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Forces & the Laws of Motion Chapter 4 4.1 Changes in Motion • Objectives: • I can explain how force affects the motion of an object • I can distinguish between contact forces and field forces • I can interpret and construct free-body diagrams Force • What is a force? • A push or pull that can change the motion of an object • SI unit is 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 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 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 Electrostatic Forces • Example of a field force • Stream of ethanol is attracted to an electrically charged probe 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 Representing Forces • Force is a vector • Free-body diagrams illustrate forces acting on an object isolated from its surroundings 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 Common Forces in Force Diagrams • • • • • • • Applied force Weight Normal force Friction Air resistance Tension Spring force Fapp Fg FN Ff Fair FT Fsp (mg) ┴ to surface Example of a Free-Body Diagram 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 Newton’s First Law of Motion • 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 uniform linear motion • When net force on an object is zero, acceleration is zero (∆v/∆t = 0) 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 Net Force • A net force is the resultant force of two or more forces • Since forces are vectors, the net (resultant) force is determined as any other resultant vector. • Example: A student pushes a book across a table with a force of 5 N Net Force • Example: A student pushes a book across a table with a force of 5 N. Frictional forces of 2 N act in the opposite direction. What is the net force acting on the book? Forces Acting on Inclined Planes 1. 2. 3. 4. 5. FN, normal force, surface acting on object Fg, weight = mg Fgx, component of g, ║ to surface Fgy, component of g ┴ surface Ff, friction 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 Equilibrium • The state of a body in which there is no change in motion • Net force acting on a body is zero 4.3 Newton’s 2nd & 3rd Laws Learning objectives 1. Describe acceleration of an object in terms of its mass and the net external force acting on it 2. Predict direction & magnitude of acceleration caused by a known net external force 3. Identify action-reaction force pairs 4. Explain why action-reaction pairs do not result in equilibrium 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 = ΣF /m , where Σ means “sum of” • ΣF = ma 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. 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. 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. 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 Weight & Normal Force • Fg = mg • Always ┴ surface of earth • Directed toward center of earth • FN = Fgcos (θ) • Always ┴ surface of contact • Always opposes Fg Identify Forces Acting on Inclined Planes 1. 2. 3. 4. 5. FN, normal force, surface acting on object Fg, weight = mg Fgx, component of g, ║ to surface Fgy, component of g ┴ surface Ff, friction 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 Static vs. Kinetic Friction 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 Problem 4D • 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 Coefficients of Friction (Approximate) Materials μs μk Steel on steel 0.74 0.57 Waxed wood on wet Materials μs μk 0.14 0.10 ---- 0.04 0.15 0.06 snow Aluminum on steel 0.61 0.47 Waxed wood on dry snow 0.80 Metal on metal Rubber on dry concrete 1.00 Rubber on wet concrete ---- 0.50 Ice on ice 0.10 0.03 Wood on wood 0.40 0.20 Teflon on Teflon 0.04 0.04 Glass on glass 0.90 0.40 Synovial joints in 0.01 0.003 (lubricated) humans Role of Surface in Friction • Static friction increases with increasing force until overcome • Kinetic friction is less than the maximum static friction Frictional Forces & Applied Force Air Resistance • When an object passes through a fluid…. • The fluid has to be pushed out of the way for the object to pass through it • i.e., Motion of objects through a fluid is hindered by the fluid Air Resistance • • • • At low speeds FR is proportional to v At higher speeds FR is proportional to v2 When FR = FA, constant speed Terminal speed – For free falling object – When FR up = Fg down – Fnet = 0 Four Fundamental Forces • All are field forces • Strong nuclear force – Holds nucleus together • Weak nuclear force – Involved in radioactive decay • Electromagnetic force • Gravitational force – weakest