keep the object from moving If an applied force F increases, so does ƒ s up to a maximum amount If an applied force F increases, so does ƒ s up to a maximum amount F s  µ s R F s  µ s R

36. Kinetic Friction The force of kinetic friction acts when the object is in motion The force of kinetic friction acts when the object is in motion Is less than the force of static friction Is less than the force of static friction F k = µ k R F k = µ k R

37. Friction Example #1 1) What is the force of friction on a 200N wooden crate moving at constant speed on a wooden floor? On a horizontal surface- W = R (in magnitude), so R = 200N Since object is moving, use F k = u k R F k = (0.30) (200 N) F k = 60 N

38. Friction Example #2 2) What is the force of friction on a 10 kg rubber tire moving at constant speed on a dry concrete highway? W = R (in magnitude), so R = 98.1N Since object is moving, use F k = u k R F k = (0.68) (98.1N) = 66.7 N Convert mass to weight: W = mg = (10kg) (9.81m/s 2 )= 98.1 N

39. Friction Example #3 3) If a force of 300 N is needed to move an 800 N desk at constant speed on a linoleum floor, determine the coefficient of kinetic friction of the floor. W = R (in magnitude), so R = 800 N Since object is moving, use F k = u k R 300 N = (u k ) (800N) u k = 0.38 Object is in equilibrium, so pulling force = Friction

40. Friction Example #4 4) A man pulls an 80kg wooden crate across a wooden floor with a force of 1000N a) Determine the Force of friction acting on the crate b) Determine the acceleration of the crate 1000N Find weight: W = mg = (80kg) (9.81m/s 2 )= 784.8 N Object is moving, so F k = u k R =(0.30) (784.8N)= 235.4 N a = F net / m= (1000N – 235.4 N ) / 80 kg = 9.6 m/s 2 to the right

41. Make a sketch of the situation described in the problem Make a sketch of the situation described in the problem Draw a free body diagram(s) for the isolated object(s) under consideration and label all the forces acting on it or them Draw a free body diagram(s) for the isolated object(s) under consideration and label all the forces acting on it or them Resolve the forces into x- and y-components, using a convenient coordinate system Resolve the forces into x- and y-components, using a convenient coordinate system Apply equations, keeping track of signs Apply equations, keeping track of signs Make the direction of motion positive Make the direction of motion positive Solve the resulting equations Solve the resulting equations Solving Newton’s Second Law Problems

42. Connected Objects Apply Newton’s Laws separately to each object Apply Newton’s Laws separately to each object The acceleration of both objects will be the same The acceleration of both objects will be the same The tension is the same in each diagram The tension is the same in each diagram Solve the simultaneous equations Solve the simultaneous equations Wood block on wood table, experiences friction

43. Example Equation for 4 kg block Equation for 4 kg block F net = T – F f F net = T – F f ma = T – u k R (R = mg) ma = T – u k R (R = mg) ma = T – u k mg ma = T – u k mg Equation for 7 kg sphere Equation for 7 kg sphere F net = W – T F net = W – T ma = mg – T ma = mg – T