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Transcript
Summary for last week: Newton’s 2nd Law + 1st Law • ! Fresultant = " ! Fi ! ! ! ! = F1 + F2 + ...+ FN = ma Object all forces acting on object due to other objects if we measure acceleration in an inertial coordinate system ! Newton’s Third Law • If object A exerts a force F AonB on object B, there is an equal and opposite force F BonA = - F AonB that B exerts on A. • Both forces have exactly same magnitude, regardless of motion (acceleration) of either object. • The two forces act on different bodies and in opposite direction. They are called a “Action-Reaction Pair”. => F Action = - F Reaction Examples I • Gravitational downwards Force - mg on object of mass m <=> equally strong upwards Force + mg on Earth • Person pulling with force F on object <=> object pulls with force -F on person • Person pushing object forward <=> object pushes back on person with equal force • Weight of object - mg pushing down on support <=> support pushing object up with normal force + mg . • Rocket “pushing out gas” - gas pushing rocket forward. Examples II: Tension • Rope, Chain etc.: Imagine “cut” at some point “upper” half exerts force on “lower” half “lower” half exerts force on “upper” half Equal : Action-Reaction Pair F U = -F L => Tension T = |F U | = |F L | at that point • Force acting at end point = Tension at that point T 1 mg T2 Important Points: • For Newton’s Second Law, use only forces acting on object to calculate ΣF = m a , not reaction forces on other objects. • No object can exert a net force on itself (Münchhausen trick): Force of one part on another exactly balanced by Reaction Force => total sum = zero. Nothing can experience a force without exerting a force HOWEVER: Effect of (reaction) force on one object may be a lot smaller than the effect of the (equal-sized) action force on the other object (cannon recoil…) Action+Reaction pair = INTERACTION (most fundamental; all forces are due to interactions) • • • How can we tell that a force is acting (and how strong it is)? • Operational definition based on Newton’s Second Law. • By looking at its effects: – the object (mass point) is accelerating – a solid is stretched or bent (spring [balance], rope, …) • From our knowledge of Force Laws: – an object of mass m will experience a force F y = - mg pointing downwards on the surface of Earth – A rope which is pulled with force of strength |F| at one end will exert force of same strength at its other end (in the direction of the rope) if it doesn’t accelerate and its weight is negligible (Newton’s 3rd Law). – General gravitational force law (later in semester), electromagnetism (even later in semester)… Web of Forces and Masses • Use Newton’s 2nd and 3rd law to create relationships between known forces and masses and unknown ones: • Masses: Standard in Paris Force Laws: Gravitation Known Forces: Springs Compare accelerations (3rd Law, 2nd Law) Balance forces (Superposition) Unknown mass • New Forces – – – – Measure a, m (2nd Law) Balance with known force (spring, pulley + weight,…) Observe reaction (3rd Law) Develop Force Law, apply to new situations Scalars and vectors • Scalars are observables which can be expressed with a simple number (and appropriate units). Examples: Time, mass, temperature,... • Vectors are observables which have both a magnitude (a number with units) and a direction. Examples: Displacement, velocity, force, acceleration… • It is very important to distinguish these! two entities: use different notation (A for scalar, A or A for vector), and clearly indicate size and direction for a vector result. a ! Example: Displacement • Size: actual distance from Point A to Point B (don’t forget units) • Direction: Describe which way to go. • Note: Vectors which have different sizes, different units, or different directions are different. BUT: starting point does not matter: Specifying a vector 1.) By giving its length (size, magnitude, absolute value with units) and its direction. Examples: “1100 m exactly northeast from here” or “0.17 m at an angle of 45o above the x-axis, in the x-y plane”. 2.) You can represent vectors by drawing arrows. The length of the arrow represents the size of the vector (e.g., 2 cm represent 2 N) and the direction of the arrow is in the direction of the vector. Seb See Vectors can be added to (or subtracted from) each other. 1.) Geometrically: See examples. Use either “tail to head” method or “parallelogram” method 2.) Mathematically (a bit too advanced for our purpose) Example: Equilibrium - car at rest • Equilibrium: All forces acting on an object add up to zero (vectorially). • The object will either be (stay) at rest or will move with constant velocity. • Example: Car sitting still on an inclined plane (or moving down with constant velocity) F Friction F Normal F Weight x α y Example: Car accelerating down ramp • Net force: All forces acting on an object add up to a net force along the ramp (vectorially). • The object will accelerate down the ramp. F Friction F Normal x F Weight α y Equilibrium - Sailboat Wind Force Drag Normal Force on Keel