Physics Lecture 5 PDF

Physics By: Dr. Engy Ragaei Abdelmaksoud E-mail: [email protected] Contents Mechanics Electricity & Magnetism 1. Physics and measurements 1. Electric Force 2. Motion in one dimension 2. Electric Field 3. Vectors...

Physics By: Dr. Engy Ragaei Abdelmaksoud E-mail: [email protected] Contents Mechanics Electricity & Magnetism 1. Physics and measurements 1. Electric Force 2. Motion in one dimension 2. Electric Field 3. Vectors 3. Capacitance 4. Motion in two dimensions 4. Voltage, Current, Resistance 5. Laws of motion 5. Magnetic Fields, Induction 6. Work and Energy Oscillations & Waves 1. Oscillatory Motion 2. Wave Motion Lecture 5  Objectives 5. Laws of motion [Chapter 5]  The Concept of Force  Newton’s First Law  Newton’s Second Law  Newton’s Third Law  Some Particular Forces  Gravitational Force  Mass and Weight  The Tension Force  The Normal Force  The Particle in Equilibrium  The Particle Under a Net Force  Newton’s Second Law Examples Force The Concept of Force  Forces in everyday experience Push on an object to move it Throw or kick a ball  Forces are what cause any change in the velocity of an object.  Forces do not always cause motion. For example: When you are sitting, a gravitational force acts on your body and yet you remain stationary. You can push (in other words, exert a force) on a large rock and not be able to move it.  The Concept of Force Classes of Forces  Contact forces involve physical contact between two objects  Field forces act through empty space (No physical contact is required)  The Concept of Force Fundamental forces The only known fundamental forces in nature are all field forces: (1) Gravitational forces between objects (2) Electromagnetic forces between electric charges (3) Strong forces between subatomic particles (4) Weak forces that arise in certain radioactive decay processes → In classical physics, we are concerned only with gravitational force.  The Concept of Force Measuring Forces  It is possible to use the deformation of a spring to measure force.  Suppose a vertical force is applied to a spring scale that has a fixed upper end.  The spring elongates when the force is applied, and a pointer on the scale reads the extension of the spring.  The Concept of Force  Force is one of many quantities in physics that are called vectors.  In the SI system, the unit of force is the newton (N).  Resolving a force vector 𝑭 into x- and y-components. We can use simple trigonometry. 𝑭𝒙 𝑭𝒙 = 𝑭 𝐜𝐨𝐬 𝜽 Since 𝐜𝐨𝐬 𝜽 = 𝑭 𝑭𝒚 𝑭𝒚 = 𝑭 𝐬𝐢𝐧 𝜽 Since 𝐬𝐢𝐧 𝜽 = 𝑭 𝑭= 𝑭𝟏 𝟐 + 𝑭𝟐 𝟐 −𝟏 𝑭𝟏 𝜽= 𝐭𝐚𝐧 𝑭𝟐  Newton’s First Law In the absence of external forces, an object at rest remains at rest and an object in motion continues in motion with a constant velocity (that is, with a constant speed in a straight line). The net force on an object: 𝑭=𝟎  The tendency of an object to resist any attempt to change its velocity is called inertia.  Mass is that property of an object that specifies how much resistance an object exhibits to changes in its velocity. Newton’s First Law  Newton’s Second Law T‫إ‬he acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Algebraically, 𝑭𝒙 = 𝐦𝒂𝒙 𝐹 𝐹 = m𝑎 𝑭𝒚 = 𝐦𝒂𝒚 𝑎∝ 𝑚 𝑭 is the net force 𝑭𝒛 = 𝐦𝒂𝒛 This is the vector sum of all the forces acting on the object.  May also be called the total force, resultant force, or the unbalanced force.  Newton’s Second Law Example: You push an object, initially at rest, across a frictionless floor with a constant force for a time interval Δt, resulting in a final speed of v for the object. You then repeat the experiment, but with a force that is twice as large. What time interval is now required to reach the same final speed v? (a) 4 Δt (b) 2 Δt (c) Δt (d) Δt /2 (e) Δt /4  Newton’s Second Law Solution: 𝒗 𝒗𝒊 = 𝟎 𝑭=𝒎 𝒗𝒇 = 𝒗 ∆𝒕 𝒕𝒊 = 𝟎 𝒗 𝒕𝒇 = 𝒕 ∆𝒕 = 𝒎 𝑭 For twice the force 𝒗 𝒗 ∆𝒕𝟐𝑭 = 𝒎 =𝒎 𝒗 𝟐𝑭 𝟐𝒎 ∆𝒕 ∆𝒕 ∆𝒕𝟐𝑭 = 𝟐  Newton’s Second Law Example: A hockey puck having a mass of 0.30 kg slides on the friction-less, horizontal surface of an ice rink. Two hockey sticks strike the puck simultaneously, exerting the forces on the puck shown in the given Figure. The force 𝑭𝟏 has a magnitude of 5.0 N, and the force 𝑭𝟐 has a magnitude of 8.0 N. Determine both the magnitude and the direction of the 𝒎 = 𝟎. 𝟑𝟎 𝒌𝒈 puck’s acceleration. 𝑭𝟏 = 𝟓. 𝟎 𝑵 𝑭𝟐 = 𝟖. 𝟎 𝑵 𝜽𝟐 = 𝟔𝟎° 𝜽𝟏 = 𝟐𝟎° 𝒂 =? ? ? ?  𝒎 = 𝟎. 𝟑𝟎 𝒌𝒈 Newton’s Second Law 𝑭𝟏 = 𝟓. 𝟎 𝑵 Solution: 𝑭𝟐 = 𝟖. 𝟎 𝑵 𝜽𝟐 = 𝟔𝟎° 𝜽𝟏 = 𝟐𝟎° 𝒂 =? ? ? ?  Newton’s Third Law If two objects interact, the force 𝑭𝟏𝟐 exerted by object 1 on object 2 is equal in magnitude and opposite in direction to the force 𝑭𝟐𝟏 exerted by object 2 on object 1. 𝑭𝟏𝟐 = −𝑭𝟐𝟏 The action force is equal in magnitude to the reaction force and opposite in direction.  Some Particular Forces Gravitational Force Normal Force Tension Force Friction Force 𝑭𝒈 𝒏 𝑻 𝒇𝒔 , 𝒇𝑘  The Gravitational Force The gravitational force 𝑭𝒈 and Weight  Is the force that the earth exerts on an object.  This force is directed toward the center of the earth. 𝑭𝒈 = 𝒎𝒈  The weight of an object, is defined as the magnitude of 𝑭𝒈 𝑭𝒈 = 𝒎𝒈  Because it depends on g, weight varies with geographic location. Because g decreases with increasing distance from the center of the Earth, objects weigh less at higher altitudes than at sea level.  Mass and Weight Mass Weight  Is an inherent property of an object.  Is equal to the magnitude of the gravitational force exerted on the  Is independent of the object’s object. surroundings.  It vary with location.  Is a scalar quantity  The SI unit of mass is kg. Example: For a person wearth = 180 lb; wmoon ~ 30 lb mearth = 2 kg; mmoon = 2 kg 1 lb = 0.453 kg  The Tension Force  When a rope attached to an object is pulling on the object, the rope exerts a force on the object in a direction away from the object, parallel to the rope. The magnitude T of that force is called the tension in the rope.  This tension force acts in the opposite direction to the applied force to keep the object in equilibrium.  The Normal Force  When an object sits on a table, the table surface exerts an upward contact force on the object.  This pushing force is directed perpendicular to the surface, and thus is called the normal force.  The Normal Force Consider a computer monitor at rest on a table: Model the object as a particle The Forces on the Object (monitor) The normal force 𝒏 and the force of gravity 𝑭𝒈 are the forces that act on the monitor.  The normal force is equal to the gravitational force of the object. 𝑭𝒚 = 𝒏 − 𝑭𝒈 = 𝟎 𝒏 = 𝑭𝒈  The Normal Force The normal force is not always equal to the gravitational force of the object.  For example, suppose a book is lying on a table and you push down on the book with a force 𝑭: 𝑭𝒚 = 𝒏 − 𝑭𝒈 − 𝑭 = 𝟎 𝒏 = 𝒎𝒈 + 𝑭 𝑭𝒈 = 𝒎𝒈 The normal force is greater than the gravitational force  The Particle in Equilibrium If the acceleration of an object that can be modeled as a particle is zero, the object is said to be in equilibrium. Mathematically, the net force acting on the object is zero. 𝑭=𝟎  A lamp is suspended from a chain of negligible mass. The forces acting on the lamp are: the downward force of gravity the upward tension in the chain 𝑭𝒚 = 𝟎 𝑻 − 𝑭𝒈 = 𝟎 𝑻 = 𝑭𝒈  The Particle Under a Net Force If an object that can be modeled as a particle experiences an acceleration, there must be a nonzero net force acting on it.  Consider a crate being pulled to the right on a frictionless, horizontal floor. 𝑭 = 𝒎𝒂 𝑻 𝑭𝒙 = 𝑻 = 𝒎𝒂𝒙 𝒂𝒙 = 𝒎 𝑭𝒚 = 𝒏 + −𝑭𝒈 = 𝟎 𝒏 = 𝑭𝒈  Newton’s Second Law Examples Example: A traffic light weighing 𝟏𝟐𝟐 𝑵 hangs from a cable tied to two other cables fastened to a support as in Figure. The upper cables make angles of 𝜽1 = 37. 𝟎° and 𝜽2 = 𝟓𝟑.𝟎° with the horizontal. These upper cables are not as strong as the vertical cable and will break if the tension in them exceeds 𝟏𝟎𝟎 𝑵. Does the traffic light remain hanging in this situation, or will one of the cables break?  Newton’s Second Law Examples Solution: The traffic light in the y direction  Newton’s Second Law Examples Solution: Apply the particle in equilibrium model to the knot Both values are less than 100 N, so the cables will not break.  Newton’s Second Law Examples Example: A person weighs a fish of mass m on a spring scale attached to the ceiling of an elevator as illustrated in the given Figure. (A) Show that if the elevator accelerates either upward or downward, the spring scale gives a reading that is different from the weight of the fish. (B) Evaluate the scale readings for a 40.0-N fish if the elevator moves with an acceleration 𝒂 = ±𝟐. 𝟎𝟎 𝒎/𝒔  Newton’s Second Law Examples Solution: (A) Show that if the elevator accelerates either upward or downward, the spring scale gives a reading that is different from the weight of the fish. Apply Newton’s second law to the fish We have chosen upward as the positive y direction. We conclude from Equation (1) that:  the scale reading T is greater than the fish’s weight mg if 𝑎 is upward. (+ 𝑎)  the scale reading T is less than the fish’s weight mg if 𝑎 is downward. (- 𝑎)  Newton’s Second Law Examples Solution: (B) Evaluate the scale readings for a 40.0-N fish if the elevator moves with an acceleration 𝒂𝒚 = ±𝟐. 𝟎𝟎 𝒎 𝒔 The scale reading if a is upward The scale reading if a is downward